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Tracking the World's Great Unsolved Math Mysteries

samzenpus posted more than 4 years ago | from the another-piece-of-pi dept.

Math 221

coondoggie writes "Some math problems are as old as the wind, experts say, and many remain truly unsolved. But a new open source-based site from the American Institute of Mathematics looks to help track work done and solve long-standing and difficult math problems. The Institute, along with the National Science Foundation, has opened the AIM Problem Lists site to offer an organized and annotated collection of unsolved problems, and previously unsolved problems, in a specialized area of mathematics research. The problem list provides a snapshot of the current state of research in a particular research area, letting experts track new developments, and newcomers gain a perspective on the subject."

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Math cannot exist before wind. (1, Interesting)

blackraven14250 (902843) | more than 4 years ago | (#30150970)

How can math problems exist before people start using mathematics? Last I checked, math was nothing more than a representation of the hypothetical that as closely models our universe as possible.

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30151050)

Ever heard of a "figure of speech"?

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30151146)

Yeah, those are as old as the wind, too.

Re:Math cannot exist before wind. (2, Funny)

JustOK (667959) | more than 4 years ago | (#30151202)

they're a dime a dozen, too.

Re:Math cannot exist before wind. (1)

socceroos (1374367) | more than 4 years ago | (#30151736)

Mum's the word. We don't want /. starting another one of those threads where everyone tries to continue the joke.

Re:Math cannot exist before wind. (4, Interesting)

John Hasler (414242) | more than 4 years ago | (#30151094)

Some say math is discovered. Others say it is invented. You are one of the latter.

Re:Math cannot exist before wind. (2)

blackraven14250 (902843) | more than 4 years ago | (#30151460)

If it is discovered, the solution already exists and the problem was solved before wind existed, because the problem never existed in a state where it didn't have a solution.
If it is invented, the problem didn't exist before the wind.
In either case, the problem isn't older than the wind.

Re:Math cannot exist before wind. (1)

PaladinAlpha (645879) | more than 4 years ago | (#30151974)

If you discover the answer to a riddle, haven't you solved the riddle?

Re:Math cannot exist before wind. (1)

wwfarch (1451799) | more than 4 years ago | (#30152322)

Nope, I just googled it

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30152164)

Are you saying that a problem which has a solution isn't a problem?

Re:Math cannot exist before wind. (0, Flamebait)

blackraven14250 (902843) | more than 4 years ago | (#30152306)

Yes, because it never existed without a known solution. I might solve the problem of global warming by using renewable energy, but that isn't a 'known' solution, it's just one that is (heavily) hypothesized to work. If it were guaranteed that it would be a solution to global warming, and it were something that had been known at least since the creation of the universe, it would have never been a true problem in the universe to begin with, but rather an intricacy of the universe's workings.

Re:Math cannot exist before wind. (3, Insightful)

Haxamanish (1564673) | more than 4 years ago | (#30152470)

I would argue the opposite: a problem is something which has a solution, something without a solution is not a problem but a circumstance.

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30152780)

Are you saying that a problem which has a solution isn't a problem?

because it never existed without a known solution

No, you just said it never existed without a solution. You did not say that the solution had to be known.

Re:Math cannot exist before wind. (4, Funny)

interkin3tic (1469267) | more than 4 years ago | (#30151968)

Some say math is discovered. Others say it is invented.

And still others (especially those in grade school and high school) say that math should neither have been invented nor discovered.

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30152454)

They're children ... give them a break.

Though, to be fair, if someone still thinks that way by the time they enter college, he or she definitely requires some counseling ...

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30152328)

Long before man had "discovered" how to count, the universe "knew" that the ratio of a circle's diameter to its circumference was a constant number that today we call "pi". We invent the names and notations for the mathematics that we discover.

Re:Math cannot exist before wind. (1, Insightful)

Anonymous Coward | more than 4 years ago | (#30152468)

Some say math is discovered. Others say it is invented. You are one of the latter.

Math is a language of symbols used to represent patterns observed in nature. Physics is the discipline of actually discovering such rules, and Physics uses the language of Math to describe those rules.

So "math" is invented because it is a language, but the things that math describes are discovered.

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30152482)

The problem must be invented (i.e. a human construct) before the solution can be discovered (i.e. a natural phenomenon)...

Disambiguation reveals the simple answer (2, Interesting)

Brain-Fu (1274756) | more than 4 years ago | (#30152766)

Those things which we use mathematics to describe (relationships of every variety) are discovered (by observation and experience)

The language with which we describe them (symbols, axioms, and rules of transformation) is invented (and refined over time, as a quick review of the history of mathematics will promptly reveal)

Additional products of this language (logical consequences of the axioms we have invented) are subsequently discovered.

We equivocate the term "Mathematics" to mean all three of these things (that described, the language of description, and logical consequences of the axioms of that language). When the word means all three of these things at once, it seems that we have both discovered and invented it, and lively (though misguided) debate ensues.

