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Bamafan77 writes "Slate has an interesting article on the relationship between the productivity of mathematicians and age. The conventional belief is that most significant mathematical leaps are all made before the age of 30. However, the author gives pretty compelling reasons for why this once may have been true, but is definitely not the rule now. Two of his more interesting pieces of evidence include Grigori Perelman's (probable) proof of the Poincare Conjecture at 40 and Andrew Wile's proof of Fermat's Last Theorem at 41."

Consulting for several large companies, I'd always done my work on Windows. Recently however, a top online investment firm asked us to do some work using Linux. The concept of having access to source code was very appealing to us, as we'd be able to modify the kernel to meet our exacting standards which we're unable to do with Microsoft's products.

Although we met several technical challenges along the way (specifically, Linux's lack of Token Ring support and the fact that we were unable to defrag its ext2 file system), all in all the process went smoothly. Everyone was very pleased with Linux, and we were considering using it for a great deal of future internal projects.

So you can imagine our suprise when we were informed by a lawyer that we would be required to publish our source code for others to use. It was brought to our attention that Linux is copyrighted under something called the GPL, or the Gnu Protective License. Part of this license states that any changes to the kernel are to be made freely available. Unfortunately for us, this meant that the great deal of time and money we spent "touching up" Linux to work for this investment firm would now be available at no cost to our competitors.

Furthermore, after reviewing this GPL our lawyers advised us that any products compiled with GPL'ed tools - such as gcc - would also have to its source code released. This was simply unacceptable.

Although we had planned for no one outside of this company to ever use, let alone see the source code, we were now put in a difficult position. We could either give away our hard work, or come up with another solution. Although it was tought to do, there really was no option: We had to rewrite the code, from scratch, for Windows 2000.

I think the biggest thing keeping Linux from being truly competitive with Microsoft is this GPL. Its draconian requirements virtually guarentee that no business will ever be able to use it. After my experience with Linux, I won't be recommending it to any of my associates. I may reconsider if Linux switches its license to something a little more fair, such as Microsoft's "Shared Source". Until then its attempts to socialize the software market will insure it remains only a bit player.

He gets his karma bonus and promptly misuses it to spread GPL FUD.

Anyway, for those who cared to read your offtopic troll: IT IS NOT necessary to publish modifications made to GPL'd s/w to all and sundry. That requirement comes onlt if you need to 'sell' those changes, and even then, the changes were made to GPL'd code - not for code that works on top of it.

This guy is trolling. Read the quote below, and then tell me whether it corresponds to the description in his comment above. This quote was taken from his
slashdot bio [slashdot.org] on May 17th, 15:31 GMT.

I work as an embedded engineer for Transmeta Corp. I'm a part time linux kernal developer and born again muslim

I think 40 is probably the peak between the tradeoff between knowledge accumulation and physical decline. But stand for a psychologist or neurologist to correct me.

A bit like athletes maybe... experience vs. physiology results in a trade off.

I disagree. Some humans are going to have different rates of cell degeneration based upon many variables. Those rates may affect certain areas befor they affect others like the brain. If a person continues to exercise their brain, then it should continue to produce, however small the amount, new cell growth almost up until death.

Re:Not too young (0)

Anonymous Coward | more than 11 years ago | (#5979420)

Clearly you are a man whose cells never die? So your body keeps expanding???

The reason we die, you know, is because cell death > cell growth... causing degregation in some body function which kills you.

Perhaps the increase in knowledge base necessary not to keep reinventing the wheel increases the experience in your equation... thereby pushing up the age of tradeoff?

Re:Not too young (0)

Anonymous Coward | more than 11 years ago | (#5979633)

Well 40 is not exactly a good estimate, it could infact be any age, depending on the way you lived/live.

If you have a very intellectual life, and you keep accumulating more knowledge and in essense keep 'training' your brain, you might be of better mind when you're in your 80s or something. As to someone in his 30s that still has most of his braincells but keeps killing them with booze. On the other hand, if you don't 'train' your mind, you're gonna get alzheimer by the time you're in your 70s.

My grandfather for example is 96 and can still write beautifull poetry, and some folks 20 years younger are living like vegetables.

Rule of /. (-1, Offtopic)

Anonymous Coward | more than 11 years ago | (#5979396)

Yes, but can anyone out there solve the legendary "Slashdot Concept of Dupes" before they hit 40?

Re:Rule of /. (0)

Anonymous Coward | more than 11 years ago | (#5979431)

The conventional belief is that most significant mathematical leaps are all made before the age of 30.

That sounds about right. According to another study, mathematicians reach their prime just before discovering sex, after which it is all downhill. It will give the old codgers some solace to know that they can expect a brief comeback after their wives stop having sex with them.

It is obvious why this is the case.. (5, Funny)

Anonymous Coward | more than 11 years ago | (#5979409)

When you get married and have some kids it is real hard do get any work done..

"Okay Dear I'll mow the lawn now"

I also suspect the growing complexity of screensavers as a factor..

Re:It is obvious why this is the case.. (4, Interesting)

Sorry, I don't have any mod points... but I'll blast away my Karma bonus... I agree.

Thinking, exploration, calculation, research, experimentation--all of these take a great deal of time. Relationships with friends, your SO, and eventually kids require a great deal of this time to keep healthy and strong.

If you want smart kids/pets, that takes time as well.

No, I am not saying that one can't be productive or creative once older; however, it just becomes more difficult. Those that do it successfully usually do it though their profession. That is... you can do it though your job if they give you the freedom to do so.

I don't think all of this is so bad... most of us would rather have healthy relationships than awards/accomplishments as we get older.

Davak

thelimitis30++ (0, Troll)

Anonymous Coward | more than 11 years ago | (#5979413)

is there anything really brain demanding or innovating you can do after 30?

Frank Lloyd Wright did his most celebrated work after the age of fifty.

Yeah. Sure.
My only problem is with the fact that many people were already experimenting with flight before this -- most were under the age of 35. At the time, the mathematics and physics necessary were tremendous, what with lift and velocity and all that, but compared to modern standards are trivial. If we look back to the experiments of Da Vinci, we can realise that the "unified theory" can simply be expressed in terms of z=y^5/... oh wait... wrong Wright...

" is there anything really brain demanding or innovating you can do after 30?"

Demanding: Writing the GPL, starting FSF, the Hurd, travelling the world over, believing in yourself despite others jeering you - RMS age 50.

Innovating: Buying an OS from someone, putting it onto someone else's h/w, building up a monopoly, driving out others (using suspect means), releasing newer and newer OSes that do essentially the same things, generate obscene profits, etc. etc. - William Gates, Age 45 (?)

We are not talking about life in general here. We are talking about maths.
Almost all the rich men have become rich late in their lifes. Most politicians are old, artists contibute throughout their lifes, most scietitsts are old, even.
Maths, due to the fact that it demands little interpersonal contacts (books are enough) and because it is almost entirely an act of the mind (unlike physics where you are related to the rules of the world), is generally assumed to be different.Intuition, originality blah, blah.....

Math can be done alone but these days a lot of it is done by people working together. A lot of the great theorems and algorithms are the product of two or more mathematicians working together.

Two of his more interesting pieces of evidence include Grigori Perelman's (probable) proof of the Poincare Conjecture at 40 and Andrew Wile's proof of Fermat's Last Theorem at 41.
Yes, but at the tender age of 22, I can not only add my bar tab together, but also figure an appropriate tip.
Young people can't do hard math my ass.

A century ago, mathematics was primarily a new field. New fields are characterized by inventiveness and a lack of prerequisite knowledge -- there isn't a lot of background to learn, and if you look at problems "the right way" you can get results very quickly. Most of mathematics is no longer a new field; in most areas, one must spend years studying before one can do anything new, and even then it's likely to be the result of long hard work rather than a quick new insight.

Computer science is moving in the same direction, but is many years behind. Thirty years ago, computer science was a new field; there were few if any courses teaching necessary background material; and someone with the right insight could find very important work very easily. Now, we're starting to see movement away from that -- there is a body of important work to build upon, and anyone who hasn't studied that work will have "new insights" which simply reinvent already existing work.

Mathematics is no longer a young man's game, and this is probably the last generation when computer science has been a young man's game. Next generation, the young will find a new field to excel in -- perhaps genomics?

A century ago, mathematics was primarily a new field.

More precisely, there were many new fields within mathematics to explore. However, there was already quite a large body of existing knowledge. It's just that it was about as much as a sophomore engineering student knows(give or take).

Now, as the article says, you are a graduate student -- and probably not a new graduate student -- before you're even looking at other people's cutting-edge work, let alone doing your own.

Hmm, so the Greeks, Euler, Descartes, and thousands of other mathematicians don't count? Math is one of the oldest fields I can think of.

And yet, someone could learn and understand all of their most important discoveries before they graduate with a B.S. in Math. From what I've read of Andrew Wiles final resolution of Fermat's Last Theorem, it would take years of specialized study to understand.

Brian

A poor education system does not help (3, Interesting)

Yes, we can learn the already discovered algorithms by the time we have a Math BS, but by then we are around 22. Our current system does not allow the best to advance at their own pace.

I was reinventing Calculus by 8th grade. I was about to win second place in an international math contest. (I was beaten by a 9th grade Canadian.) I usually ignored whatever was being taught in Math class, since I could literally get an A without waking up.

I was attempting to find the area under a curve defined by a formula. It seemed appropriate to do the work in math class. One day, my eight grade math teacher asked what I was doing. I showed him my current theory. He told me that there was already a proof that it was impossible, so I moved it from active work to the "known impossible, but cannot stop trying" category that includes a simple formula for discovering factorials.

If he had mentioned the word "calculus", I would have researched what was already done and continued with new discoveries. Or he could have encouraged me to repeat the discovery. Instead, he told me it was PROVEN IMPOSSIBLE.

Personal note: This was an important event in my life, because a few years later they tried to teach Pre-Calculus. I immediately absorbed the entire book, and then taught myself Calculus. But I could have done that a few years earlier. And it was the first time that I had proof an authority figure lied to me. The realization that adults have no clue even in their specialty was a major part of my maturing. Now I question facts even when the person giving them is the "top authority".

If our education system helped students that showed an aptitude for math to advance at their own rate, they would probably be finding better algorithms for known problems, with the possibility of discovering something new, as a teenager. Tiger Woods specialized in golf starting at age 3. Most Ice skaters, gymnasts, and dancers start before they are 6. Why should mathematicians need to wait until college before specializing?

--- Off-topic details: I was reinventing Newtonian Calculus. Newton invented a system about the same time the current system was discovered by the French. Both systems were used for a time, but further advances (Differentials) were only possible using the French version, so Newtonian Calculus was dropped. So it was unlikely my redicovery would help advance today's knowledge, since it was on a dead branch.

Greeks made some discoveries in geometry. But very little in other fields. They lacked our number system, so number theory was quite the pain. With the roman number system, this was even worse. On top of that, most of the mathematical knowledge of the greeks came from the pythagoreans, but they wouldn't let anyone in on their discoveries. So their knowledge died with them.

In the middle ages people weren't very interestes in mathematics

Then we finally get descartes, Euler, Fermat end those dudes, who finally got the math ball rolling. But it didn't get REALLY interesting until in the twentieth century.

