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Mathematician Solves a Big One After 140 Years

kdawson posted more than 6 years ago | from the works-with-holes dept.

Math 144

TaeKwonDood notes that ScientificBlogging.com has just written about a development in applied math that was published last year. "The Schwarz-Christoffel transformation is an elegant application of conformal mapping to make complex problems faster to solve. But it didn't do well with irregular geometries or holes, so it simplified too much for a lot of modern-day mechanical engineering applications. 140 years after Schwarz and Christoffel's work, a professor at Imperial College London has generalized the equation. MatLab users rejoice!"

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wow (5, Funny)

Anonymous Coward | more than 6 years ago | (#22631348)

That guy must be pretty old

Re:wow (3, Funny)

nwf (25607) | more than 6 years ago | (#22631444)

But can you prove it? There's got to be a limit somewhere here...

I solved a big one this morning too (3, Funny)

BadAnalogyGuy (945258) | more than 6 years ago | (#22631548)

I give credit to all the bran I've been eating lately.

Re:I solved a big one this morning too (4, Funny)

sakusha (441986) | more than 6 years ago | (#22632092)

You could have worked it out with a pencil.

Re:I solved a big one this morning too (1)

Simon Brooke (45012) | more than 6 years ago | (#22633388)

You could have worked it out with a pencil.

A real mathematician would have worked it out with logs (an engineer would have worked it out with a slide rule).

Yes, the old ones are the best.

Re:I solved a big one this morning too (1)

aproposofwhat (1019098) | more than 6 years ago | (#22633530)

An a physicist would have worked it out to the first approximation - hence the skid marks.

Re:I solved a big one this morning too (1)

Brian Gordon (987471) | more than 6 years ago | (#22634690)

Anyone want to spend $20 for the journal article so we can all take a gander at the actual formula? Hey, tenured university profs have to make their money somehow, right? Right?

Re:I solved a big one this morning too (2, Funny)

WgT2 (591074) | more than 6 years ago | (#22633980)

Is there no limit to potty-humor?

Why must it be integrated into our lives so often?

Re:I solved a big one this morning too (1)

Bloodoflethe (1058166) | more than 6 years ago | (#22634950)

For a second there I thought you said "brains." I was afraid this would become another zombie thread. I guess it's going to the down the toilet instead.

Re:I solved a big one this morning too (0)

Anonymous Coward | more than 6 years ago | (#22635228)

Brains! Brains! Poo-, er, BRAINS!

Re:wow (0)

Anonymous Coward | more than 6 years ago | (#22633708)

Gee... I wonder if he's BLACK.

Say it ain't so! He ISN'T? You're kidding me!

And I thought "We're all the same" and that black people weren't functionally useless idiots who are busy ruining every white country they've invaded...

Math Forfront (4, Insightful)

Bananatree3 (872975) | more than 6 years ago | (#22631374)

It always amazes me how applicable math becomes hundreds of years after it's written. Think if Maxwell's equations, Newton's equations, Einstein's equations. Fluid Dynamics equations were probably pioneered well before they were applied to human machines. Modern-day aircraft would not operate without their understanding. Where the math goes, human technology will probably soon follow.

Re:Math Forfront (2, Insightful)

siride (974284) | more than 6 years ago | (#22631388)

I think they would operate. The universe doesn't need to know the math. It Just Works (TM).

Design (2, Funny)

Bananatree3 (872975) | more than 6 years ago | (#22631470)

of course pilots don't need to know the math behind why their plane works. I sure hope the designers of the planes knew their math! Without them the planes wouldn't work.

Re:Design (1, Funny)

Anonymous Coward | more than 6 years ago | (#22631590)

If the designers don't know the math, It Just Crashes (TM).

Re:Design (4, Insightful)

ceoyoyo (59147) | more than 6 years ago | (#22631890)

Designers designed planes long before they could work out the math. They experimented a lot. The math lets you make things faster, cheaper and gives you ideas for new designs. I wouldn't fly in anything based solely on the math though.

Re:Design (4, Insightful)

Bananatree3 (872975) | more than 6 years ago | (#22631986)

I agree. The Wright Brothers knew only some basic math and mostly built their airplane through ingenious yet fairly simple experimentation.