When we establish clarity about our topic of discussion (through disambiguation of our terms), then whether it was invented or discovered becomes clear, as I have just demonstrated.

Strange point (2, Interesting)

2.7182 (819680) | more than 4 years ago | (#30151110)

Julius Shaneson and Sylvain Cappell claimed to have solve a famous problem about counting the lattice points in a circle. It's been out for years, even earlier than this arxiv paper:

http://arxiv.org/abs/math/0702613 [arxiv.org]

Thing is, even though it is a famous problem, no one cares enough to check. So this notion of "famous" is shaky.

Re:Strange point (4, Informative)

Feminist-Mom (816033) | more than 4 years ago | (#30151188)

It's even worse than that. The problem of counting lattice points is closely related to the Riemann Hypothesis, the "most" important unsolved math problem. Clearly that is what Shaneson and Cappell are after. I've looked at the paper, and it is only 40 pages (compare with the 200+ of Wiles work), and these guys are respected mathematicians. No one has said it is wrong. I don't know the area, but it shouldn't be as hard to check as the Wiles paper. Maybe people are waiting to see if they announce a proof of the Riemann-Hypothesis.

Re:Strange point (1, Interesting)

Anonymous Coward | more than 4 years ago | (#30151634)

Nobody bothers to check it because it's published on Arxiv. In the math community, Arxiv is basically a very detailed blog. Say anything you want, and some people will read it and maybe be interested. But nobody will really take you seriously. After all, there's tons of flat-out wrong papers on Arxiv and no form of quality control whatsoever.

There are many, many peer-reviewed journals. If this paper is good, it should be published in one of those. The fact that it's not raises doubts about its quality.

Re:Strange point (0)

Anonymous Coward | more than 4 years ago | (#30151778)

Indeed. Arxiv is a pre-print archive. I was about to post about how it's not fair to judge it just because it's in Arxiv when the peer review and publication process can take some time, but then I thought I'd better check the date of the paper, which meant I had to rewrite this post. If it had merit it would have been published by now.

Re:Strange point (1, Insightful)

Anonymous Coward | more than 4 years ago | (#30152094)

The preprint first appeared less than three years ago, and as ridiculous as it may seem, some journals do take that long or more to publish papers. The Annals of Mathematics, for example, can take several years between the decision to accept and the final publication, and since many journals can take a year or more to referee a paper (especially one with as much detailed computation as this one) before that decision is even made it's not impossible to believe that this paper is silently working its way toward publication as we speak.

As for the comment above this, the math community most certainly does *not* view the arXiv as a blog. Most papers are put there before they're submitted to journals, so that they can be freely and quickly accessed, and from respected mathematicians like Cappell and Shaneson it's expected that the papers are worth reading and correct. People do read papers on the arXiv regularly and take them very seriously -- it's the only way to stay up to date in certain fast-moving areas of math -- and if a mistake is found and the authors aren't cranks, they'll either post a new version correcting it or retract the paper completely. Since nothing of the sort has happened with this paper, and nobody has pointed out any mistakes, it's more likely that the paper is correct and just stuck in the middle of a slow editorial process.

Re:Strange point (0)

Anonymous Coward | more than 4 years ago | (#30152376)

But this work was circulating around in the late 90's. They only put it up in 2007. No one has wanted to read it or listen to them for 12 years or so.

Re:Math cannot exist before wind. (3, Interesting)

invisiblerhino (1224028) | more than 4 years ago | (#30151124)

The requirement to model our universe as closely as possible is a requirement of physics, not mathematics. The fact that mathematics, even very abstract mathematics, accurately models the natural world is a deep mystery.

Re:Math cannot exist before wind. (1)

CannonballHead (842625) | more than 4 years ago | (#30151260)

The fact that mathematics, even very abstract mathematics, accurately models the natural world is a deep mystery.

That depends on your worldview.

Re:Math cannot exist before wind. (1)

Tynin (634655) | more than 4 years ago | (#30151368)

Care to elaborate?

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30151860)

I'm not the parent, but here is my take. Mathematics is the study of well-defined objects. Since natural world seems to be relatively well-behaved, it might be expected that objects which can be well-defined accurately model the natural world.

If you are wondering what I mean about well-defined, consider two examples. The integers can be well-defined. The integers that I think about are the same as the integers that you think about. It doesn't seem that right and wrong can be well-defined. I say this because after centuries of trying, we can't get people to agree on exactly what these terms mean.

Re:Math cannot exist before wind. (1)

geekoid (135745) | more than 4 years ago | (#30151520)

It shouldn't be a mystery because we created it to model the world around us.

