## Mathematician Solves a Big One After 140 Years 144

Posted
by
kdawson

from the works-with-holes dept.

from the works-with-holes dept.

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!"*
## wow (Score:5, Funny)

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

## Re:I solved a big one this morning too (Score:5, Funny)

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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.

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Is there no limit to potty-humor?

Why must it be integrated into our lives so often?

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## Math Forfront (Score:5, Insightful)

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## Design (Score:3, Funny)

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## Re:Design (Score:5, Insightful)

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 (Score:5, Interesting)

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.

## But does the patient survive (Score:2)

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.

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is* slashdot## Re:Design (Score:4, Informative)

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).## Re: (Score:2)

## Re:Design (Score:5, Funny)

Not to mention pilots.

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## Re:Math Forfront (Score:5, Interesting)

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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.

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

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

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## Re:Math Forfront (Score:5, Insightful)

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

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

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Dude, you need new friends...

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## Re:Math Forfront (Score:5, Insightful)

alsoproved 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 (Score:4, Informative)

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.

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I've always considered them to have been largely independent not least because of the different notations adopted. It was calculus's time, if not Newton or Leibniz some other genius

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Heck, physics these days seems to be nothing more than experimental mathematics with string theory and the like.## Re: (Score:2)

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.

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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.

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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 event

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

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It's just as important that our maths be independent of representation as it is that we use clear, concise symbology. So it is vital for understanding that we use the correct symbols (and logic in the sentence structure of our proofs), and it is crucial that the choice of individual symbols be arbitrary and

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## Re:Math Forfront (Score:5, Insightful)

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.

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

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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 (Score:5, Insightful)

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

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So it's a very understandable mental module -- being able to say whether two natural language statements are equivalent or not -- that gives us all of math and physics.

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You're right, our brains must be wired to recognize reasonable rules for -> in normal circumstances, but why do those rules continue to hold outside of our everyday experience? The picking and choosing sc

## No it doesn't (Score:2)

We only understand gravity because we observe it by falling on our diapered butts as babies. Therefore gravity becomes part of our logic.

Heavier than air flight was impossible (our logic told us), until proven otherwise and we had to modify our logic.

Going faster than 60mph, then 100mph, then sound would certainly kill people, until it was done.

Our logic tells us the world is flat, etc etc.

Stuff like q

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Logic, on the other hand, always seems to work. If your theory doesn't work you examine it for errors and check your assumptions. You don't go back and wonder whether logical deduction has failed.

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Are you refering to that

man madetheory 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?

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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.

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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.

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becauseof my hallucinogenic experiences...## Re: (Score:2)

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

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Layne

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## Math is invented AND discovered (Score:2)

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 arit

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## Tell me... (Score:2)

## Article text (Score:4, Informative)

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.

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http://sinews.siam.org/old-issues/2008/januaryfebruary-2008/breakthrough-in-conformal-mapping [siam.org]

## Not quite a breakthrough (Score:5, Insightful)

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.

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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 (Score:5, Interesting)

No, it feels like there is the

wrongmath 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.

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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 (Score:3, Funny)

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

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## Octave, Scilab and SAGE users rejoice (Score:4, Interesting)

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