# Mathematician Solves a Big One After 140 Years

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

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!"*

## wow (5, Funny)

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

## Re:wow (3, Funny)

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

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

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

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

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

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

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

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)

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

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

## 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)

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

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

## Re:wow (0)

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

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)

## Re:Math Forfront (2, Insightful)

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

## Design (2, Funny)

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

## Re:Design (1, Funny)

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

## Re:Design (4, Insightful)

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

## Re:Design (4, Insightful)

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

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)

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)

## But does the patient survive (1)

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

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)

## Re:Design (3, Informative)

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

## Re:Design (2, Insightful)

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

is* slashdot## Re:Design (3, Informative)

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

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)

modernestandadvancedestturbine-driven commercial aircraft wing (at the moment).## Re:Design (4, Funny)

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

Not to mention pilots.

## Re:Design (1)

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

## Re:Design (0)

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

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)

## Re:Math Forfront (1)

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

## Re:Math Forfront (5, Interesting)

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

## Re:Math Forfront (2, Insightful)

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

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)

"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)

## Re:Math Forfront (2, Interesting)

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

## Re:Math Forfront (4, Insightful)

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

## Re:Math Forfront (1)

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

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)

## Re:Math Forfront (1)

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

## Re:Math Forfront (1)

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

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

## Re:Math Forfront (1)

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

## Re:Math Forfront (1)

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

## Re:Math Forfront (4, Insightful)

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

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 (3, Informative)

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

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)

## Re:Math Forfront (1)

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

## Re:Math Forfront (1)

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

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)

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)

## Re:Math Forfront (1)

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

## Re:Math Forfront (1)

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

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)

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)

## 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)

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)

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)

Not so sure there..heard of quantum physics?

## Re:Math Forfront (1)

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

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?

## Re:Math Forfront (1)

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

## Re:Math Forfront (2, Interesting)

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

## Re:Math Forfront (1)

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

## 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)

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

## Re:Math Forfront (2, Funny)

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

Layne

## Re:Math Forfront (1)

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

## Re:Math Forfront (1)

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

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.

## Math is invented AND discovered (1)

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

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)

## Re:Math Forfront (1, Informative)

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

## Re:Math Forfront (1)

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

Were they discovered for a specific purpose or were they

invented as a curiosity?

## Re:Math Forfront - the bernoulli's (1)

## starbird (409793) | more than 6 years ago | (#22632718)

http://mysite.du.edu/~jcalvert/tech/fluids/bernoul.htm [du.edu]

## Tell me... (1)

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

## Re:Math Forfront (1)

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

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)

## 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)

## Re:Article text (2, Informative)

## tqft (619476) | more than 6 years ago | (#22631902)

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

## 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)

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.

## Re:Not quite a breakthrough (1)

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

## Re:Not quite a breakthrough (1)

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

## Re:Not quite a breakthrough (1)

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

## Re:Not quite a breakthrough (1)

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

## Re:Not quite a breakthrough (2, Informative)

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

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)

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)

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)

LK

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

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

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 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)

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

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

## Ancient problem solved. (1)

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

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

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

## MethLab users rejoice? (0)

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