That's why I emphasized modern-day aircraft. Designing a 777 or the new 7E7 off pure experimentation would take insanely more amounts of time and money. Math makes it a LOT easier, and its probable all turbine-driven commercial craft wouldn't exist at their current efficiencies without math being in the design process. Laugh all you want about their gas-guzzling reputations, but it would be interesting to see someone design such a sophisticated aircraft without advanced math.

Re:Design (4, Interesting)

ceoyoyo (59147) | more than 6 years ago | (#22632284)

It makes it cheaper, but you can certainly have sophisticated turbine aircraft without the math. We've only had the computers to make a respectable stab at simulating airflow over a reasonably complex wing recently. It's great as a design aid, and invaluable as a tool for understanding, in the abstract, but the real world is often too complex for our computational capabilities. Surprises crop up all the time. The A380 wing for example. Its probably the modernest and advancedest turbine-driven commercial aircraft wing (at the moment). The wing in practice isn't as efficient as it was supposed to be. It also failed its strength certification the first time around.

In most engineering applications the math is a nice tool to let designers do a bunch of experimenting inside the computer before they have to move on to real world testing. We're not at the point yet where math is more important than experience and experiment. Not just aircraft design. I work in medical imaging and there are no shortage of ideas where the (idealized) math works great, the simulations are wonderful, but the idea doesn't survive first contact with patient data.

Re:Design (0)

Anonymous Coward | more than 6 years ago | (#22633732)

Actually, in the industry, it's widely acknowledged that Boeing has superior wing technology to Airbus. Just because the A380 has the biggest and newest wing doesn't make it the best wing; the 787 wing is, in a lot of ways, much more innovative and sophisticated. Japan became a major backer of the 787 almost solely because Boeing allowed Japanese companies to replicate its wing technology.

But does the patient survive (1)

crovira (10242) | more than 6 years ago | (#22634212)

first contact with the medical engineering?

You couldn't have tomography without computer assistance, true, but you have lots of people going around with radiation burns from improperly calibrated X-ray equipment.

Re:But does the patient survive (1)

ceoyoyo (59147) | more than 6 years ago | (#22636034)

Thus the extensive testing. We still can't accurately calculate the absorbed radiation dose for a patient, only approximations, so guidelines are based on some simulations but also a lot of experiment. Plus a hefty safety factor. Accidents are actually remarkably rare, because of the testing required, but when they do happen they can be pretty horrific.

Re:Design (3, Informative)

Zed is not Zee (996730) | more than 6 years ago | (#22634280)

I am a designer for a large gas turbine engine manufacturer, and I have to agree that there is still a lot that we just don't understand well enough or can't model adequately. Combustion noise, liquid atomization, fatigue/creep interaction, etc. We do all kinds of FEA and CFD analysis, but still spend tens of millions of dollars on testing to back up those simulations.

Re:Design (2, Insightful)

Bloodoflethe (1058166) | more than 6 years ago | (#22635038)

It makes it cheaper, but you can certainly have sophisticated turbine aircraft without the math.
Your opening argument has no supporting statement whatsoever. You don't refer to a single instance of making sophisticated aircraft without math in this whole post. When you make a radical statement such as that, you really should back yourself up with a source. But, then again, this *is* slashdot

Re:Design (3, Informative)

ceoyoyo (59147) | more than 6 years ago | (#22636658)

Well, the 757 was designed in 1983. Certain versions of it have a reputation for being very fuel efficient. The U2 and SR-71 were designed and built in the 40s and 50s, and the SR-71 is still the fastest aircraft to take off under its own power. The H-4 Hercules was designed and built in the 40s and has the largest wingspan and height of any aircraft in history. The 747, one of the most successful commercial aircraft, was designed during the 60s.

So it depends what you mean by "math." The Wright brothers undoubtedly needed to add and subtract measurements to build their plane. That's math. Those designers in the 50s and 60s used pencils, slide rules and tables to work out some equations to help guide them (there was some talk of using the new electronic computers, but aircraft designers weren't overly enamored of them). The big aircraft manufacturers started developing 2D computational fluid dynamics software in the 70s, and two major packages were developed in the 80s.