Re:Math cannot exist before wind. (1)

mario_grgic (515333) | more than 4 years ago | (#30151566)

It's not a deep mystery at all. It's by design. We chose our axioms to resemble what we observe. Just take Euclid axioms of the plane geometry, or natural number axioms (like Peano's), etc.

It's no wonder then that what we construct out of them resembles what is out there (at least somewhat). Other modeling problems try to be even stricter and model the observed phenomena even closer than axioms could ever hope to describe.

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30152668)

It's not a deep mystery at all. It's by design. We chose our axioms to resemble what we observe. Just take Euclid axioms of the plane geometry, or natural number axioms (like Peano's), etc.

It's no wonder then that what we construct out of them resembles what is out there (at least somewhat). Other modeling problems try to be even stricter and model the observed phenomena even closer than axioms could ever hope to describe.

The fact you are so nonchalant about the effectiveness of mathematics in the natural sciences tells me you have a limited understanding of mathematics and the natural world.

Re:Math cannot exist before wind. (1)

Beetle B. (516615) | more than 4 years ago | (#30152744)

We chose our axioms to resemble what we observe.

You don't hang around mathematicians, do you? Go play with a number theorist and you'll realize how wrong you are.

It's certainly true that some mathematicians are motivated by modeling the world. But many, and perhaps most, aren't. They'll freely construct mathematical objects that have little basis in the physical world.

Re:Math cannot exist before wind. (3, Interesting)

Evil Pete (73279) | more than 4 years ago | (#30152184)

YES! This has long been acknowledged [wikipedia.org] by people who we usually assume know a little bit about the physical world. It seems reasonable to me, but demonstrating why it is reasonable is another thing.

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30151204)

You beg the question "does wind necessarily precede intelligence," which it does not.

And yes, I only posted this for the sake of using "beg the question" in a sentence. :(

Re:Math cannot exist before wind. (5, Interesting)

jd (1658) | more than 4 years ago | (#30151610)

I would claim that the ratio of a circle to its diameter is independent of being observed, or indeed there being an observer. I would also claim that the laws of geometry, probability and topology are universal and also do not depend on the existence of observers, let alone their ability to perform maths.

Radioactive decay follows an exponential decay curve. It will have done so long before anyone could add, let alone handle irrational numbers like e.

This puts me firmly in the category of maths being discovered, not invented. Mathematical tools, however, are invented and not discovered. I consider these to be quite different. If you were to imagine an alien lifeform on some distant world, they'll have an identical math but their experience of it, the way they treat it, the systems they use, those will all be unique to them because those are inventions and not anything fundamental to maths itself.

In a simpler example of the same concept, we can use ancient Greek maths today even though they didn't have a concept of zero and had (to modern eyes) very alien views on the way maths worked. We can use ancient Greek maths because the results don't depend on any of that.

We can use Roman results, too, despite the fact that their numbering system doesn't really follow a number base in any way we'd understand. It doesn't matter, though, because the important stuff all takes place below such superficial details. Even more remarkable, we can read many of the numbers written in Linear A, even though we can't read the language itself and know very little about the culture or people.

None of this would be possible if what lay under maths was invented. It's very hard to rediscover lost inventions, as there's many ways of producing similar results. But when you can rediscover lost number systems with comparative ease - well, doesn't that tell you there has to be something a bit more universal to it?

(I won't get into parrots being able to discover the notion of zero, but it's again pertinent as it's an example of a universality that transcends the invented language it's described in.)

Re:Math cannot exist before wind. (4, Interesting)

Obfuscant (592200) | more than 4 years ago | (#30151752)

I would claim that the ratio of a circle to its diameter is independent of being observed, or indeed there being an observer. I would also claim that the laws of geometry, probability and topology are universal and also do not depend on the existence of observers, let alone their ability to perform maths.

Since the existance of a perfect circle depends on the thoughts of an observer, the ratio of the diameter to the circumference of such an object must depend on there being an observer. Nature can produce approximate circles, but not perfect ones.

Radioactive decay follows an exponential decay curve. It will have done so long before anyone could add, let alone handle irrational numbers like e.

"Exponential decay curve" and "irrational numbers" are two different concepts. (1/2)^N is an exponential decay curve -- which defines the half-life of a radioactive substance. For no integer value of N is the result "irrational".

This puts me firmly in the category of maths being discovered, not invented.

Right destination, wrong reason.

Re:Math cannot exist before wind. (1)

PaladinAlpha (645879) | more than 4 years ago | (#30152050)

I would claim that the ratio of a circle to its diameter is independent of being observed, or indeed there being an observer. I would also claim that the laws of geometry, probability and topology are universal and also do not depend on the existence of observers, let alone their ability to perform maths.

Since the existance of a perfect circle depends on the thoughts of an observer, the ratio of the diameter to the circumference of such an object must depend on there being an observer. Nature can produce approximate circles, but not perfect ones.

Radioactive decay follows an exponential decay curve. It will have done so long before anyone could add, let alone handle irrational numbers like e.