In that light, mathematics, at least modern mathematics could be considered young in the beginning of this century.

In the middle ages people weren't very interestes in mathematics

s/people/Europeans

You neglect the contributions of the Arabic and Indian mathematicians at your peril. There's a reason they call them "Arabic numerals," and the word "algebra" comes from the Latin mistransliteration of the Arabic mathematician who first wrote a dicourse on it.

I might have picked a different example for a new field -- IMO, doing serious research work in genomics will require a very large body of context. Very substantial knowledge of both organic chemistry and cellular biology would seem to be mandatory, plus the rapidly growing body of knowledge about genomics itself. IIRC, human scientific knowledge is currently doubling roughly every ten years. The amount of time needed to learn enough to reach the "leading edge" where research is done is getting longer and longer in all fields.

The counter-argument to that is that it is "insights" that count in making breakthrough discoveries. Since that often involves looking at things from a different direction, knowing too much about the conventional thinking within a chosen field may be a bad thing. Speaking from personal experience, as I have grown older it has become more difficult for me to recognize when my own assumptions are restricting the ways I think about a particular problem.

Finally, any field in which research requires large amounts of money is going to be problematic for young people. Raising such money requires a reputation of sorts and a network of contacts and experience, all of which take years to acquire. And people who control large sums of money do tend to be inclined to conservative approaches -- evolution, not revolution.

I was looking forward to a hypothetical future where working out the structure of a folded protein is easy, given the nucleotide sequence, but constructing a sequence which will result in a given structure is harder. I can imagine that the "programmers" who would construct such sequences would be very much like early assembly language programmers.

Phases of Life... (4, Funny)

Anonymous Coward | more than 11 years ago | (#5979421)

0 to 5: Curious phase 5 to 15: Productive phase 15 to 40: Reproductive phase (some like to begin early and post longer:-) 40 to 60: Consumer phase 60 to...: Irrelevant phase (atleast that's how it's treated by others)

Huh !! (0)

Anonymous Coward | more than 11 years ago | (#5979422)

Just remind me. The old guy, lots of white hair and a big moustache, worked at Princeton. Ein something or other, what was his name ?

True, true- but Einstein's best year was probably 1905. In 1905, he published papers that explained the photoelectric effect in terms of Planck's quantum hypothesis, explained Brownian motion, and used his explanation to estimate the size of atoms, and oh yeah, special relativity. He was 26 years old at the time. This is amazing, and yet not unusual for those involved in the revolution taking place in physics at the time- Enrico Fermi, for instance, invented Fermi statistics (now usually known as Fermi-Dirac) at 24. Ten years after his "year of miracles," Einstein published papers on general relativity. While the popular depiction of Einstein is as a genial old man with wild gray hair, I'd argue that most of his best work was accomplished by the age of 36.

As far as age and mathematics go, though, I'd have to agree that the effects of age are, if not disappearing, then at least being shifted back a number of years. Not long ago, I had the fascinating realization that after 3 years of college, I know more mathematics than Euclid, Diophantus, al-Kwahrizmi, Fermat, Newton, Leibniz, Euler, Hamilton, and Abel. This is not because I'm some sort of mathematics genius (I'm not even a math major), but rather because there is simply more mathematics to learn now, and I merely came later than those guys. For centuries, the situation was such that almost all of the human race's mathematics knowledge could exist in few enough books to carry in your hands- namely, Euclid's Elements and Diophantus's Arithmetica, eventually followed by a few others like Fibbonacci's Liber Abacci. In the 17th-19th centuries, mathematics used these simple foundations to create an incredible wave of new mathematics. (Just take a look at Fermat's annotated copy of the Arithemetica.) Now the number of books written on some specialized part of mathematics like Lie algebras or K-theory could fill a library.

Also, mathematics works a bit differently than the natural sciences- it's harder to create a general survey course in mathematics. Just look at the way these subjects are taught- you generally take high school science courses in physics, chemistry, and biology, but math courses in algebra, geometry, and calculus. The specialization has to start much sooner because eachthing builds off of the previous. In my high school chemistry courses, I remember covering some basic p-chem, some orgo, etc, and in my physics courses there was mechanics, E&M, optics, etc.. I of course returned to all of these in excrutiating detail in my college course, but the simple point is that you couldn't do a similar thing with math. In physical sciences, you can give a broad overview of a subject, and then later reurn in depth, because there isn't such an elaborate hierarchy connecting all of the fields. Conversely, mathematics works more like a pipeline, shuttling students from simpler subjects (basic arithmetic, simple Euclidean geometry) to harder ones (integral calculus, diff eq, set theory). The pipe opens up at the top- areas of specialization become apparent, and a frontier is reached where knowledge in one field is not necessary for knowledge in another.

In fact, there are so many fields and subdisciplines now that it has become incredibly difficult to become a polymath (in the quite literal sense of the term) in the vein of Euler or Gauss or Riemann. The idea of a single person making revolutionary discoveries in both, say, topology and number theory is steadily becoming more remote. If this were to happen, it would have to be someone who spent a long time mastering several disciplines, i.e., an old person. It's a sublime paradox- in the past, incredible leaps of insight that would connect disparate theorems and fields of math could only be made by the young mathematicians with the creativity and the daring to do so (or, if you're cynical, the neuronal plasticity), but now such individuals will still be in grad school learning the ropes.

Look at Andrew Wiles- it took him years to learn enough about elliptic equations, modular forms, and Galois groups to prove the Taniyama-Shimura Conjecture (and thus Fermat's Last Theorem). It took Perelman several years of work to complete his proof of the Geometrization Conjecture. The problems left on the table are in some sense getting harder- they might not take any more genius than the problems Euler or one of the Bernoullis solved, but they do require more information. The age of the brilliant dilettante is over- it now takes years of learning and research just to be able to start composing a proof. It would now take a singular genius of the sort that comes around once a generation to be able to grasp difficult mathematics at such an early age that they could then make major contributions in their early 20s. It's not impossible- the next Ramanujan may be picking up his/her first math text at age 3 right now- but in general, I have a feeling that 50 or even 55 will become "the new 40" in mathematical circles.

Hey, it's my 100th post!

moron wondering if payper liesense scammage (-1, Troll)

Anonymous Coward | more than 11 years ago | (#5979425)

is an old softwar felon's gangbang.

please have the SourceForgerIE(tm) focused marketing program(tm), aim this post towards redmoaned. thanks robbIE, you're such a 'community' member.

The problem is with modern mathematics... (2, Interesting)

...that young mathematician are forced to spend 10 years or so learning old and flawed terminology and concepts.
After that brainwashing people aren't simply able to do anything outstanding anymore. There are some accidential great scores, but they are very rare.
I think we should change our mathematics education to tackle with this problem. And we should indeed already start in school were the first and the most foul foundations are laid. Instead of teaching children basic counting, set theory and algebra which draws in the whole rubbish of non-intentionistic mathematics, we should start with Lie groups and algebraic varities.
Indeed most "Joe Adverage" problems can be reduced to Lie/algebraic geometry problems.
I can give a simple example why this is necessary:
Imagine the Kleinian bottle in R^4.
You'll say now: "That's not possible nobody can visualized 4 dimensional spaces." But this is only because your basic mathematical education fucked up your brain.
If a decent education would start like mentioned above, we all would have no trouble at all to visualized arbitrary n-dimensional spaces.
And because of using different logical concepts wouldn't have to use the problematic axiom of choice. So, no trouble with the Banach-Tarski paradox, inmesaurable sets and non-holomorphic refractions in H^p_2.

This is even a serious political issue. Anyone into math research will agree with me that in the last 15 years we saw a rise of a generation of brilliant new chinese mathematicians.
And why did we saw it ? Because China went back to its Confucian tradition in teaching which avoids the above mentioned problems in Western math education. So, if we don't act now we'll loose our technological leader within the next 30 years forever.

Re:The problem is with modern mathematics... (2, Interesting)

Very impressive, no doubt you will gain the +5 insightful mod you're trolling for.

In the meantime, WTF is a Lie group? WTF is an algebraic varity? Non-holomorphic sounds very impressive, but WTF is it?

You might be right; I've observed that certain Asian groups do seem to have a handle on maths that many Western brains don't, and I doubt it's entirely due to genetics. But if you actually want to change things, as opposed to sounding clever, people have to understand what you're on about. I don't, and I'm three-quarters of the way through an engineering degree. Thank you.

Re:The problem is with modern mathematics... (5, Funny)

You'll say now: "That's not possible nobody can visualized 4 dimensional spaces."

An architect, a physicist and a mathematician were asked whether they could imagine a 4-dimensional space.
The architect said: "That's impossible! I can't draw that!"
The physicist said: "Well, that can be done, if we say that time is the fourth dimension..."
The mathematician said: "Let us imagine an n-dimensional space. Now, let n equal four..."

Check out "A mathematician's apology" by G. Hardy (2, Interesting)

For great insights into the mind of a world class mathematician, please read A mathematician's apology [amazon.com] by G. H. Hardy. Hardy was one of the top mathematician's of his era (1877-1947). Hardy is perhaps most famous for his discovery of Ramanujan [amazon.com] and "A mathematician's apology" has a great Foreword by C. P. Snow documenting some of the details of the Hardy-Ramanujan collaboration.

Here are some nuggets from "A mathematician's apology". (Hope the copyright police are busy elsewhere.)

"No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." [Section 1.4, page 70]

"Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty."[Section 1.4, page 71]. Also see Men of Mathematics [amazon.com] for more on Galois.

"I do not know an instance of a major mathematical advance initiated by a man past fifty." [Section 1.4, page 71].

And later in the book,

"There are then two mathematics. There is the real mathematics of the real mathematicians, and there is what I will call the 'trivial' mathematics, for want of a better word" [Section 1.28, page 139].

Dude can you please post that again in english?
Since I wanted to know if you were trolling or if you were seriously trying to contribute something I looked at your posting history.Most of the posts were either classified as trolls or modded up as funny (though the posts seemed very similar to what you said in the post above).
Since I still have not figured out what you are trying to accomplish I have no other choice but to ask you to repost that in a Language atleast some of us can understand.

Re:The problem is with modern mathematics... (0)

Anonymous Coward | more than 11 years ago | (#5979572)

I think that's because he always mixes some potentially interesting, insightful or funny comments with some rampant flamebaiting.

Yes, nice idea not to teach rigidities... but Confucious teachings of math?! Confucious did not teach topological methods, he likely used an abacus.

Visualization vs. Manipulation (0)

Anonymous Coward | more than 11 years ago | (#5979596)

You'll say now: "That's not possible nobody can visualized 4 dimensional spaces."
But this is only because your basic mathematical education fucked up your brain.
If a decent education would start like mentioned above, we all would have no trouble at all to visualized arbitrary n-dimensional spaces.

Nobody can visualize n-dimensional geometry if n is greater than four. You can imagine a 3-dimensional retine and proyect on it 4-dimensional geometry. You get a 3-dimensional projection of a 4-dimensional object, which your brain can handle. But it's not the same than projecting n-dimensional objects on (n-1)-dimensional retina cuz' your brain can't visualize it, it's just not made for that.