So what about today? Well, you won't find a test pilot who's willing to fly a new design that hasn't been tested in a wind tunnel. There's no way I would fly on an aircraft that hadn't been tested in real flight, unless I was being paid (and trained) as a test pilot. Aircraft companies spend billions on wind tunnels. It seems even today the math is awfully useful but it's no substitute for putting an aircraft in an airstream and seeing what happens.

Sources:
http://en.wikipedia.org/wiki/Computational_fluid_dynamics [wikipedia.org]
Cosner, RR and Roetman, EL, "Application of Computational Fluid Dynamics to Air Vehicle Design and Analysis", IEEE Aerospace Proceedings, 2: 129-42 (2000).

Math and grammar in Re:Design (0)

Anonymous Coward | more than 6 years ago | (#22635132)

Its probably the modernest and advancedest turbine-driven commercial aircraft wing (at the moment).
Indeed, it's not only math that hases applicationses in design. Clearly aircraft design requires itses ownses grammarses.

Re:Design (4, Funny)

h4rm0ny (722443) | more than 6 years ago | (#22632950)


Designing a 777 or the new 7E7 off pure experimentation would take insanely more amounts of time and money.

Not to mention pilots.

Re:Design (1)

Ngarrang (1023425) | more than 6 years ago | (#22635402)

Designers designed planes long before they could work out the math. They experimented a lot. The math lets you make things faster, cheaper and gives you ideas for new designs. I wouldn't fly in anything based solely on the math though.
Fancy math is what keeps the F-117A from falling out of the sky.

Re:Design (0)

Anonymous Coward | more than 6 years ago | (#22635542)

It's a pretty good idea not to fly in anything solely on math. From the wiki on fluid dynamics:

Most flows of interest have Reynolds numbers too high for DNS to be a viable option (see: Pope), given the state of computational power for the next few decades. Any flight vehicle large enough to carry a human (L > 3 m), moving faster than 72 km/h (20 m/s) is well beyond the limit of DNS simulation (Re = 4 million). Transport aircraft wings (such as on an Airbus A300 or Boeing 747) have Reynolds numbers of 40 million (based on the wing chord). In order to solve these real life flow problems, turbulence models will be a necessity for the foreseeable future.

By the way DNS stands for Direct Numerical Simulation. Wind tunnels and dimensionless numbers will be needed to model aerodynamics for a long time.

 

Re:Math Forfront (1)

Secret Rabbit (914973) | more than 6 years ago | (#22631920)

Sure the forces, etc, that enable such things to work would be there. But, that means nothing when it comes to us building something that takes advantage of such forces, etc. For that to happen, it takes math and science i.e. understanding.

Re:Math Forfront (1)

kalirion (728907) | more than 6 years ago | (#22636292)

Kind of like an operating system doesn't need to know the machine language?

Re:Math Forfront (5, Interesting)

HungSoLow (809760) | more than 6 years ago | (#22631394)

There is a saying that goes something like "for every new discovery in math, a new field of science begins".

Re:Math Forfront (2, Insightful)

ceoyoyo (59147) | more than 6 years ago | (#22632058)

A saying in math.

Reality is more like, for every discovery in science, a mathematician developed the relevant math in the abstract a hundred years earlier.

Not as catchy, I know.

Re:Math Forfront (1)

sconeu (64226) | more than 6 years ago | (#22632396)

Semi related: a sig seen on /.:

"An interesting anagram of "BANACH TARSKI" is "BANACH TARSKI BANACH TARSKI".

Apparently, the B-T theorems can be used to describe quark behavior.

Re:Math Forfront (1)

ceoyoyo (59147) | more than 6 years ago | (#22635976)

There are hints that the non-trivial zeros of the zeta function, besides being related to the distribution of the prime numbers, also form an operator that describes a particular quantum mechanical system. You wouldn't say that the zeta function created quantum mechanics, but it might come in handy at some point in the development of QM.

Re:Math Forfront (2, Interesting)

nwf (25607) | more than 6 years ago | (#22631402)

I think that rather than math becoming applicable, it actually enables discovery and enables people to think about problems. Without many seemingly uselessly arcane topics, we'd be back in the 1900s. Calculus comes to mind. Heck, physics these days seems to be nothing more than experimental mathematics with string theory and the like.