"Exponential decay curve" and "irrational numbers" are two different concepts. (1/2)^N is an exponential decay curve -- which defines the half-life of a radioactive substance. For no integer value of N is the result "irrational".

This puts me firmly in the category of maths being discovered, not invented.

Right destination, wrong reason.

The circles Nature creates can be approximate only because the "perfect" circle is constant. No perfect circle = no circle = no approximate circles (what is a circle?). The immutables have existed for all time.

The remark about irrational numbers is irrelevant to the point about exponential decay, but for this reason pi has always been a universal constant. All manner of physical relations involve second, third, and fourth roots, which of course easily gives rise to irrational numbers.

Re:Math cannot exist before wind. (3, Interesting)

Evil Pete (73279) | more than 4 years ago | (#30152400)

Ideal circles do not exist. Before human beings they didn't exist, and they still do not exist. We define them. Can you think of a perfect circle? If you can you must have perfect visual processing in your brain. This is a hard problem I admit, and I'm not going to pretend my answer is absolutely correct. However, mathematics proceeds from axioms, which are fundamental assumptions ... sometimes based on physical intuitions, but sometimes not.

I think mathematics is so effective because in the realm of physics our discoveries have few degrees of freedom and can therefore be represented by simple rules. Since the rules must be consistent we have the basis for physics and a tie in to mathematics.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? — Albert Einstein

There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology. — Alexandre Borovik

Quotes shamelessly stolen from here [wikipedia.org] .

Re:Math cannot exist before wind. (1)

Obfuscant (592200) | more than 4 years ago | (#30152568)

No perfect circle = no circle = no approximate circles (what is a circle?).

Au contraire, mon frere. Nature can produce approximate circles and does so quite happily. The cross section through a bubble is a very good approximation to a perfect circle, and most people not into arguing philosophy would simply CALL it a circle. This is all without knowing the definition of circle that mathematicians have come up with. Nature, however, does not care what pi is.

The remark about irrational numbers is irrelevant to the point about exponential decay,

The OP decided there must be come relevance, else he would not have included it in a paragraph talking about radioactive decay. I was the one pointing out the irrelevance. One need not know anything about 'e' to know exponential decay. The fact that 'e' came along relatively recently doesn't say anything about the origin of math.

...but for this reason pi has always been a universal constant.

I am unclear what antecedant to "this" you are using. What reason? And IS pi a "universal constant? It is only in flat space (like ours appears to be) that the ratio of circumference to diameter in a circle involves pi. In curved space, (the surface of a sphere, e.g.), the ratio will be different. Does the universe consist only of flat space? We are far enough from our sun that the effects are minimal but non-zero. Would living in a region of space in the region of an object more massive than the earth yeild beings who think the circumference of a circle is 3*diameter, and that this "3" is a universal constant? Or would they say "3 if facing east, 4 if facing north?"

Re:Math cannot exist before wind. (1)

Sosetta (702368) | more than 4 years ago | (#30153068)

Exponential decay uses e most of the time, because the derivatives and integrals are a lot less messy. e is irrational. What makes you think you're using 2? And what makes you think that the decay only has values for integer time? What's 1/3 of the way between (1/2)^3 and (1/2)^4? An irrational number.

Re:Math cannot exist before wind. (1)

Beetle B. (516615) | more than 4 years ago | (#30152782)

I would claim that the ratio of a circle to its diameter is independent of being observed, or indeed there being an observer.

What's a circle? What's a diameter? What's a ratio? Who defines these?

And while we're at it, you do realize that the universe is non-Euclidean? So how do we view the results from Euclidean geometry, given that reality is not Euclidean?

Radioactive decay follows an exponential decay curve. It will have done so long before anyone could add, let alone handle irrational numbers like e.

That some mathematics models the real world does not mean most of mathematics is not invented. It need not be a binary scenario. What would you say of mathematical constructs that have no analogs in nature (but that could be depicted if desired)?

Your arguments are along the lines of "The bicycle was not invented, because the laws of the universe would always have allowed a bicycle to work and exist."

Re:Math cannot exist before wind. (1)

TheVelvetFlamebait (986083) | more than 4 years ago | (#30152122)

Actually, mathematics is considerably more than a model for our universe. We can (and do) study mathematical objects which have no immediate instances in the universe.

Re:Math cannot exist before wind. (1)

blackraven14250 (902843) | more than 4 years ago | (#30152324)

Do you have any proof these constructs don't exist?

Yes. (1)

gbutler69 (910166) | more than 4 years ago | (#30152500)

There exist no empty sets in the Universe! We can construct all of Mathematics beginning only with the Empty set. So, all of mathematics can be constructed from something that does not exist in the real world. Hmm? Makes you think.

Re:Math cannot exist before wind. (1)

Beetle B. (516615) | more than 4 years ago | (#30152790)

Do you have any proof these constructs don't exist?