If you do so, probably you are neither visualizing the clasic hypercube correctly. It's not about a theorical visualization but a real one. It's easy manipulate n-dimensional spaces, but it is biologicaly immposible to visualize it if n is greater than four, as i said, your brain is not made for that...

I don't mean to troll/flame but it's really difficult to take someone seriously when they post about education and can't spell simple words like 'Average'. Can anyone follow this guy?

Maybe his basic mathematical education was proper but his basic english education was done by daffy duck.

Re:The problem is with modern mathematics... (3, Funny)

On a serious note, I am an advocate of teaching The Calculus right after arithmatic. Algebra is almost a complete waste of time as is demonstrated when compairing many algebra problems and the number of steps taught to solve, vs. the "answer one line later" of The Calculus.

Algebra can be relegated to classes dealing with spreadsheets and accounting.

The counter "arguement" I have gotten from Mathematics teachers at all levels boils down to "the proper appreciation of [calc/algebra] will not be gained by teaching them 'out of order'".

Well, sorry teach, I do not recall anything from algebra that was ESSENTIAL for Calc. Not a thing! Plenty of simple arithmatic required resulting in an elegant, precise, answer.

Writtren English is quite another matter.

Re:The problem is with modern mathematics... (0)

Anonymous Coward | more than 11 years ago | (#5980051)

That is crazy.

How do you do calculus? Not simple differential of a parabola by subtracting-one-from-the-power-following-rote-teac her-taught-to-get-basic-grades..., but calculus is done from first principals... which is albegra!

How is calculus worked out? Through albebra.

Now go crawl back under your rock, TROLL.

Re:The problem is with modern mathematics... (3, Insightful)

Well, sorry teach, I do not recall anything from algebra that was ESSENTIAL for Calc.

Eh?

Can you demonstrate exactly how you'd go about calculating a limit without knowledge of algebraic manipulations? How about deriving/proving one of the rules for taking derivatives? What about any but the simplest of symbolic integration?

The only thing I can think of that you *can* do in calc without at least some knowledge of algebraic manipulation is taking simple derivatives. And even then, you'd be doing it without understanding why the rules work, and you'd be unable to do many of the calculations that make derivatives interesting.

There is plenty of more advanced algebra that is taught prior to calculus that teaches complex, laborious methods that are replaced by much simpler, cleaner ones when you learn calc, and you can argue that those could be bypassed. Personally, I found it valuable to learn the non-calc techniques first, both for what I learned for the process and for the appreciate it gave me of the ideas in calculus.

Re:The problem is with modern mathematics... (1, Interesting)

Anonymous Coward | more than 11 years ago | (#5979805)

Very true. But remember that the original motivation of teaching set theory and logic was to inculcate formal thinking in students, and remember that very few of them would go on to become mathematicians. However, traditionally, this has been counterbalanced by also teaching synthetic geometry(euclidean geometry) that fosters imaginative and creative thinking on the part of students. There have been two developments of late: 1. There has been a compromise and less of geometry is being taught, as it is considered "hard". This must be reversed. 2. I think it is feasible to segregate students based on espoused areas of interests. A couple of decades ago this would have been accused of elitism. However, with the growth of awareness among students and parents, not being especially interested in math is not tantamount to mediocrity.

Actually, I'd ask you what a Kleinian bottle is and why you need a 4-dimensional space when 6 billion people manage with 3.

That's if I didn't know what a Kleinina bottle was and that in 4D space it doesn't have the intersecting planes that it does in 3D.

It's probably not because basic mathematical education fucked up my brain, it's because, for some stupid reason, I live in a 3 dimensional world. The insect the lives on the rotating record player doesn't understand 3d objects as well as I do.

If you want to teach your kids Lie matrix groups then you might want to start with matrix theory, and with..shit, counting and algebra.

You don't reduce "Joe Average" problems to Lie groups, you generalize them, you encompass them in a mathematically correct proof, Joe doesn't want this, he want's to know how much tax he has to pay this year.

You gave the example of a Kleinian bottle, why? Surely a better education would be had by not limiting yourself to specific examples of 4D non-intersecting geometries? If you think teaching a 14 year old to visualise n dimensional space (instead of just algebra and math) when 99% will never need to use it, you may as well tell the proletariat to learn latin so they can understand their remote control.

We may need a 'permanent revolution' in education, not just to maintain our 'lead' but to improve our society, Your method isn't the best way to do it.

Also worked on the proof for Fermat's theorem for 7 years in secret(which in the mathematics community is a rather odd thing to do). He was dreaming of solving it while he was still a child. There is quite a good book on the subject for anyone with any level of knowledge called fermats last theorem. I'd give you a link but i'm tired..

Check it out over at Simon Singh's [simonsingh.com] website. Fermat's Last Theorem is great reading, not to mention The Code Book if you fancy cryptography, technology or just drama.

The Book is "Fermat's Enigma" by Simon Singh. I highly recommend it. Singh has a talent for writing about deeply analytical subjects. He also wrote "The Code Book" about the history of cryptography, and he's written a Nova episode or two.

I wish he'd written more books; an Amazon search turns up little else than these two.

Fermat had said it was simple !!! And he didn't think it needed as much space as While took, just a little bit more than the margin, that's all it needed

Whose game? And who said it was a game? (5, Insightful)

Definitely this is the women-not-invited dept., as billed, but it reminds me of a conversation I had with a 98 year old woman in 1982. I was 28, had a toddler and an infant, and was very much afraid that motherhood would be the end of any other kind of creative work for me. (The exhaustion factor alone was daunting.)

Miss Mae said to me, in a Miss-Daisy sort of Southern accent, "Honey, women are not like men -- we get better with age. After all, you can't think straight until your parts settle. I promise, when you are 45, you'll know what you want to do with yourself, and it won't have anything to do with diapers."

She was right about women, or about me, at any rate. I'm 48 and in my first year of professional school while the "baby" is at his first year of college. (What this has to do with my "parts" I am less sure.)

What I notice is that my younger colleagues are quick and bright, but that what I lack in speed I make up in context. And all of us are passionate about what we are doing, but the flavor is a little different depending on age. When we are working well together, the combination of gifts is truly wonderful. Perhaps instead of framing the "game" (of math or of anything else) as a contest, we ought to be looking at ways to make progress that makes use of both the experience of age and the quickness of youth.

Re: Whose game? And who said it was a game? (-1, Flamebait)

Perhaps instead of framing the "game" (of math or of anything else) as a contest, we ought to be looking at ways to make progress that makes use of both the experience of age and the quickness of youth.

Perhaps you should realize that since you've fulfilled your primary purpose as a human being (reproduction), all you're doing is taking up space and resources needed by the next generation to raise its offspring.

In other words, hurry up and die. Your life past this point is merely an exercise in selfish indulgence.

Re: Whose game? And who said it was a game? (0)

Anonymous Coward | more than 11 years ago | (#5979545)

>>In other words, hurry up and die. Your life past this point is merely an exercise in selfish indulgence.

I used this weeks mod points about 12 hours ago. If I had them now, I'd send you down to -15 you prick.

Perhaps you should realize that since you've fulfilled your primary purpose as a human being (reproduction), all you're doing is taking up space and resources needed by the next generation to raise its offspring.

In other words, hurry up and die. Your life past this point is merely an exercise in selfish indulgence.

I assume this was just a joke, but...

Au contraire. Given that there are 6 billion people and growing on this planet, and given that a depressingly large fraction of them live in crushing poverty, overpopulation is a huge problem, and it's only getting worse. The solution? Fewer offspring. Nowadays, the selfish indugence is having kids. Sure, we want the species to continue, but there's no worry about that at the moment. (It's like spaying your dog or cat; there's no anger that there won't be kittens and puppies, so it's best for all concerned to spay.)

I'm not saying nobody should have kids. But if we want to have any hope of the people on this planet living in relative comfort and prosperity, we need to overcome that evolutionary programmed urge to procreate-- which is selfish on a species level, if not an individual level. Sure, evolution designed us so that our purpose is to reproduce, but unless we want the whole world to live in squalor, we now have to redefine that purpose.

So go on to professional school and develop your brain when you're older. Learn math, contribute to human knowledge even when you're past the age when "tradition" dictates you can make your best contribution. Bettering ourselves and our world should be the purpose of existence now, not just producing more and more kids to use the dwindling resources of this planet. Meanwhile, we need to figure out a way to seriously limit the number of kids produced each year while preserving as much personal freedom as we can.

-Rob

Re: Whose game? And who said it was a game? (4, Interesting)

Actually the grandmother hypothesis of why humans are the only primates where women live a significant period of time following menopause give other reasons for women to survive following their reproductive period.[1 (PDF) [utah.edu](Google PDFtoHTML) [216.239.51.100] ]

In a nutshell the grandmother can provide additional food resources to the weaned children of her child or her childrens mates (to increase their fertility) since she no longer has to provide those resources to her direct children and can produce excess to what she consumes.

Thus there is an evolutionary advantage to women surviving following their fertile years, and this advantage likely continues in different ways now.

In a nutshell the grandmother can provide additional food resources to the weaned children of her child or her childrens mates (to increase their fertility) since she no longer has to provide those resources to her direct children and can produce excess to what she consumes.

Interesting. That supports my current favorite perception about menopause, which is that it actually seems to make a woman operate more efficiently in a lot of ways. "Gains weight easily" translates to "needs less food." "Insomnia" translates into "needs less sleep." Hot flashes, however, only have utility in the wintertime.

Re: Whose game? And who said it was a game? (2, Interesting)

Definitely this is the women-not-invited dept., as billed, but it reminds me of a conversation I had with a 98 year old woman in 1982. I was 28, had a toddler and an infant, and was very much afraid that motherhood would be the end of any other kind of creative work for me. (The exhaustion factor alone was daunting.)

Hey, would somebody mod this up? I love women, they are so mysterious. I would love an intelligent discussion of the differences between men and women's intellectual development.

..."Honey, women are not like men -- we get better with age. After all, you can't think straight until your parts settle. I promise, when you are 45, you'll know what you want to do with yourself, and it won't have anything to do with diapers."

She was right about women, or about me, at any rate. I'm 48...

What I notice is that my younger colleagues are quick and bright, but that what I lack in speed I make up in context...

I am a 46 year old male, and I experience something like this too. That quick, bright mind might skip over something old, boring, slow and steady, Mr or Ms Methodical picks up on.

And all of us are passionate about what we are doing, but the flavor is a little different depending on age. When we are working well together, the combination of gifts is truly wonderful. Perhaps instead of framing the "game" (of math or of anything else) as a contest, we ought to be looking at ways to make progress that makes use of both the experience of age and the quickness of youth.

I am reminded, again, of what Leo Szilard [dannen.com] wrote, in one of his science fiction stories, written after he gave up Physics, after his central role in the Manhattan Project.

He wrote about humanity's cleverness having outstripped its wisdom. In the story his hero sets up a foundation to retard the progress of scientific knowledge, to give our wisdom a chance to catch up.

About the widely spread notion that math, physics etc, are fields were only the young come up with the paradigm shifting insights... I have also read the suggestion that it is new arrival in the field that really counts, and that the older person who switches fields can come up with the paradigm shifting notion too.