Re:Math Forfront (4, Insightful)

644bd346996 (1012333) | more than 6 years ago | (#22631544)

Calculus is one of those things that was created more or less with a real-world application in mind (ie. physics). A better example would be how abstract algebra (in specific, group theory) has recently found application in quantum mechanics. Both fields have been around for quite a while, but they only recently connected.

Re:Math Forfront (1)

colfer (619105) | more than 6 years ago | (#22631592)

Coding theory, crypto, general relativity... there are tons of examples where the math(s) anticipated the physics by decades or more. But solid applications keep math healthy too.

We used to have this saying in the pure math dept.: hey does this have any applications? Yes, it has applications to number theory!

Re:Math Forfront (1)

colfer (619105) | more than 6 years ago | (#22631612)

Cool thing about math for g.r. is the most bizarre dimension is 4, by a long shot.

Re:Math Forfront (1)

nwf (25607) | more than 6 years ago | (#22631632)

Calculus also birthed differential equations, which are used all through engineering, and even the Fourier transform, without which we wouldn't have cell phones or MP3s. But, abstract algebra is a good example, but I haven't used it much since college. And number theory is the basis of modern cryptology.

Re:Math Forfront (1)

The One and Only (691315) | more than 6 years ago | (#22633250)

Calculus is one of those things that was created more or less with a real-world application in mind (ie. physics).

That was certainly Newton's intention. Leibniz had other goals in mind.

Re:Math Forfront (1)

hawkfish (8978) | more than 6 years ago | (#22635174)

Considering the Greek attitude towards practical applications of mathematics, I sort of doubt Archimedes invented integral calculus with physics in mind.

Re:Math Forfront (1)

colfer (619105) | more than 6 years ago | (#22631546)

...and really really big frocking machines.

Re:Math Forfront (4, Insightful)

zippthorne (748122) | more than 6 years ago | (#22631562)

Except, Calculus, specifically, was invented by the same guy who used it to basically describe classical physics. And he also proved all of his theorems using geometry, since the new-fangled calculus might not be acceptable for proofs just yet, having only just been invented, by him.

The point is, how can you separate the invention of calculus from his work in classical physics? They were obviously developed hand-in-hand.

Re:Math Forfront (3, Informative)

bjorniac (836863) | more than 6 years ago | (#22631652)

Really? Leibniz invented physics?

OK, I know what you're saying, but really, Newton takes too much credit here. In his early work he even credited Leibniz then in a later edition of his work removed the statement.

Re:Math Forfront (2, Insightful)

moderatorrater (1095745) | more than 6 years ago | (#22631824)

It's a good thing this argument is still going on since they both discovered/invented calculus pretty much independently, perhaps with some borrowing between the two. Newton started before Leibniz, Leibniz did a better job making it useful, and Newton definitely did more with it. The both invented it, end of story. Seriously, this is over two centuries old, let it die.

Re:Math Forfront (1)

KevinKnSC (744603) | more than 6 years ago | (#22631940)

I agree. Now, with that out of the way, let's get back to the Cardano-Tartaglia debate. That's where the real action is.

Re:Math Forfront (1)

blahplusplus (757119) | more than 6 years ago | (#22631614)

"It always amazes me how applicable math becomes hundreds of years after it's written."

All mathematics is descriptions of geometry, hence why math is applicable. You have a sphere: How are you going to describe it? Math is just an abstract representational system to describe structure, shapes and relationships.

Re:Math Forfront (1)

hardburn (141468) | more than 6 years ago | (#22632070)

That's a very limiting definition. Mathematics is really about the manipulation of symbols. That particular revelation led to the thought behind the Universal Turing Machine.

Re:Math Forfront (1)

blahplusplus (757119) | more than 6 years ago | (#22634026)

"That's a very limiting definition."

Actually it's not, when you say "symbol" a symbol IS A SHAPE, therefore it has structure, therefore it is geometric. Fin.

Math For3front (1)

greedyturtle (968401) | more than 6 years ago | (#22635358)

But a symbol isn't a shape, it's an idea.

Re:Math Forfront (1)

Bloodoflethe (1058166) | more than 6 years ago | (#22635732)

He said "manipulation of," not "definition of." Mathematics is not intended to describe the shapes of the symbols that are being manipulated for the use of said science, although it *can* be a functionality thereof; QED, geometry is not necessarily the intended use of mathematics.