Can you prove that there aren't unicorn like creatures in one of the craters of the moon?

Your point?

Re:Math cannot exist before wind. (1)

TheVelvetFlamebait (986083) | more than 4 years ago | (#30153074)

Do you have any proof these constructs don't exist?

I have absolutely no idea. Evidence suggests no, but I have no proof of my ability one way or the other.

/being intentionally dense

Notice that I said "no immediate instances", that is, the mathematics was created before any instances were discovered, if they were discovered at all.

Re:Math cannot exist before wind. (1)

Evil Pete (73279) | more than 4 years ago | (#30152132)

Hypothetical?

Mathematics is a collection of logically consistent statements about abstractions such as structure and number. "Hypothetical" implies it needs to be tested, a mathematical proof does not need a 'test'.

Re:Math cannot exist before wind. (1)

Sosetta (702368) | more than 4 years ago | (#30153048)

That's just the notation. Math is abstract concepts. Abstract concepts existed before the wind. They're abstract.

Re:Math cannot exist before wind. (0)

Anonymous Coward | more than 4 years ago | (#30153054)

The universe is nothing more than an imperfect approximation to our mathematical models

Solve this (0)

Anonymous Coward | more than 4 years ago | (#30151046)

Why is it that after taking some, the day after I always get a splitting headache?

Oh wait, math mysteries.

Re:Solve this (1)

dazjorz (1312303) | more than 4 years ago | (#30151352)

Don't worry, that works for math too, in a metaphorical way of "taking some" and for "the day after" you read "until the day after" ;-)

Re:Solve this (0)

Anonymous Coward | more than 4 years ago | (#30152110)

Easy. That was methanol, not methamphetamine. Be glad you still can see. Next!

Check out the Collatz Conjecture... (5, Interesting)

Oxford_Comma_Lover (1679530) | more than 4 years ago | (#30151054)

http://en.wikipedia.org/wiki/Collatz_conjecture [wikipedia.org] Speaking of unsolved math mysteries, the 3n+1 problem is a fabulous way to spend days and days of your life. It's particularly fun if you think about it in binary. Whatever the answer is, it's either simple and elegant or complex beyond imagination.

Re:Check out the Collatz Conjecture... (2, Funny)

ae1294 (1547521) | more than 4 years ago | (#30151480)

WHOA... Gotta love that little meme..

If the starting value n = 27 is chosen, the sequence, listed and graphed below, takes 111 steps, climbing to over 9,000 before descending to 1.

        { 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1 }

Re:Check out the Collatz Conjecture... (1)

mister_playboy (1474163) | more than 4 years ago | (#30151748)

I noticed that too... LOL.

That conjecture is interesting and simple enough to be understandable without being a math person. I looked at the wiki article for the above mentioned Riemann Hypothesis, and that's a bit too complex for me.

Re:Check out the Collatz Conjecture... (1)

ae1294 (1547521) | more than 4 years ago | (#30151842)

That conjecture is interesting and simple enough to be understandable without being a math person. I looked at the wiki article for the above mentioned Riemann Hypothesis, and that's a bit too complex for me.

Yeah same here, not really a math person but you gotta love how simple it would be to write a program to play around with it. Who knows, if you picked the right starting number you might even prove it wrong! but I'm not really sure how one would ever be able to prove it right!

Re:Check out the Collatz Conjecture... (1)

Tynin (634655) | more than 4 years ago | (#30151600)

Wish I hadn't posted in this discussion, I'd love to toss you an interesting mod. This will no doubt steal hours of my life, thanks :-)

Re:Check out the Collatz Conjecture... (1)

hazem (472289) | more than 4 years ago | (#30153028)

If you like life-stealers like that, you might want to check out Project Euler: http://projecteuler.net/ [projecteuler.net]

But don't say I didn't warn you!

Re:Check out the Collatz Conjecture... (1)

Shikaku (1129753) | more than 4 years ago | (#30151760)

This is something Ruby is DESIGNED for.

http://pastebin.com/m25fc9de4 [pastebin.com]

I popped this out in a few minutes, but if it can be modified to save every valid Collatz number it finds and not recalculate anything at all it can go pretty fast for very little code and eat all your RAM in the process :)

Re:Check out the Collatz Conjecture... (1)

Shikaku (1129753) | more than 4 years ago | (#30151840)

Oh, I should mention that I mash very large random numbers into this ruby script and it doesn't overflow. Instead it gets a stack error...

So small update, nonrecursive edition:

http://pastebin.com/m29c38ed3 [pastebin.com]

It worked fine for a 40+ digit whole number pasted about 20 times...