My knowledge of pure math is not sufficient to know this. Are these two recent, famous developments really paradigm shifting? Or are they admirable accomplishments, but more developments of existing ideas? Can anyone set me straight?

Re: Whose game? And who said it was a game? (-1, Troll)

Anonymous Coward | more than 11 years ago | (#5979629)

And all of us are passionate about what we are doing, but the flavor is a little different depending on age. When we are working well together, the combination of gifts is truly wonderful.

Yeah, you're definitely a skirt. I'm glad I'm not working with you. Math is not about "warm and fuzzy" or "embracing our differences". It's about correct or incorrect, logically consistent or logically flawed, useful or useless. Couldn't you infect some other, softer discipline?

Career path (4, Insightful)

Anonymous Coward | more than 11 years ago | (#5979466)

Let's not forget that most pure mathematicians are University faculty members, and that the longer you're on faculty, the more committees you sit on and the more non-research responsibilities you end up stuck with.

The real question is whether or not great discoveries in a field come from someone being young and having therefore enough mental clarity or from an amount of exposure to a field, resulting a certain level of understanding.

I know, I know: math, like so many of the things discussed here on/., is primarily an activity of men.

But it seems to me that we would be much better served if we talked about how to get more women in the field, not how we could keep old men in it. I mean, aren't there enough old men around anyway?

(spoken by a future old guy - hopefully)

Re:Young MAN'S? (-1, Troll)

Anonymous Coward | more than 11 years ago | (#5979525)

Math is too impersonal and abstract for women. As a general rule, women are only interested in sexual matters, like family, friends, fashion, society, etc. They don't much care for computers, math, space, science, philosophy, etc. That's why they haven't acheived anything of note in any field.

Re:Young MAN'S? (-1, Troll)

Anonymous Coward | more than 11 years ago | (#5979558)

What about young women?
I know, I know: math, like so many of the things discussed here on/., is primarily an activity of men.

Call me old fashioned, but a female's role is to make and raise babies to continue the race and to keep the house clean. It is like that in all species. That has been a woman's primary role for 10,000 years and only recently do they have some awkward notion that they should be involved in men's work.

The decline of American society is directly proportional to the decline of the American woman's role in the household and the so-called "Women's Liberation" movement during the mid-1960's. Take for instance the rise in women in primarily male-dominated jobs during the 1990's. We ended up with situations where both the male and female of the house were both employed in good, well-paying jobs.

It isn't suprising that at the same time the rate of unemployment rose among men and the breakdown of the American family began! Jobs that would have normally gone to the male head-of-household were being consumed by females in other households bringing in dual-incomes instead of being home raising children and letting the male support the family. It's an unpopular opinion because we've let females gain too much independence too quickly, but I'm sure in 20 years we'll be looking back and saying "You know, he was right!". Get those women pregnant, get them back in the kitchen, and somebody bake me a god damn pie already. It's time for breakfast yet my wife feels she needs to be working. GOD DAMNIT!

Re:Young MAN'S? (0)

Anonymous Coward | more than 11 years ago | (#5979595)

What decline of American society?

Seriously, what are you talking about? Sometimes people talk about the good old days "when this country (The United States) was great", but I'm never sure when they mean. The 50's? I guess so, unless you were any kind of minority.

But it seems to me that we would be much better served if we talked about how to get more women in the field

It depends on the reasons that women aren't going into the field. If it is because of some "old boy's club" keeping them down, then that is wrong. If it is because women in general, for whatever reason, don't necessarily want to go down that path then no one should push them on it. Just make it equal for the women who want to be mathematicians.

Women don't generally go to Star Trek conventions, but no one accuses Star Trek conventions of being sexist.

At the university I study, in the course "applied mathematics", more than half of the students are, in fact, women.

(I have to admit, I don't know the exact men:women ratio, but being a computer science student myself, it definately seems an overwhelming lot of women;))

It's simple: Young mathemetician's aren't getting laid -- so they work like hell on on their maths. Since male sex drive peaks at 18, the less sex drive you have, the less driven you are to find another way to spend the time.

Or maybe they got married and their wife nags at them to death and ruins their concentration.

Or maybe they got married and their wife nags at them to death and ruins their concentration.

Speaking from experience, there, matey? *wink* *wink* *nudge* *nudge* Depending on what the nagging is all about, it might not be a bad thing, you know. With mathematicians working "like hell on on their maths", they may be nagging about being neglected in the bedroom -- I wouldn't mind being nagged about that... not at all...

When visiting
mathtutor [st-and.ac.uk]
one can see that even 200 years ago, many important discoveries
were done in the later stages of the Mathematicians career.
Stories like the ones about Abel or Galois distort the picture.

More and more discoveries of younger mathematicians are
achieved through collaboration or by standing on the
shoulders of people with more experience (who tend also to
be more generous with sharing their ideas without expecting
credit).

Mathematical knowledge continues to accumulate in a fast
pace and only few of this knowledge has been absorbed
in books. Chances grow that a young mathematician will
discover something already known or to be a special
case of a much more general result. Fortunately, there are
better and better online
databases [ams.org] but
it also needs more and more time to dig through that material.

The most productive age for a mathematician will grow also
in the future. The same will happen in physics or
computer science (as a previous post has pointed out already).

I can't believe that statement! I'll have you know that at 38 I'm just as...um...uh...what was I going to say? Hey, today's Saturday! The buffet has the early bird special today for dinner at 4pm! I'd better get the oil changed in my Oldsmobile first...

The truth is I don't feel any older than I did at 25 (still like the same age women as a matter of fact), I'm in better shape than I was then, and if coding skills are any indication I'm sharper than my 20-ish coworkers. So there!

Now if you'll excuse me I have to knock back my Ensure before I chase the kids off my lawn.

It can definitely be said that some mathematicians produced work at an early age. As the article said, many died early, some continued to produce work throughout their lives. And the body of maths has increased so much that it's much more work getting an good overview of a field.
Note also that before the 19th century, scientific research didn't have the same place in society: it has grown quite a lot.

But regardless of the mathematician's age, what has to be taken into account is the relationship between groundbreaking work, and sturdy, low-profile, everyday work that is achieved by the mathematics community as a whole.

Without that, the breakthrough cannot happen: it loses its value, as it has no ground to stand on.

This is of course relevant physics and astrophysics as well: if you didn't have people studying and cataloguing stellar spectra, you couldn't develop theories about distances, and, more crucially, n-dimensional cosmological models. Now remember, stellar spectra themselves are boring as hell, so are atomic spectra (the spectra that prompted quantum mechanics, etc.)

There are a lot of romantic ideas in the non-scientific public about science: I meet them every day. Sometimes they are just funny, but other times you wonder about the image that society has of your work. Of course I am by no means degrading the value of scientific breakthroughs and original thinking: any deep thought is a process that I consider to be mysterious in essence.

Damn old schmucks (-1, Troll)

Anonymous Coward | more than 11 years ago | (#5979590)

we oughta run them in their damn wheelchairs and walkers off the grand canyon. fucking colonoscopy bags. fucking buicks going 10 mph under the posted speed limit. always fly Lufthansa if you can!!

It took Andrew Wiles seven years to write a rigorous proof for Fermat's Last 'Theorem'. If he had started when he was 23 instead of 34, he would have proved it while he was 30, instead of 41.

The real problem, of course, is that it wasn't until Andrew learned about the Taniyama-Shimura conjecture that he figured out the method for proving Fermat's Last Theorem. He then waited for 2 years before starting.

Who I think is a better example of mathematician burnout is Yutaka Taniyama himself. He started his career at 28 - way old for a mathematician - and killed himself at age 31. A year after his mathematical prime. Coincidence? Maybe. But you never know...

Paul Erdös. Read about him in this [amazon.com] book.

The man did math until he died of old age, at a pace of about 18 hours per day. He cared not for material things, as he lived out of a suitcase. He cared not for life's physical pleasures, as he (almost!) never even had a girlfriend, or boyfriend for that matter. He had his doctor perscribe speed to him, so he could work more hours on mathematics.

An amazing read about a guy who I am amazed by, but also whose qualities I am glad I don't have.

No, back to studying linear & nonlinear programming, stochastic processes, dynamic programming, and queueing theory for my qualifier on Monday.

Interesting article on Fermat's Last Theorem (2, Interesting)

The article [theonion.com] is written, of course, from the viewpoint of the Theorem itself.

A highlight:

Did Yarosh, Cauchy or Kummer--or even Euler, for that matter--care that I was French? Or that I was born in 1637 in Castres? Okay, Euler might have. At first, he seemed different from the others. He'd spend every waking moment thinking about me. Oh, how that made me feel! But understand me? No. In the end, he was just like the rest, interested only in what I could do for his career.

That's funny-- I always find it odd when the British and Indian folks call math "maths." It's an interesting cultural difference. And I disagree with your abbreviation argument-- "math" is a prefix of "mathematics" while "maths" is not. In fact, pluralizing "math" makes it seem like you concede that there does exist a "mathematic" singular, which you abbreviate to "math," and then pluralize again to mimic the original word.

Do you call economics "econs" . . . ? (0)

Anonymous Coward | more than 11 years ago | (#5979920)

No, I didn't think so. You call it "econ" like the rest of us. There are countless additional examples as well, but going into them would be a waste of time. Believing that your abbreviation is the only correct one is both naive and arrogant. It's obvious that ours is the only correct one;-)

Generally it is, there are exceptions (2, Insightful)

A lot of very tallented mathematicians go down a dark road in their 20s, trying to prove the impossible, giving up prime years to fail at something and a few actually do prove something important and then are spent. Godel was nuts to start with and the work he did in his 20s pushed over the top.

Of course, mathematics is a young man's game. But it's also old man's game. If you're willing to devote yourself to mathematics, it's yours!

In most cases when people "get old" they just tend to drop mathematics to spend some time with their kids or whatnot. It's not like they lost their ability to think.

Of course the real reason that scientists might make more discoveries at advanced age than in past times is simple. Viagra. What's more inspiring than getting some tail?

"The reader who's seen other nontechnical accounts of the subject will forgive me, I hope, for perpetuating the fiction that the whole field of topology is actually confined to the study of spheres and doughnuts. There are other shapes, I promise: They're just harder to describe."

snif, snif... is there a conspiracy against the this is the klein bottle second time [slashdot.org] on slash dot that it is expressively not mentioned ??

Andrew Wiles' proof of the famous x^n + y^n = z^n equation having no proofs wasn't really just a breakthrough at the age of 41. He'd caught interest on this equation at the tender age of 10, and had been working on the thing his entire career. This was probably the dedication required to solve such a proof. Most people would have given up in the time it took him.

Anyway, read Fermat's Enigma, It's a great book, even though it's about math, it is surprisingly interesting

I think that the proposition that mathematical breakthroughs are predominantly made in youth, whether true or not, relates not to the vigour of youth, but to the settling in of dogma.

I've seen this proposition about physicists in more than one lay venue. It was made clear that most breakthroughs in physics were made by minds that had the flexibility to "think outside the box." The gist of the "youth" paradigm is that the more years dedicated to a subject, the more that the thought patterns get set in their ways, precluding the intuitive leaps that change the intellectual landscape.