Re:Math Forfront (1)

DuckDodgers (541817) | more than 6 years ago | (#22635604)

Once you get past 3-dimensions, you can have mathematical concepts that you can't associate with any shape our minds are capable of accurately imagining.

You can also use mathematics to manipulate infinitely large numbers, or irrational numbers - what shape do they represent?

Or consider a very simple form of substitution algebra:
a = pq
x = by
qb = ag
You can prove ax = ppqgy. How would you represent that geometrically?

Your definition is too limiting.

Re:Math Forfront (1)

YttriumOxide (837412) | more than 6 years ago | (#22635804)

Once you get past 3-dimensions, you can have mathematical concepts that you can't associate with any shape our minds are capable of accurately imagining

I hear this a lot and am not sure that I agree... I can, quite clearly, picture a hypercube in my mind. I can't describe it verbally (or at least, not without starting well but finishing lamely with a "sort of, the other direction to those three"), draw it on paper or model it in clay, but I can definitely picture it clearly.
The first time, as a young child, that I was introduced to the idea, I really couldn't picture it at all, but then I just became more and more accustomed to the idea and could eventually picture it with my eyes closed, and now, with barely a second thought. Other 4 dimensional objects also (although I must admit that hyperspheres and other more "rounded" objects require a little concentration due to the lack of corners to use as starting points). I can, with a great deal of effort, also picture 5 dimensional objects, but only VERY simple ones. I can't get the hang of more than 5 though.

Re:Math Forfront (1)

YttriumOxide (837412) | more than 6 years ago | (#22635846)

I should have mentioned this in my last post (just above)... I forgot to mention that you are still actually completely correct though that we can't accurately model it with physical geometry, nor are we able to explain it sensibly and accurately without the language of mathematics, regardless of whether it's possible to mentally imagine it. So your point is still 100% valid.

Re:Math Forfront (4, Insightful)

pclminion (145572) | more than 6 years ago | (#22631662)

It always amazes me how applicable math becomes hundreds of years after it's written. Think if Maxwell's equations, Newton's equations, Einstein's equations. Fluid Dynamics equations were probably pioneered well before they were applied to human machines. Modern-day aircraft would not operate without their understanding. Where the math goes, human technology will probably soon follow.

It's often debated whether mathematics is invented or discovered. I think the question is irrelevant. Mathematics is clearly a human endeavor. Whether it has some deeper meaning outside of human existence is not something we can even address, seeing as we can never step outside our human condition. But it is indisputable that mathematics has allowed us to move far beyond the boundaries of any other physical organism that we yet know of. Whether it's "real" or not, it is certainly real in the context of our own existence. The philosophical arguments between mathematicians and physicists are petty at best. Ultimately, all new math seems to find application in the physical world. We should not be surprised, given that we are physical beings.

I feel pride, not in humanity, but in the universe itself, that it has the capacity to create physical beings which are capable of comprehension, at least at a basic level, of the true nature of reality. It may be colored by our nature, but the triumphs of modern science, in particular nuclear energy, show that we may actually be aware of some fundamental truth. The law of mass-energy equivalence can be demonstrated through purely geometric arguments -- you need not even understand calculus in order to grasp the math. We have grasped the power of stars. That proves something about us, but I am not sure what.

Re:Math Forfront (1)

greg_barton (5551) | more than 6 years ago | (#22631992)

...seeing as we can never step outside our human condition.

Genetic engineering and/or cybernetics, enabled by mathematics, may well change that.

Re:Math Forfront (1)

melikamp (631205) | more than 6 years ago | (#22632060)

And then, may be, one day, math will finally calculate the exact limit to the Human Pride. Or may be the whole sum of it will just diverge to +00.

Re:Math Forfront (4, Insightful)

ceoyoyo (59147) | more than 6 years ago | (#22632080)

We should also not be surprised since we construct math from its basic axioms to make sense to us logically - i.e., to work the same way reality does.

The really amazing thing is that the universe appears to respect our ideas of logic.

Re:Math Forfront (0)

Anonymous Coward | more than 6 years ago | (#22632894)

"The really amazing thing is that the universe appears to respect our ideas of logic."

Not so sure there..heard of quantum physics?