Re:Check out the Collatz Conjecture... (1)

SanguineV (1197225) | more than 4 years ago | (#30152212)

A python version that returns the cycle length is available here [pastebin.com] . Of course it can be optimised by storing known concluding cycles and terminating immediately if you hit one. But the code works for stupidly large numbers without any issues (can't paste example as the filter complains)

Re:Check out the Collatz Conjecture... (2, Informative)

Undead NDR (1252916) | more than 4 years ago | (#30152064)

"Very little code"? Bah! Kids these days...

This [pastebin.com] will run on any system where `dc` is installed.

Re:Check out the Collatz Conjecture... (3, Interesting)

ACS Solver (1068112) | more than 4 years ago | (#30151950)

I have fond memories of that one. On the subject of teaching and education...

One of my math teachers once showed me the problem. The teacher knew I'm decent at math and would occasionally show me interesting or unusual problems. The interesting part is, the teacher told me to have a try at proving the proposition of this problem, without telling me that it's an unsolved problem. So I had a good amount of fun trying to prove this. Of course, it's not like I could make a proof with my high school knowledge, but it challenged my mind and was a fun thing to do. And had the teacher told me right away that it's an unsolved problem, I wouldn't have had the motivation to think about it, knowing beforehand that I wouldn't be able to find a proof.

That was one of my educational highlights, though. Way to provide a mental challenge!

I'm still amazed by how part of the problem's beauty is that it's easy to understand the actual proposition. That isn't true for most unsolved problems, after all. Take the recently proven Poincaré conjecture, just understanding what it states takes some math knowledge, though it has a nice approximation in layman's terms. As for the example of the Hodge conjecture [wikipedia.org] , I probably don't know half the mathematical concepts required to understand the problem.

Re:Check out the Collatz Conjecture... (1)

TheVelvetFlamebait (986083) | more than 4 years ago | (#30152152)

Whatever the answer is, it's either simple and elegant or complex beyond imagination.

Actually, if you believe this guy [arxiv.org] , it's not only complex beyond imagination, it's complex beyond any possible finite representation, that is, it's unprovable.

Re:Check out the Collatz Conjecture... (1, Informative)

Anonymous Coward | more than 4 years ago | (#30152418)

CAF is a notorious usenet troll. You can safely ignore anything he writes. (Also note: arxiv is not peer reviewed.)

Re:Check out the Collatz Conjecture... (0)

Anonymous Coward | more than 4 years ago | (#30152956)

Anyone can say a number that dont work for 3n+3? (ending with 3, not 1)

Why 3n? (1)

snowwrestler (896305) | more than 4 years ago | (#30153040)

Why is the alternative to halving, 3n+1? Why 3? I'm curious. If it were just n+1 it seems like it would converge to 1 pretty quickly (since most non-even numbers become even if you add 1).

10 gives you:
10 5 6 3 4 2 1

100 gives you:
100 50 25 26 13 14 7 8 4 2 1

What if it were 4n+1? Then 10 gives you:
10 5 21 85 341 1365 5461 21845 uh oh

What if it were 5n+1? Then 10 gives you:
10 5 26 13 76 38 19 96 48 24 12 6 3 16 8 4 2 1

I have this proof. (5, Funny)

140Mandak262Jamuna (970587) | more than 4 years ago | (#30151080)

I have this wonderful proof for this conjecture, but unfortunately the 80 char limit for sig in slashdot is too small for it.

Re:I have this proof. (3, Funny)

JustOK (667959) | more than 4 years ago | (#30151212)

try twitter, it goes up to and includes 140 chars

Re:I have this proof. (0)

Anonymous Coward | more than 4 years ago | (#30151382)

HA! I was just thinking that.

Hey wait... HOW DARE YOU STEAL MY COMMENT! I had a scathing reply to your post all thought up, but unfortunately the 80 char limit for sig in slashdot is too small for it.

Re:I have this proof. (1)

selven (1556643) | more than 4 years ago | (#30151766)

Use a real website, char limits are stu

Re:I have this proof. (1, Interesting)

Anonymous Coward | more than 4 years ago | (#30152162)

I proved that there are infinite primes in a twitter comment for a friend doing her homework:

Assume some set of primes is all of them. Multiply them all. Add 1. None of primes go into new #; its factors are additional primes

Re:I have this proof. (1)

Evil Pete (73279) | more than 4 years ago | (#30152200)

But the attention span doesn't change.

Re:I have this proof. (2, Funny)

interkin3tic (1469267) | more than 4 years ago | (#30151468)

I have this wonderful proof for this conjecture, but unfortunately the 80 char limit for sig in slashdot is too small for it.

And thus was born the famous "140Mandak262Jamuna's Last Theorem" which was not fully proven until 2367 AD.

Re:I have this proof. (0)

Anonymous Coward | more than 4 years ago | (#30152850)

god dammit fermat, just give us a hint!

Nice Move (0)

Anonymous Coward | more than 4 years ago | (#30151138)

So they finally discovered the Merits Of The Bug Tracker.