That being said, Wiles didn't just make some brilliant leaps. He worked damn hard on the details. It may have been more than 10% inspiration for him to prove Taniyama-Shimura (the real achievement for which Fermat was a by-product). Still, from what I've read about his accomplishment, his work was definitely more than half perspiration.

I read about a study some time back about how much more productive, in terms of publishing, Professors in Academia are until they get tenure.

I've worked in and around Academic departments and I can tell you that you can sure see it. The Assistant Professors are busting their butts, late nights and weekends on their research and that immediately changes the day they get tenure.

Some tenured Professors work hard on their research, those that really love the field. People who really love their field are what we should be encouraging in Academia, they also make the best teachers, but the current tenure system doesn't really select for this very well.

I'm just ranting. I don't really have any good ideas on what to do about it.

Maybe there should be some way that good pedagogical performance should be factored into whether tenure is granted, but in most higher education settings I've seen, being a good teacher is considered a stain on your Academic Credentials.

## The GPL (-1, Offtopic)

## Michael's a Jerk! (668185) | more than 11 years ago | (#5979376)

Consulting for several large companies, I'd always done my work on

Windows. Recently however, a top online investment firm asked us to do

some work using Linux. The concept of having access to source code was

very appealing to us, as we'd be able to modify the kernel to meet our

exacting standards which we're unable to do with Microsoft's products.

Although we met several technical challenges along the way

(specifically, Linux's lack of Token Ring support and the fact that we

were unable to defrag its ext2 file system), all in all the process

went smoothly. Everyone was very pleased with Linux, and we were

considering using it for a great deal of future internal projects.

So you can imagine our suprise when we were informed by a lawyer that

we would be required to publish our source code for others to use. It

was brought to our attention that Linux is copyrighted under something

called the GPL, or the Gnu Protective License. Part of this license

states that any changes to the kernel are to be made freely available.

Unfortunately for us, this meant that the great deal of time and money

we spent "touching up" Linux to work for this investment firm would

now be available at no cost to our competitors.

Furthermore, after reviewing this GPL our lawyers advised us that any

products compiled with GPL'ed tools - such as gcc - would also have to

its source code released. This was simply unacceptable.

Although we had planned for no one outside of this company to ever

use, let alone see the source code, we were now put in a difficult

position. We could either give away our hard work, or come up with

another solution. Although it was tought to do, there really was no

option: We had to rewrite the code, from scratch, for Windows 2000.

I think the biggest thing keeping Linux from being truly competitive

with Microsoft is this GPL. Its draconian requirements virtually

guarentee that no business will ever be able to use it. After my

experience with Linux, I won't be recommending it to any of my

associates. I may reconsider if Linux switches its license to

something a little more fair, such as Microsoft's "Shared Source".

Until then its attempts to socialize the software market will insure

it remains only a bit player.

Thank you for your time.

## Michael's a Jerk's a Jerk! (-1, Offtopic)

## jkrise (535370) | more than 11 years ago | (#5979408)

Anyway, for those who cared to read your offtopic troll:

IT IS NOT necessary to publish modifications made to GPL'd s/w to all and sundry. That requirement comes onlt if you need to 'sell' those changes, and even then, the changes were made to GPL'd code - not for code that works on top of it.

Feeding the trolls, maybe..

## Michael outed (1)

## geoswan (316494) | more than 11 years ago | (#5979593)

## Not too young (4, Insightful)

## Uber Banker (655221) | more than 11 years ago | (#5979395)

A bit like athletes maybe... experience vs. physiology results in a trade off.

## Re:Not too young (0)

## Neuropol (665537) | more than 11 years ago | (#5979410)

## Re:Not too young (0)

## Anonymous Coward | more than 11 years ago | (#5979420)

The reason we die, you know, is because cell death > cell growth... causing degregation in some body function which kills you.

## Re:Not too young (2, Insightful)

## Uber Banker (655221) | more than 11 years ago | (#5979427)

## Re:Not too young (0)

## Anonymous Coward | more than 11 years ago | (#5979633)

If you have a very intellectual life, and you keep accumulating more knowledge and in essense keep 'training' your brain, you might be of better mind when you're in your 80s or something. As to someone in his 30s that still has most of his braincells but keeps killing them with booze.

On the other hand, if you don't 'train' your mind, you're gonna get alzheimer by the time you're in your 70s.

My grandfather for example is 96 and can still write beautifull poetry, and some folks 20 years younger are living like vegetables.

## Rule of /. (-1, Offtopic)

## Anonymous Coward | more than 11 years ago | (#5979396)

Yes, but can anyone out there solve the legendary "Slashdot Concept of Dupes" before they hit 40?

## Re:Rule of /. (0)

## Anonymous Coward | more than 11 years ago | (#5979431)

## Re:Rule of /. (0)

## morganjharvey (638479) | more than 11 years ago | (#5979438)

You ever try to sell a kidney on ebay? You know how they stop you real quick?

Both filters use the same algorithm...

## I agree, math's a young man's game (4, Funny)

## Anonymous Coward | more than 11 years ago | (#5979397)

I'm so old, I lost count. Damn wippersnappers and their meaningless symbols.

## Re:I agree, math's a young man's game (2, Funny)

## Subcarrier (262294) | more than 11 years ago | (#5979561)

The conventional belief is that most significant mathematical leaps are all made before the age of 30.That sounds about right. According to another study, mathematicians reach their prime just before discovering sex, after which it is all downhill. It will give the old codgers some solace to know that they can expect a brief comeback after their wives

stophaving sex with them.## It is obvious why this is the case.. (5, Funny)

## Anonymous Coward | more than 11 years ago | (#5979409)

"Okay Dear I'll mow the lawn now"

I also suspect the growing complexity of screensavers as a factor..

## Re:It is obvious why this is the case.. (4, Interesting)

## Davak (526912) | more than 11 years ago | (#5979511)

Thinking, exploration, calculation, research, experimentation--all of these take a great deal of time. Relationships with friends, your SO, and eventually kids require a great deal of this time to keep healthy and strong.If you want smart kids/pets, that takes time as well.

No, I am not saying that one can't be productive or creative once older; however, it just becomes more difficult. Those that do it successfully usually do it though their profession. That is... you can do it though your job if they give you the freedom to do so.

I don't think all of this is so bad... most of us would rather have healthy relationships than awards/accomplishments as we get older.

Davak

## thelimitis30++ (0, Troll)

## Anonymous Coward | more than 11 years ago | (#5979413)

## Frank Lloyd Wright (2, Offtopic)

## handy_vandal (606174) | more than 11 years ago | (#5979440)

## Re:Frank Lloyd Wright (0)

## Anonymous Coward | more than 11 years ago | (#5979539)

did itsitting down andsold itto people over 80## Re:Frank Lloyd Wright (1)

## morganjharvey (638479) | more than 11 years ago | (#5979591)

Frank Lloyd Wright did his most celebrated work after the age of fifty.Yeah. Sure.

My only problem is with the fact that many people were already experimenting with flight before this -- most were under the age of 35. At the time, the mathematics and physics necessary were tremendous, what with lift and velocity and all that, but compared to modern standards are trivial. If we look back to the experiments of Da Vinci, we can realise that the "unified theory" can simply be expressed in terms of z=y^5/... oh wait... wrong Wright...

## Re:thelimitis30++ (4, Interesting)

## jkrise (535370) | more than 11 years ago | (#5979448)

Demanding: Writing the GPL, starting FSF, the Hurd, travelling the world over, believing in yourself despite others jeering you - RMS age 50.

Innovating: Buying an OS from someone, putting it onto someone else's h/w, building up a monopoly, driving out others (using suspect means), releasing newer and newer OSes that do essentially the same things, generate obscene profits, etc. etc. - William Gates, Age 45 (?)

Life begins after 30, methinks.

## Re:thelimitis30++ (2, Insightful)

## watzinaneihm (627119) | more than 11 years ago | (#5979632)

Almost all the rich men have become rich late in their lifes. Most politicians are old, artists contibute throughout their lifes, most scietitsts are old, even.

Maths, due to the fact that it demands little interpersonal contacts (books are enough) and because it is almost entirely an act of the mind (unlike physics where you are related to the rules of the world), is generally assumed to be different.Intuition, originality blah, blah.....

## really ?? (1)

## dorfsmay (566262) | more than 11 years ago | (#5979959)

Almost all the rich men have become rich late in their lifes"Well to just take Gates example from the parent post, how old was he when he made is first 10 M$ ?

## Re:thelimitis30++ (1)

## NonSequor (230139) | more than 11 years ago | (#5980031)

## I prove you wrong! (3, Funny)

## morganjharvey (638479) | more than 11 years ago | (#5979415)

Two of his more interesting pieces of evidence include Grigori Perelman's (probable) proof of the Poincare Conjecture at 40 and Andrew Wile's proof of Fermat's Last Theorem at 41.Yes, but at the tender age of 22, I can not only add my bar tab together, but also figure an appropriate tip.

Young people can't do hard math my ass.

## Re:I prove you wrong! (2, Funny)

## spyderbyte23 (96108) | more than 11 years ago | (#5979444)

allmembers of the group "young people" can do hard math.## Re:I prove you wrong! (5, Funny)

## morganjharvey (638479) | more than 11 years ago | (#5979483)

A single example is not a proofEXACTLY!!!The proof comes from the side of the bottle. You should tip the bartender more the

higher the proof.I'm going to hell for that one...

## New field vs. old fields (4, Insightful)

## cperciva (102828) | more than 11 years ago | (#5979417)

Computer science is moving in the same direction, but is many years behind. Thirty years ago, computer science was a new field; there were few if any courses teaching necessary background material; and someone with the right insight could find very important work very easily. Now, we're starting to see movement away from that -- there is a body of important work to build upon, and anyone who hasn't studied that work will have "new insights" which simply reinvent already existing work.

Mathematics is no longer a young man's game, and this is probably the last generation when computer science has been a young man's game. Next generation, the young will find a new field to excel in -- perhaps genomics?

## Re:New field vs. old fields (5, Interesting)

## spyderbyte23 (96108) | more than 11 years ago | (#5979455)

Now, as the article says, you are a graduate student -- and probably not a new graduate student -- before you're even looking at other people's cutting-edge work, let alone doing your own.

## Re:New field vs. old fields (5, Insightful)

## Omkar (618823) | more than 11 years ago | (#5979468)

## Re:New field vs. old fields (4, Insightful)

## Brian_Ellenberger (308720) | more than 11 years ago | (#5979732)

Hmm, so the Greeks, Euler, Descartes, and thousands of other mathematicians don't count? Math is one of the oldest fields I can think of.And yet, someone could learn and understand all of their most important discoveries before they graduate with a B.S. in Math. From what I've read of Andrew Wiles final resolution of Fermat's Last Theorem, it would take years of specialized study to understand.

Brian

## A poor education system does not help (3, Interesting)

## solprovider (628033) | more than 11 years ago | (#5980029)

I was reinventing Calculus by 8th grade. I was about to win second place in an international math contest. (I was beaten by a 9th grade Canadian.) I usually ignored whatever was being taught in Math class, since I could literally get an A without waking up.