Re:Math Forfront (1)

marcosdumay (620877) | more than 6 years ago | (#22635472)

"The really amazing thing is that the universe appears to respect our ideas of logic."

Not so sure there..heard of quantum physics?

Are you refering to that man made theory that predict lots of weird things? Like that a photon would interfere with itself and, thus, light creates an interference pattern even when photons are throwed one at a time?

And you are not amazed that nature agrees with such ideas?

Re:Math Forfront (1)

12357bd (686909) | more than 6 years ago | (#22634188)

The really amazing thing is that the universe appears to respect our ideas of logic.
Well, only in the part of the universe that we already know, not that much in this light.

Re:Math Forfront (2, Interesting)

3D-nut (687652) | more than 6 years ago | (#22634670)

If you haven't already, you might want to read Eugene Wigner's essay, on The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Here's one link: http://nedwww.ipac.caltech.edu/level5/March02/Wigner/Wigner.html [caltech.edu]

Re:Math Forfront (1)

ceoyoyo (59147) | more than 6 years ago | (#22636054)

Hey, thanks. I read it somewhere before, but there's nothing like having a copy. A link to the original journal too.

Re:Math Forfront (1)

mgblst (80109) | more than 6 years ago | (#22634460)

Mathematics is clearly a human endeavor.

Are you suggesting that, in the case that there is other life out there, that they won't come up with the same mathematical system that we have? Of course not.

Re:Math Forfront (1)

pclminion (145572) | more than 6 years ago | (#22636174)

Are you suggesting that, in the case that there is other life out there, that they won't come up with the same mathematical system that we have? Of course not.

That conclusion is unjustified. A physical being which is incapable of distinguishing "numbers" is obviously not going to have any sort of mathematics, or logic for that matter, even remotely close to ours. If you think math is obviously universal, you clearly haven't taken hallucinogens before.

Re:Math Forfront (1)

JasterBobaMereel (1102861) | more than 6 years ago | (#22634484)

Go and look at the areas of Physics that don't have a sound basis in Maths, there are the ones that don't work yet, don't actually predict anything, and are often put down as speculative.... the various Sting theories spring to mind...

Whereas many new theories in Physics that were based on well known maths (or were found to be...) very quickly became applicable in the real world and are now used in everyday life not just in physics labs or physicts heads ...experiemt is all very well but unless you know what to try then how do you start experimenting?

Re:Math Forfront (2, Funny)

SQLGuru (980662) | more than 6 years ago | (#22634734)

What does Gordon Sumner's http://www.imdb.com/name/nm0001776/ [imdb.com] theories have to do with anything?

Layne

Re:Math Forfront (1)

FreeGamer (1001924) | more than 6 years ago | (#22634516)

It's often debated whether mathematics is invented or discovered. I think the question is irrelevant.
Y'know, if this were a software solution, it would be patentable... imagine how set back science would be if mathematics was as patentable as software? Perhaps that's a strong way to position the case against software patents.

Re:Math Forfront (1)

greedyturtle (968401) | more than 6 years ago | (#22636184)

Math you can't use [google.com]
I'm not sure if you were being sacrastic about patenting math or not, either way, this is still a great book!

Re:Math Forfront (1)

wikdwarlock (570969) | more than 6 years ago | (#22635754)

The law of mass-energy equivalence can be demonstrated through purely geometric arguments -- you need not even understand calculus in order to grasp the math. We have grasped the power of stars. That proves something about us, but I am not sure what.

Link?

Math is invented AND discovered (1)

clonan (64380) | more than 6 years ago | (#22635918)

Math has two distinct aspects.

First there is math as is relates to physics principles. 1 + 1 must equal 2. In a classical wphysics world there is no getting around that. Arithmetic, Pi, e and a few others are discoverable math principles.

But, second is how we as human beings understand math, this is invented. There is no fundamental reason why calculus is as it was developed. Caculus represents our understanding of math and is an invention of convinience.

Remember, all math COULD be done with basic arithmetic....I just wouldn't want to do it by hand.

Re:Math Forfront (1)

Dutch Gun (899105) | more than 6 years ago | (#22631814)

Quaternions, first described in the mid 1800s, were essentially a solution without a problem until they became relevant for computer-generated animation and graphics. Until then, I believe they were mostly just considered a mathematical curiosity.