But i hope they don't switch to math 2.0 anytime soon, that'll just introduce a bunch of regressions and won't do anyone any good. They've already spent some thousands of years just to get their project management straight, it's about time they delivered.

The Millennium Prize Problems (1)

lazy_nihilist (1220868) | more than 4 years ago | (#30151144)

They can probably add the remaining unsolved millennium prize problems [wikipedia.org] to the list.

1 + 1 = 3 (0)

Anonymous Coward | more than 4 years ago | (#30151154)

For very large values of 1

Re:1 + 1 = 3 (2, Funny)

JustOK (667959) | more than 4 years ago | (#30151240)

or small values of 3

Sadly... (5, Funny)

cosm (1072588) | more than 4 years ago | (#30151162)

their servers will explode when they take a stab at Navier-Stokes [wikipedia.org] . I asked Wolfram-Alpha, but it simply returned the exact solution of a degenerate case, the solution being 'Fuck you.'

Re:Sadly... (2)

TapeCutter (624760) | more than 4 years ago | (#30151378)

You need one of these [wikipedia.org] to get a good aproximation.

Re:Sadly... (3, Funny)

DoninIN (115418) | more than 4 years ago | (#30151442)

Can you imagine a Beowulf cluster of these?

Re:Sadly... (0)

Anonymous Coward | more than 4 years ago | (#30152218)

But does it run Linux?

If you really want to run into trouble (4, Informative)

JoshuaZ (1134087) | more than 4 years ago | (#30151218)

See http://rjlipton.wordpress.com/2009/11/12/more-on-mathematical-diseases/ [wordpress.com] for unsolved problems which are all really simple and also really addicting to think about. For many of these, the best way to stop thinking about one of them is to start thinking about another.

I'm actually a bit puzzled as to why this is a Slashdot article. If I wanted to point to something new in the way people are doing math I'd point to Math Overflow http://mathoverflow.net/ [mathoverflow.net] where many professional mathematicians, grad students and others are active. It is essentially a centralized system for people to post math questions and get math answers from people who know. It is very cool. It also is highly addictive to read.

Re:If you really want to run into trouble (-1, Redundant)

tonycheese (921278) | more than 4 years ago | (#30151404)

The site you gave seems to be like a WikiAnswers for math problems. The site this article is talking about is more of a collaboration tool on unsolved problems that will allow any and all known progress be open to be expanded upon.

The issue I see with this is how do you dish out credit for something like this? If 20 different people solve varying amounts of a problem and then one last person pieces everything together, who solved the problem? Or will we move away from "Smith's Proof" into "Proof of May 2009" by a list of 90 people? I always thought that part of the fun of solving impossible math problems was to take the glory at the end of the day... but, then again, I'm not a mathematician.

Massively collaborative "Polymath" efforts (5, Interesting)

Anonymous Coward | more than 4 years ago | (#30151306)

As of about a year ago, a new kind of collaborative math project known as "polymath" is emerging. These research projects are completely open for any interested scholar to drop in and make contributions to the problem at hand. The technical infrastructure is based on well-known tools such as wikis and forum discussions

The very first such project successfully explored a new approach to the density Hales-Jewett thorem--a significant problem in combinatorics--in about six weeks of effort, with a fully preserved record of about a thousand contributions from dozens of participants.

See Polymath Wiki [michaelnielsen.org] for the details. This new contribution from the AIM will provide a focus point for such efforts and encourage similar massively collaborative projects.

And of course, the emerging field of computer-verified mathematics [vdash.org] is also dependent on massive collaboration, in order to translate existing results into a fully-formalized form that computes will understand and verify as correct. A wiki-based project could be a great help there as well.

why not hide them in video games so we can (4, Funny)

Joe The Dragon (967727) | more than 4 years ago | (#30151690)

why not hide them in video games so we can get more people to look at them.

Re:why not hide them in video games so we can (1)

robinesque (977170) | more than 4 years ago | (#30152474)

Higher math crowd-sourcing. I like this idea.

Re:why not hide them in video games so we can (0)

Anonymous Coward | more than 4 years ago | (#30152618)

Because this isn't Stargate: University

Encyclopedia of Integer Sequences (2, Interesting)

Rockoon (1252108) | more than 4 years ago | (#30151702)

Only (very) loosely related but deserving mention is the Encyclopedia of Integer Sequences. [att.com]

This encyclopedia has proven very useful for me in that I have avoided 'solving' many problems with it.

These problems are easily solved... (1)

jkiller (1030766) | more than 4 years ago | (#30152026)

maybe (AIM) should ask Smarterchild for the answers.

Meh. (3, Insightful)

jd (1658) | more than 4 years ago | (#30152154)

Mathematically modelling the brain would seem to be a very trivial problem. The problem is that there's a lot of brain to model. I've posted (admittedly non-rigorous) mathematical models of the brain on Slashdot before, but narry a grant check from it. Bah.