I was attempting to find the area under a curve defined by a formula. It seemed appropriate to do the work in math class. One day, my eight grade math teacher asked what I was doing. I showed him my current theory. He told me that there was already a proof that it was impossible, so I moved it from active work to the "known impossible, but cannot stop trying" category that includes a simple formula for discovering factorials.

If he had mentioned the word "calculus", I would have researched what was already done and continued with new discoveries. Or he could have encouraged me to repeat the discovery. Instead, he told me it was PROVEN IMPOSSIBLE.

Personal note: This was an important event in my life, because a few years later they tried to teach Pre-Calculus. I immediately absorbed the entire book, and then taught myself Calculus. But I could have done that a few years earlier. And it was the first time that I had proof an authority figure lied to me. The realization that adults have no clue even in their specialty was a major part of my maturing. Now I question facts even when the person giving them is the "top authority".

If our education system helped students that showed an aptitude for math to advance at their own rate, they would probably be finding better algorithms for known problems, with the possibility of discovering something new, as a teenager. Tiger Woods specialized in golf starting at age 3. Most Ice skaters, gymnasts, and dancers start before they are 6. Why should mathematicians need to wait until college before specializing?

---

Off-topic details: I was reinventing Newtonian Calculus. Newton invented a system about the same time the current system was discovered by the French. Both systems were used for a time, but further advances (Differentials) were only possible using the French version, so Newtonian Calculus was dropped. So it was unlikely my redicovery would help advance today's knowledge, since it was on a dead branch.

## Re:New field vs. old fields (3, Interesting)

## popmaker (570147) | more than 11 years ago | (#5979938)

In the middle ages people weren't very interestes in mathematics

Then we finally get descartes, Euler, Fermat end those dudes, who finally got the math ball rolling. But it didn't get REALLY interesting until in the twentieth century.

In that light, mathematics, at least modern mathematics could be considered young in the beginning of this century.

And that's the same math that's getting old now.

## Re:New field vs. old fields (3, Informative)

## spyderbyte23 (96108) | more than 11 years ago | (#5980023)

You neglect the contributions of the Arabic and Indian mathematicians at your peril. There's a reason they call them "Arabic numerals," and the word "algebra" comes from the Latin mistransliteration of the Arabic mathematician who first wrote a dicourse on it.

## Re:New field vs. old fields (2, Interesting)

## michael_cain (66650) | more than 11 years ago | (#5979609)

The counter-argument to that is that it is "insights" that count in making breakthrough discoveries. Since that often involves looking at things from a different direction, knowing too much about the conventional thinking within a chosen field may be a bad thing. Speaking from personal experience, as I have grown older it has become more difficult for me to recognize when my own assumptions are restricting the ways I think about a particular problem.

Finally, any field in which research requires large amounts of money is going to be problematic for young people. Raising such money requires a reputation of sorts and a network of contacts and experience, all of which take years to acquire. And people who control large sums of money do tend to be inclined to conservative approaches -- evolution, not revolution.

## Re:New field vs. old fields (1)

## cperciva (102828) | more than 11 years ago | (#5979762)

## Phases of Life... (4, Funny)

## Anonymous Coward | more than 11 years ago | (#5979421)

5 to 15: Productive phase

15 to 40: Reproductive phase (some like to begin early and post longer

40 to 60: Consumer phase

60 to

## Huh !! (0)

## Anonymous Coward | more than 11 years ago | (#5979422)

## Science, Math, and Age (4, Interesting)

## reverseengineer (580922) | more than 11 years ago | (#5979968)

As far as age and mathematics go, though, I'd have to agree that the effects of age are, if not disappearing, then at least being shifted back a number of years. Not long ago, I had the fascinating realization that after 3 years of college, I know more mathematics than Euclid, Diophantus, al-Kwahrizmi, Fermat, Newton, Leibniz, Euler, Hamilton, and Abel. This is not because I'm some sort of mathematics genius (I'm not even a math major), but rather because there is simply more mathematics to learn now, and I merely came later than those guys. For centuries, the situation was such that almost all of the human race's mathematics knowledge could exist in few enough books to carry in your hands- namely, Euclid's

Elementsand Diophantus'sArithmetica, eventually followed by a few others like Fibbonacci'sLiber Abacci. In the 17th-19th centuries, mathematics used these simple foundations to create an incredible wave of new mathematics. (Just take a look at Fermat's annotated copy of theArithemetica.) Now the number of books written on some specialized part of mathematics like Lie algebras or K-theory could fill a library.Also, mathematics works a bit differently than the natural sciences- it's harder to create a general survey course in mathematics. Just look at the way these subjects are taught- you generally take high school science courses in physics, chemistry, and biology, but math courses in algebra, geometry, and calculus. The specialization has to start much sooner because eachthing builds off of the previous. In my high school chemistry courses, I remember covering some basic p-chem, some orgo, etc, and in my physics courses there was mechanics, E&M, optics, etc.. I of course returned to all of these in excrutiating detail in my college course, but the simple point is that you couldn't do a similar thing with math. In physical sciences, you can give a broad overview of a subject, and then later reurn in depth, because there isn't such an elaborate hierarchy connecting all of the fields. Conversely, mathematics works more like a pipeline, shuttling students from simpler subjects (basic arithmetic, simple Euclidean geometry) to harder ones (integral calculus, diff eq, set theory). The pipe opens up at the top- areas of specialization become apparent, and a frontier is reached where knowledge in one field is not necessary for knowledge in another.

In fact, there are so many fields and subdisciplines now that it has become incredibly difficult to become a polymath (in the quite literal sense of the term) in the vein of Euler or Gauss or Riemann. The idea of a single person making revolutionary discoveries in both, say, topology and number theory is steadily becoming more remote. If this were to happen, it would have to be someone who spent a long time mastering several disciplines, i.e., an old person. It's a sublime paradox- in the past, incredible leaps of insight that would connect disparate theorems and fields of math could only be made by the young mathematicians with the creativity and the daring to do so (or, if you're cynical, the neuronal plasticity), but now such individuals will still be in grad school learning the ropes.

Look at Andrew Wiles- it took him years to learn enough about elliptic equations, modular forms, and Galois groups to prove the Taniyama-Shimura Conjecture (and thus Fermat's Last Theorem). It took Perelman several years of work to complete his proof of the Geometrization Conjecture. The problems left on the table are in some sense getting harder- they might not take any more genius than the problems Euler or one of the Bernoullis solved, but they do require more information. The age of the brilliant dilettante is over- it now takes years of learning and research just to be able to start composing a proof. It would now take a singular genius of the sort that comes around once a generation to be able to grasp difficult mathematics at such an early age that they could then make major contributions in their early 20s. It's not impossible- the next Ramanujan may be picking up his/her first math text at age 3 right now- but in general, I have a feeling that 50 or even 55 will become "the new 40" in mathematical circles.

Hey, it's my 100th post!

## moron wondering if payper liesense scammage (-1, Troll)

## Anonymous Coward | more than 11 years ago | (#5979425)

please have the SourceForgerIE(tm) focused marketing program(tm), aim this post towards redmoaned. thanks robbIE, you're such a 'community' member.

## The problem is with modern mathematics... (2, Interesting)

## Krapangor (533950) | more than 11 years ago | (#5979433)

After that brainwashing people aren't simply able to do anything outstanding anymore. There are some accidential great scores, but they are very rare.

I think we should change our mathematics education to tackle with this problem. And we should indeed already start in school were the first and the most foul foundations are laid. Instead of teaching children basic counting, set theory and algebra which draws in the whole rubbish of non-intentionistic mathematics, we should start with Lie groups and algebraic varities. Indeed most "Joe Adverage" problems can be reduced to Lie/algebraic geometry problems.

I can give a simple example why this is necessary:

Imagine the Kleinian bottle in R^4.

You'll say now: "That's not possible nobody can visualized 4 dimensional spaces."

But this is only because your basic mathematical education fucked up your brain.If a decent education would start like mentioned above, we all would have no trouble at all to visualized arbitrary n-dimensional spaces.

And because of using different logical concepts wouldn't have to use the problematic

axiom of choice. So, no trouble with the Banach-Tarski paradox, inmesaurable sets and non-holomorphic refractions in H^p_2.This is even a serious political issue. Anyone into math research will agree with me that in the last 15 years we saw a rise of a generation of brilliant newchinesemathematicians. And why did we saw it ? Because China went back to its Confucian tradition in teaching which avoids the above mentioned problems in Western math education. So, if we don't act now we'll loose our technological leader within the next 30 years forever.## Re:The problem is with modern mathematics... (2, Interesting)

## u38cg (607297) | more than 11 years ago | (#5979470)

In the meantime, WTF is a Lie group? WTF is an algebraic varity? Non-holomorphic sounds very impressive, but WTF is it?

You might be right; I've observed that certain Asian groups do seem to have a handle on maths that many Western brains don't, and I doubt it's entirely due to genetics. But if you actually want to change things, as opposed to sounding clever, people have to understand what you're on about. I don't, and I'm three-quarters of the way through an engineering degree. Thank you.

## Re:The problem is with modern mathematics... (5, Funny)

## bj8rn (583532) | more than 11 years ago | (#5979482)

You'll say now: "That's not possible nobody can visualized 4 dimensional spaces."An architect, a physicist and a mathematician were asked whether they could imagine a 4-dimensional space.

The architect said: "That's impossible! I can't draw that!"

The physicist said: "Well, that can be done, if we say that time is the fourth dimension..."

The mathematician said: "Let us imagine an n-dimensional space. Now, let n equal four..."

## Check out "A mathematician's apology" by G. Hardy (2, Interesting)

## anandrajan (86137) | more than 11 years ago | (#5979967)

Here are some nuggets from "A mathematician's apology". (Hope the copyright police are busy elsewhere.)

"No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." [Section 1.4, page 70]

"Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty."[Section 1.4, page 71]. Also see Men of Mathematics [amazon.com] for more on Galois.

"I do not know an instance of a major mathematical advance initiated by a man past fifty." [Section 1.4, page 71].

And later in the book,

"There are then two mathematics. There is the real mathematics of the real mathematicians, and there is what I will call the 'trivial' mathematics, for want of a better word" [Section 1.28, page 139].

## Re:The problem is with modern mathematics... (1)

## watzinaneihm (627119) | more than 11 years ago | (#5979536)

Since I wanted to know if you were trolling or if you were seriously trying to contribute something I looked at your posting history.Most of the posts were either classified as trolls or modded up as funny (though the posts seemed very similar to what you said in the post above).

Since I still have not figured out what you are trying to accomplish I have no other choice but to ask you to repost that in a Language atleast some of us can understand.

## Re:The problem is with modern mathematics... (0)

## Anonymous Coward | more than 11 years ago | (#5979572)

Yes, nice idea not to teach rigidities... but Confucious teachings of math?! Confucious did not teach topological methods, he likely used an abacus.

## Visualization vs. Manipulation (0)

## Anonymous Coward | more than 11 years ago | (#5979596)

Nobody can visualize n-dimensional geometry if n is greater than four. You can imagine a 3-dimensional retine and proyect on it 4-dimensional geometry. You get a 3-dimensional projection of a 4-dimensional object, which your brain can handle. But it's not the same than projecting n-dimensional objects on (n-1)-dimensional retina cuz' your brain can't visualize it, it's just not made for that.