Re:Math Forfront (1, Informative)

Anonymous Coward | more than 6 years ago | (#22632064)

Your math history is actually completely wrong. Hamilton actually was looking for a way of extending an algebra of vectors to 3 dimensional space to do stuff with classical mechanics. In fact, for awhile during the 19th century that was the way to do it, and there was also a bit of dispute about using the vector calculus methods vs. quaternions as well. So no, they actually did come about for a reason.

Re:Math Forfront (1)

jeti (105266) | more than 6 years ago | (#22633804)

Interesting. Do you know the history of wavelets as well?
Were they discovered for a specific purpose or were they
invented as a curiosity?

Tell me... (1)

jd (1658) | more than 6 years ago | (#22633932)

Based on these notes [princeton.edu] , placed on a public web server by one of Princeton's greatest mathematical minds, where would humans go?

Re:Math Forfront (1)

maxume (22995) | more than 6 years ago | (#22635794)

An equation can be said to describe a thing(maybe approximately;). People interested in a thing often find it useful to have a description of it. They have two choices: use an existing description, or come up with their own.

So, how often does human technology follow math, and how often does math follow human interest?

Article text (3, Informative)

melikamp (631205) | more than 6 years ago | (#22631654)

The article [ic.ac.uk] is available at the author's website [ic.ac.uk] .

As far as I can tell, the original result provided a conformal map [wikipedia.org] from a disk onto a polygon. Prof. Crowdy extended this result to provide a map from a disk with circular holes poked in it onto a domain with polygonal holes. Why is it useful? I am sure someone in the applied camp would know.

Re:Article text (1)

everphilski (877346) | more than 6 years ago | (#22631790)

Have you ever tried putting a round peg in a square hole before? It's not easy!

Re:Article text (1)

hardburn (141468) | more than 6 years ago | (#22632094)

Then you're not using a big enough hammer.

Re:Article text (3, Funny)

jo42 (227475) | more than 6 years ago | (#22632288)

a) Make the square hole bigger, or, b) Put the round peg in a lathe and turn it down so that it fits in said hole.

Not quite a breakthrough (4, Insightful)

l2718 (514756) | more than 6 years ago | (#22631730)

Read the paper. This is not the first S-C formula for multiply connected regions. The claimed "key result" is a formula for a case where a formula is already known. More work will be needed to a adapt the MATLAB technology from singly- and doubly-connected regions to multiply connected regions.

This paper seems to be part of ongoing work by a small community and is probably useful, but it's not a major mathematical breakthrough -- more of an incremental step. Small technical improvements in one field of mathematics shouldn't make up a slashdot story. Just because someone put "140 year old" in the press release doesn't mean it's really important. A math story belongs on /. when a big result is announced -- on the level of Poincare's Conjecture, or the Modularity Theorem.

Re:Not quite a breakthrough (1)

melikamp (631205) | more than 6 years ago | (#22631906)

Does it really feel like there is too much math on Slashdot? Only reporting the likes of Poincare's Conjecture would be similar to only reporting "P=NP" and "computer passes full Turing test" for computer science.

Re:Not quite a breakthrough (5, Interesting)

l2718 (514756) | more than 6 years ago | (#22633428)

Does it really feel like there is too much math on Slashdot?

No, it feels like there is the wrong math on Slashdot. What is needed are stories explaning accessible mathematics to a general audience. Not needed are stories about technical advances in mathematics. Two years ago there was a big hoopla about the calculation of the unitary dual of the split real form of $E_8$, which was a more important result and still completely irrelevant to the general public and impossible to explain even in the vaguest terms. There exists blogs by mathematicians where new math results are discussed. Slashdot should find stories which explain ideas of math, and report the occasional genuine breakthrough.

For CS, which is closer to the readership than Math, the bar should be lower. Deterministic poly-time primality testing was reported; a faster matrix multiplication algorithm, or even a faster factorization algorithm should be reported even if the details of the algorithm will not be reportable.

Re:Not quite a breakthrough (1)

cbart387 (1192883) | more than 6 years ago | (#22633970)

You may be correct. To me, however, it's heartening to see something more technical in nature. Would you rather see another Microsoft, iPhone or XML etc article? I'm tired of seeing the buzzword articles. Hopefully this is the start (yeah right) of a new trend.