Computational fluid dynamics for foams, liquid crystals, et al, isn't any harder than for anything else. The equations are chaotic by nature, but chaotic systems can be well-behaved on aggregate under certain conditions. CFD as generally done relies on some specifically hand-picked special case or cases being universally true. They never are, which is why most CFD differs from how systems actually behave in practice.

If you were to treat CFD as a problem in chaos theory, rather than as isolated collections of imperfect examples of special cases, there would be no problem. It is always when engineers try to take shortcuts and oversimplify the maths to make it easy on themselves that they run into problems. They should be locked up for their own safety. If you want to really annoy them, lock them up with some airgel foam.

The problem with chaotic systems is that the system is sensitive to initial conditions, which means the only way to get "correct" results is to use infinite precision and zero step sizes. This isn't useful, but is a good way to annoy experts in CFD.

This leaves two options - use very very big, very very fast computers (the option used by F1 teams), or find an equivalent problem you CAN solve (the idea behind transforms).

Ok, does chaos look like a good place to use transforms? If you could identify and classify the Strange Attractors in the system, can you do anything useful? Probably not, at least not in the "solving the problem" sense. Chaos is fully deterministic, but it is utterly unpredictable. The only solution is the whole solution.

What knowing the Strange Attractors might tell you is how to vary the precision and step-size to get the best results for a given level of compute power. But it's going to be all raw horsepower from thereon out.

The best way to invest money on such work is to design a co-processor that performs a handful of fairly high-level maths functions directly (optimized purely for speed, not physical or logical space) so that you can do Navier-Stokes almost at the level of raw hardware rather than through clunky software. Then cluster the living daylights out of the co-processor.

It's necessary to optimize commodity hardware for space, because chip real-estate is expensive. However, if you're building what is basically a SOP (single-operation processor) for a dedicated market that can afford things like Earth Simulator, the only time you care about space is when it impacts speed.

Ideally, if the speed of light wasn't an issue, you'd want each bit in the output to be produced by wholly independent logic, duplicating the input bits as necessary to accomplish this. In practice, you'd probably want to start with that conceptually but in reality have something that was somewhere between that and a highly compressed form. Too parallel and the delays in communication exceed the benefits from the parallelization.

But this is all obvious. Anyone here who has done multi-threading or any other form of parallelization knows about synchronization issues and communication overheads. It's even one of the biggest chunks of any course on the subject of parallel design. There's nothing new there, certainly nothing "unsolved".

But, yeah, a well-designed Navier-Stokes co-processor would likely give you greater accuracy and greater performance than the modern pure software solutions. Especially those using ugly protocols to do the communications.

If Intel can conceptulalize 80 Pentium 4 cores on a wafer, it would seem reasonable enough to imagine modern fabrication methods being able to put at least a couple of hundred dedicated Navier-Stokes processors into the same space. Since the input for an iteration would be based on output from that and other processors, there's no need for cache, just on-board generic high-speed memory and some communication lines (ala the Transputer). With the savings there, you might even squeeze in a few more cores.

If people are willing to spend gigantic sums of money on 100,000,000 core computers to do CFD work, I can see no serious problem with them spending what is surely only a few percent more at that scale on building a dedicated SOP cluster that's tens of thousands of times faster and infinitely easier to extend.

sp-called experts steal work (1)

gr8_phk (621180) | more than 4 years ago | (#30152224)

The problem list provides a snapshot of the current state of research in a particular research area, letting experts track new developments

So when a promising idea comes along, the "expert" can follow up and hopefully get credit for the solution. I see this is the workplace and on the net in various places. Technical discussion forums are lurked by "experts" in industry who look for ideas without contributing anything to the discussion. Some people don't mind, others don't realize, and others are bothered by it.

Re:sp-called experts steal work (0)

Anonymous Coward | more than 4 years ago | (#30152852)

ideas are a dime a dozen

you have ideas. why aren't you rich?

Hilbert problems (2, Interesting)

aws4y (648874) | more than 4 years ago | (#30152408)

I am pretty sure that some of the problems at least will be Hilbert Problems that do not currently have a solution. http://en.wikipedia.org/wiki/Hilbert_problems [wikipedia.org]

This is a great idea. (2, Insightful)

Phantasmagoria (1595) | more than 4 years ago | (#30152462)

This is a great idea. It whould promote more interest in the specific problems and unsolved math problems in general. Besides, more collaboration should result in better research.

Christmas gifts,look,nike air max jordan shoes, (-1, Offtopic)

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HHGTTG (0)

Anonymous Coward | more than 4 years ago | (#30152882)

42

can we get the good will hunting guy to work on th (0)

Joe The Dragon (967727) | more than 4 years ago | (#30152932)

can we get the good will hunting guy to work on them or rainman. may even Kazan?

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