If you do so, probably you are neither visualizing the clasic hypercube correctly. It's not about a theorical visualization but a real one. It's easy manipulate n-dimensional spaces, but it is biologicaly immposible to visualize it if n is greater than four, as i said, your brain is not made for that...

## Re:The problem is with modern mathematics... (1)

## Paleomacus (666999) | more than 11 years ago | (#5979663)

Maybe his basic mathematical education was proper but his basic english education was done by daffy duck.

## Re:The problem is with modern mathematics... (3, Funny)

## tuxedo-steve (33545) | more than 11 years ago | (#5979794)

PretentiousMensa member, beware of the masturbation. For those of you in the first few rows, safety goggles have been provided.## Re:The problem is with modern mathematics... (1)

## GMontag (42283) | more than 11 years ago | (#5979803)

taughtto solve, vs. the "answer one line later" of The Calculus.Algebra can be relegated to classes dealing with spreadsheets and accounting.

The counter "arguement" I have gotten from Mathematics teachers at all levels boils down to "the proper appreciation of [calc/algebra] will not be gained by teaching them 'out of order'".

Well, sorry teach, I do not recall anything from algebra that was ESSENTIAL for Calc. Not a thing! Plenty of simple arithmatic required resulting in an elegant, precise, answer.

Writtren English is quite another matter.

## Re:The problem is with modern mathematics... (0)

## Anonymous Coward | more than 11 years ago | (#5980051)

How do you do calculus? Not simple differential of a parabola by subtracting-one-from-the-power-following-rote-tea

How is calculus worked out? Through albebra.

Now go crawl back under your rock, TROLL.

## Re:The problem is with modern mathematics... (3, Insightful)

## swillden (191260) | more than 11 years ago | (#5980054)

Well, sorry teach, I do not recall anything from algebra that was ESSENTIAL for Calc.Eh?

Can you demonstrate exactly how you'd go about calculating a limit without knowledge of algebraic manipulations? How about deriving/proving one of the rules for taking derivatives? What about any but the simplest of symbolic integration?

The only thing I can think of that you *can* do in calc without at least some knowledge of algebraic manipulation is taking simple derivatives. And even then, you'd be doing it without understanding why the rules work, and you'd be unable to do many of the calculations that make derivatives interesting.

There is plenty of more advanced algebra that is taught prior to calculus that teaches complex, laborious methods that are replaced by much simpler, cleaner ones when you learn calc, and you can argue that those could be bypassed. Personally, I found it valuable to learn the non-calc techniques first, both for what I learned for the process and for the appreciate it gave me of the ideas in calculus.

## Re:The problem is with modern mathematics... (1, Interesting)

## Anonymous Coward | more than 11 years ago | (#5979805)

1. There has been a compromise and less of geometry is being taught, as it is considered "hard". This must be reversed.

2. I think it is feasible to segregate students based on espoused areas of interests. A couple of decades ago this would have been accused of elitism. However, with the growth of awareness among students and parents, not being especially interested in math is not tantamount to mediocrity.

## Re:The problem is with modern mathematics... (1)

## BuilderBob (661749) | more than 11 years ago | (#5979997)

Actually, I'd ask you what a Kleinian bottle is and why you need a 4-dimensional space when 6 billion people manage with 3.

That's if I didn't know what a Kleinina bottle was and that in 4D space it doesn't have the intersecting planes that it does in 3D.

It's probably not because basic mathematical education fucked up my brain, it's because, for some stupid reason, I live in a 3 dimensional world. The insect the lives on the rotating record player doesn't understand 3d objects as well as I do.

If you want to teach your kids Lie ..shit, counting and algebra.

matrixgroups then you might want to start with matrix theory, and withYou don't reduce "Joe Average" problems to Lie groups, you

generalizethem, you encompass them in a mathematically correct proof, Joe doesn't want this, he want's to know how much tax he has to pay this year.You gave the example of a Kleinian bottle, why? Surely a better education would be had by not limiting yourself to specific examples of 4D non-intersecting geometries? If you think teaching a 14 year old to visualise n dimensional space (instead of just algebra and math) when 99% will never need to use it, you may as well tell the proletariat to learn latin so they can understand their remote control.

We may need a 'permanent revolution' in education, not just to maintain our 'lead' but to improve our society, Your method isn't the best way to do it.

## Andrew Wile (5, Interesting)

## Andrast (670757) | more than 11 years ago | (#5979441)

## Re:Andrew Wile (3, Informative)

## spaic (473208) | more than 11 years ago | (#5979554)

## Re:Andrew Wile (1)

## eddy (18759) | more than 11 years ago | (#5979560)

You mean Fermat's Enigma [amazon.com] ? My review here [gazonk.org] .

## Re:Andrew Wile (4, Funny)

## Paul87 (201172) | more than 11 years ago | (#5979628)

## The Book on Andrew Wiles and Fermat's Theorem (1)

## lildogie (54998) | more than 11 years ago | (#5979974)

I wish he'd written more books; an Amazon search turns up little else than these two.

## What an idiot (1)

## dorfsmay (566262) | more than 11 years ago | (#5979999)

simple!!! And he didn't think it needed as much space as While took, just a little bit more than the margin, that's all it needed## Whose game? And who said it was a game? (5, Insightful)

## mactov (131709) | more than 11 years ago | (#5979451)

Miss Mae said to me, in a Miss-Daisy sort of Southern accent, "Honey, women are not like men -- we get better with age. After all, you can't think straight until your parts settle. I promise, when you are 45, you'll know what you want to do with yourself, and it won't have anything to do with diapers."

She was right about women, or about me, at any rate. I'm 48 and in my first year of professional school while the "baby" is at his first year of college. (What this has to do with my "parts" I am less sure.)

What I notice is that my younger colleagues are quick and bright, but that what I lack in speed I make up in context. And all of us are passionate about what we are doing, but the flavor is a little different depending on age. When we are working well together, the combination of gifts is truly wonderful. Perhaps instead of framing the "game" (of math or of anything else) as a contest, we ought to be looking at ways to make progress that makes use of both the experience of age and the quickness of youth.

## Re: Whose game? And who said it was a game? (-1, Flamebait)

## User 956 (568564) | more than 11 years ago | (#5979506)

Perhaps instead of framing the "game" (of math or of anything else) as a contest, we ought to be looking at ways to make progress that makes use of both the experience of age and the quickness of youth.Perhaps you should realize that since you've fulfilled your primary purpose as a human being (reproduction), all you're doing is taking up space and resources needed by the next generation to raise its offspring.

In other words, hurry up and die. Your life past this point is merely an exercise in selfish indulgence.

## Re: Whose game? And who said it was a game? (0)

## Anonymous Coward | more than 11 years ago | (#5979545)

I used this weeks mod points about 12 hours ago. If I had them now, I'd send you down to -15 you prick.

So at what age are YOU planning to die? Bastard.

## Re: Whose game? And who said it was a game? (1)

## mactov (131709) | more than 11 years ago | (#5979559)

Your life past this point is merely an exercise in selfish indulgence.And yours is an exercise in

## Re: Whose game? And who said it was a game? (4, Insightful)

## rknop (240417) | more than 11 years ago | (#5979567)

Perhaps you should realize that since you've fulfilled your primary purpose as a human being (reproduction), all you're doing is taking up space and resources needed by the next generation to raise its offspring.In other words, hurry up and die. Your life past this point is merely an exercise in selfish indulgence.I assume this was just a joke, but...

Au contraire. Given that there are 6 billion people and growing on this planet, and given that a depressingly large fraction of them live in crushing poverty, overpopulation is a huge problem, and it's only getting worse. The solution? Fewer offspring. Nowadays, the selfish indugence is

having kids. Sure, we want the species to continue, but there's no worry about that at the moment. (It's like spaying your dog or cat; there's no anger that there won't be kittens and puppies, so it's best for all concerned to spay.)I'm not saying nobody should have kids. But if we want to have any hope of the people on this planet living in relative comfort and prosperity, we need to overcome that evolutionary programmed urge to procreate-- which is selfish on a species level, if not an individual level. Sure, evolution designed us so that our purpose is to reproduce, but unless we want the whole world to live in squalor, we now have to redefine that purpose.

So go on to professional school and develop your brain when you're older. Learn math, contribute to human knowledge even when you're past the age when "tradition" dictates you can make your best contribution. Bettering ourselves and our world should be the purpose of existence now, not just producing more and more kids to use the dwindling resources of this planet. Meanwhile, we need to figure out a way to seriously limit the number of kids produced each year while preserving as much personal freedom as we can.

-Rob

## Re: Whose game? And who said it was a game? (4, Interesting)

## puppet10 (84610) | more than 11 years ago | (#5979605)

In a nutshell the grandmother can provide additional food resources to the weaned children of her child or her childrens mates (to increase their fertility) since she no longer has to provide those resources to her direct children and can produce excess to what she consumes.

Thus there is an evolutionary advantage to women surviving following their fertile years, and this advantage likely continues in different ways now.

## Re: Whose game? And who said it was a game? (1)

## mactov (131709) | more than 11 years ago | (#5979658)

In a nutshell the grandmother can provide additional food resources to the weaned children of her child or her childrens mates (to increase their fertility) since she no longer has to provide those resources to her direct children and can produce excess to what she consumes.Interesting. That supports my current favorite perception about menopause, which is that it actually seems to make a woman operate more efficiently in a lot of ways. "Gains weight easily" translates to "needs less food." "Insomnia" translates into "needs less sleep." Hot flashes, however, only have utility in the wintertime.

## Re: Whose game? And who said it was a game? (2, Interesting)

## geoswan (316494) | more than 11 years ago | (#5979549)

He wrote about humanity's cleverness having outstripped its wisdom. In the story his hero sets up a foundation tothe progress of scientific knowledge, to give our wisdom a chance to catch up.

retardAbout the widely spread notion that math, physics etc, are fields were only the young come up with the paradigm shifting insights... I have also read the suggestion that it is new arrival in the field that really counts, and that the older person who switches fields can come up with the paradigm shifting notion too.

My knowledge of pure math is not sufficient to know this. Are these two recent, famous developments really paradigm shifting? Or are they admirable accomplishments, but more developments of existing ideas? Can anyone set me straight?

## Re: Whose game? And who said it was a game? (-1, Troll)

## Anonymous Coward | more than 11 years ago | (#5979629)

And all of us are passionate about what we are doing, but the flavor is a little different depending on age. When we are working well together, the combination of gifts is truly wonderful.Yeah, you're definitely a skirt. I'm glad I'm not working with you. Math is not about "warm and fuzzy" or "embracing our differences". It's about correct or incorrect, logically consistent or logically flawed, useful or useless. Couldn't you infect some other, softer discipline?

## Career path (4, Insightful)

## Anonymous Coward | more than 11 years ago | (#5979466)

## Age or Exposure? (1)

## Theovon (109752) | more than 11 years ago | (#5979473)

## Life expectancy (5, Interesting)

## glgraca (105308) | more than 11 years ago | (#5979486)

people usually didnt live

beyond 40?