Re:Not quite a breakthrough (1)

siwelwerd (869956) | more than 6 years ago | (#22631946)

Not to mention the linked article is so poorly written and lacking in details that after reading it I had no idea what had actually been shown. As to why this is important, I'm no analyst so I'm not going to read the entire paper, but it appears that he's made improvements to computing such a conformal map, which was previously more computationally difficult.

Re:Not quite a breakthrough (1)

ceoyoyo (59147) | more than 6 years ago | (#22632102)

When I saw the headline I remembered when Fermat's last theorem was solved and immediately thought of the Poincaire conjecture and the Reimann Hypothesis. I was disappointed.

Re:Not quite a breakthrough (1)

Es Esmu Adams (1200809) | more than 6 years ago | (#22632400)

Poincare conjectures been solved already, and well Reimann we can only hope. But Honestly, more math on /. would be nice.

Re:Not quite a breakthrough (2, Informative)

gardyloo (512791) | more than 6 years ago | (#22635044)

Indeed. See this 1956 paper: http://links.jstor.org/sici?sici=0002-9947(195605)82%3A1%3C128%3AOTCMOM%3E2.0.CO%3B2-P [jstor.org] (warning: links to only an abstract on JSTOR).

      Conformal mapping is pretty easy to explain to a lay audience (no, not necessarily hookers); the original article did a horrible job.

High school math tests (2, Funny)

syousef (465911) | more than 6 years ago | (#22631892)

I knew I could have scored better if there were no time limit!

Miss, I'd like 140 years to finish my paper!

My company went through numerous GPL violations (-1, Troll)

Anonymous Coward | more than 6 years ago | (#22632118)

As a consultant 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 tough 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.

Re:My company went through numerous GPL violations (0, Offtopic)

Lord Kano (13027) | more than 6 years ago | (#22632688)

Why in the fuck is your company writing "investment firm" software in the kernel?

LK

Re:My company went through numerous GPL violations (1)

pimpimpim (811140) | more than 6 years ago | (#22633314)

Didn't you read it? The exacting standards don't work without changing the kernel. And how would YOU write investment firm software without exacting standards, I ask you that. Or the ability to defrag ext2 (which, according to a quick google search, is possible (if it would ever be needed) with the appropriately called program 'defrag'). Or the ability to use token ring (the mini-how-to of token-ring for linux had version 4.1 in 1998). I guess this is one of those straight-out-of-college consultants? Damn waste of money (actually everyone's money, you pay for it indirectly, e.g. by higher inflation, when big investment companies don't have their things at order and are on their way to a collapse)

Then again, maybe the guy just needed to do these things now and just trolled to get the answers from slashdot posters that are stupid enough to respond ;)

Re:My company went through numerous GPL violations (1)

neomunk (913773) | more than 6 years ago | (#22635204)

Nice analysis, but wasted. This is a standard FUD troll post. If you need confirmation of the fact, just pick an unlikely phrase from the article and google it with quotes. This post has been on slashdot A LOT, and has made it's rounds to other sites as well.

Nice counters though, good to see someone out there vigilant against the FUD machine.

Re:My company went through numerous GPL violations (1)

phozz bare (720522) | more than 6 years ago | (#22633188)

My advice to you would be to get some new lawyers.

Re:My company went through numerous GPL violations (0)

Anonymous Coward | more than 6 years ago | (#22633554)

Well... here we seem to have some sort of MS-based viral marketing spam. Totally off-topic? Check! Anti-OSS? Check! Full of technoblather and moderate trolling? Check! Now get off my damn lawn... Um, website!

Ancient problem solved. (1)

Aegis Runestone (1248876) | more than 6 years ago | (#22632352)

"And verily in that day, it came to pass that the doctors rattled their canes and rejoiced." (Old Matth 3:14)

Octave, Scilab and SAGE users rejoice (4, Interesting)

Curl E (226133) | more than 6 years ago | (#22633894)

Should the rejoicing be limited to users of proprietry linear algebra systems?

MethLab users rejoice? (0)

Anonymous Coward | more than 6 years ago | (#22635020)

Why, are they selling Sudafed in bulk again?
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