## Re:Life expectancy (1, Informative)

## Anonymous Coward | more than 11 years ago | (#5979882)

Before the 20th century, science was just a wealthy-men's hobby and the they usually lived longer than the average people of that time.

## Young MAN'S? (2, Insightful)

## backlonthethird (470424) | more than 11 years ago | (#5979491)

I know, I know: math, like so many of the things discussed here on

But it seems to me that we would be much better served if we talked about how to get more women in the field, not how we could keep old men in it. I mean, aren't there enough old men around anyway?

(spoken by a future old guy - hopefully)

## Re:Young MAN'S? (-1, Troll)

## Anonymous Coward | more than 11 years ago | (#5979525)

## Re:Young MAN'S? (-1, Troll)

## Anonymous Coward | more than 11 years ago | (#5979558)

What about young women? I know, I know: math, like so many of the things discussed here on /., is primarily an activity of men.Call me old fashioned, but a female's role is to make and raise babies to continue the race and to keep the house clean. It is like that in all species. That has been a woman's primary role for 10,000 years and only recently do they have some awkward notion that they should be involved in men's work.

The decline of American society is directly proportional to the decline of the American woman's role in the household and the so-called "Women's Liberation" movement during the mid-1960's. Take for instance the rise in women in primarily male-dominated jobs during the 1990's. We ended up with situations where both the male and female of the house were both employed in good, well-paying jobs.

It isn't suprising that at the same time the rate of unemployment rose among men and the breakdown of the American family began! Jobs that would have normally gone to the male head-of-household were being consumed by females in other households bringing in dual-incomes instead of being home raising children and letting the male support the family. It's an unpopular opinion because we've let females gain too much independence too quickly, but I'm sure in 20 years we'll be looking back and saying "You know, he was right!". Get those women pregnant, get them back in the kitchen, and somebody bake me a god damn pie already. It's time for breakfast yet my wife feels she needs to be working. GOD DAMNIT!

## Re:Young MAN'S? (0)

## Anonymous Coward | more than 11 years ago | (#5979595)

What decline of American society?

Seriously, what are you talking about? Sometimes people talk about the good old days "when this country (The United States) was great", but I'm never sure when they mean. The 50's? I guess so, unless you were any kind of minority.

## Re:Young MAN'S? (2, Insightful)

## Brian_Ellenberger (308720) | more than 11 years ago | (#5979781)

But it seems to me that we would be much better served if we talked about how to get more women in the fieldIt depends on the reasons that women aren't going into the field. If it is because of some "old boy's club" keeping them down, then that is wrong. If it is because women in general, for whatever reason, don't necessarily want to go down that path then no one should push them on it. Just make it equal for the women who want to be mathematicians.

Women don't generally go to Star Trek conventions, but no one accuses Star Trek conventions of being sexist.

## Re:Young MAN'S? (1)

## sirius_bbr (562544) | more than 11 years ago | (#5980033)

(I have to admit, I don't know the exact men:women ratio, but being a computer science student myself, it definately seems an overwhelming lot of women

## An evolutionary biologist says... (4, Funny)

## Saint Stephen (19450) | more than 11 years ago | (#5979499)

Or maybe they got married and their wife nags at them to death and ruins their concentration.

## Re:An evolutionary biologist says... (1)

## Sherloqq (577391) | more than 11 years ago | (#5979573)

Or maybe they got married and their wife nags at them to death and ruins their concentration.Speaking from experience, there, matey? *wink* *wink* *nudge* *nudge*

Depending on what the nagging is all about, it might not be a bad thing, you know.

With mathematicians working

"like hell on on their maths", they may benagging about being neglected in the bedroom -- I wouldn't mind being nagged about that...

not at all...

## Re:An evolutionary biologist says... (2, Funny)

## sonoronos (610381) | more than 11 years ago | (#5979656)

## competing with discoveries from the past (5, Interesting)

## e**(i pi)-1 (462311) | more than 11 years ago | (#5979501)

More and more discoveries of younger mathematicians are achieved through collaboration or by standing on the shoulders of people with more experience (who tend also to be more generous with sharing their ideas without expecting credit).

Mathematical knowledge continues to accumulate in a fast pace and only few of this knowledge has been absorbed in books. Chances grow that a young mathematician will discover something already known or to be a special case of a much more general result. Fortunately, there are better and better online databases [ams.org] but it also needs more and more time to dig through that material.

The most productive age for a mathematician will grow also in the future. The same will happen in physics or computer science (as a previous post has pointed out already).

## Who thinks 40 is not young? (4, Funny)

## Call Me Black Cloud (616282) | more than 11 years ago | (#5979508)

The truth is I don't feel any older than I did at 25 (still like the same age women as a matter of fact), I'm in better shape than I was then, and if coding skills are any indication I'm sharper than my 20-ish coworkers. So there!

Now if you'll excuse me I have to knock back my Ensure before I chase the kids off my lawn.

## flash vs slow advances (4, Insightful)

## fiiz (263633) | more than 11 years ago | (#5979515)

Note also that before the 19th century, scientific research didn't have the same place in society: it has grown quite a lot.

But regardless of the mathematician's age, what has to be taken into account is the relationship between groundbreaking work, and sturdy, low-profile, everyday work that is achieved by the mathematics community as a whole.

Without that, the breakthrough cannot happen: it loses its value, as it has no ground to stand on.

This is of course relevant physics and astrophysics as well: if you didn't have people studying and cataloguing stellar spectra, you couldn't develop theories about distances, and, more crucially, n-dimensional cosmological models. Now remember, stellar spectra themselves are boring as hell, so are atomic spectra (the spectra that prompted quantum mechanics, etc.)

There are a lot of romantic ideas in the non-scientific public about science: I meet them every day. Sometimes they are just funny, but other times you wonder about the image that society has of your work. Of course I am by no means degrading the value of scientific breakthroughs and original thinking: any deep thought is a process that I consider to be mysterious in essence.

## Damn old schmucks (-1, Troll)

## Anonymous Coward | more than 11 years ago | (#5979590)

we oughta run them in their damn wheelchairs and walkers off the grand canyon. fucking colonoscopy bags. fucking buicks going 10 mph under the posted speed limit. always fly Lufthansa if you can!!## Andrew Wiles at age 41 (3, Interesting)

## sonoronos (610381) | more than 11 years ago | (#5979622)

The real problem, of course, is that it wasn't until Andrew learned about the Taniyama-Shimura conjecture that he figured out the method for proving Fermat's Last Theorem. He then waited for 2 years before starting.

Who I think is a better example of mathematician burnout is Yutaka Taniyama himself. He started his career at 28 - way old for a mathematician - and killed himself at age 31. A year after his mathematical prime. Coincidence? Maybe. But you never know...

## In the spirit of mathematics: (3, Interesting)

## stomv (80392) | more than 11 years ago | (#5979636)

Paul Erdös. Read about him in this [amazon.com] book.

The man did math until he died of old age, at a pace of about 18 hours per day. He cared not for material things, as he lived out of a suitcase. He cared not for life's physical pleasures, as he (almost!) never even had a girlfriend, or boyfriend for that matter. He had his doctor perscribe speed to him, so he could work more hours on mathematics.

An amazing read about a guy who I am amazed by, but also whose qualities I am glad I don't have.

No, back to studying linear & nonlinear programming, stochastic processes, dynamic programming, and queueing theory for my qualifier on Monday.

## Interesting article on Fermat's Last Theorem (2, Interesting)

## The-Bus (138060) | more than 11 years ago | (#5979640)

A highlight:

## "Math" Arrrrrgggghhhh!!!!! (2, Funny)

## CowboyBob500 (580695) | more than 11 years ago | (#5979691)

The abbreviation "math" really grates on me (outside the US it's called "maths"). It's not mathematic, it's mathematic

s.Don't get me started on sulfur either...

Bob

## Re:"Math" Arrrrrgggghhhh!!!!! (2, Interesting)

## markov_chain (202465) | more than 11 years ago | (#5979756)

## Do you call economics "econs" . . . ? (0)

## Anonymous Coward | more than 11 years ago | (#5979920)

## Generally it is, there are exceptions (2, Insightful)

## AxelTorvalds (544851) | more than 11 years ago | (#5979739)

A lot of very tallented mathematicians go down a dark road in their 20s, trying to prove the impossible, giving up prime years to fail at something and a few actually do prove something important and then are spent. Godel was nuts to start with and the work he did in his 20s pushed over the top.

## achievements before 30 (1)

## samhalliday (653858) | more than 11 years ago | (#5979769)

## Yes... (1)

## fi-greenie (514665) | more than 11 years ago | (#5979770)

In most cases when people "get old" they just tend to drop mathematics to spend some time with their kids or whatnot. It's not like they lost their ability to think.

Want proof?

I can't give you one, but here's a conjecture.

Paul Erdös!

## Modern Elders of Science (2, Funny)

## MisterMook (634297) | more than 11 years ago | (#5979845)

realreason that scientists might make more discoveries at advanced age than in past times is simple. Viagra. What's more inspiring than getting some tail?## Conspiracy ??? (1)

## dorfsmay (566262) | more than 11 years ago | (#5979921)

The reader who's seen other nontechnical accounts of the subject will forgive me, I hope, for perpetuating the fiction that the whole field of topology is actually confined to the study of spheres and doughnuts. There are other shapes, I promise: They're just harder to describe."snif, snif... is there a conspiracy against the this is the klein bottle second time [slashdot.org] on slash dot that it is expressively not mentioned ??

## Wiles' proof of Fermat's theorem (2, Informative)

## CastrTroy (595695) | more than 11 years ago | (#5979983)

Anyway, read Fermat's Enigma, It's a great book, even though it's about math, it is surprisingly interesting

## Expounding against the tide (3, Interesting)

## lildogie (54998) | more than 11 years ago | (#5980007)

I've seen this proposition about physicists in more than one lay venue. It was made clear that most breakthroughs in physics were made by minds that had the flexibility to "think outside the box." The gist of the "youth" paradigm is that the more years dedicated to a subject, the more that the thought patterns get set in their ways, precluding the intuitive leaps that change the intellectual landscape.

That being said, Wiles didn't just make some brilliant leaps. He worked damn hard on the details. It may have been more than 10% inspiration for him to prove Taniyama-Shimura (the real achievement for which Fermat was a by-product). Still, from what I've read about his accomplishment, his work was definitely more than half perspiration.

## Had to say it (1)

## Faust7 (314817) | more than 11 years ago | (#5980008)

Is Math a Young Man's Game?Well, if virgins are men, then yes.

## Tenure and research productivity (1)

## JordanH (75307) | more than 11 years ago | (#5980032)

I've worked in and around Academic departments and I can tell you that you can sure see it. The Assistant Professors are busting their butts, late nights and weekends on their research and that immediately changes the day they get tenure.

Some tenured Professors work hard on their research, those that really love the field. People who really love their field are what we should be encouraging in Academia, they also make the best teachers, but the current tenure system doesn't really select for this very well.

I'm just ranting. I don't really have any good ideas on what to do about it.

Maybe there should be some way that good pedagogical performance should be factored into whether tenure is granted, but in most higher education settings I've seen, being a good teacher is considered a stain on your Academic Credentials.