Mathematician Solves a Big One After 140 Years

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!"

Comments

Math Forfront

[Bananatree3]

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

[siride]

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

Re:Math Forfront

[644bd346996]

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

[zippthorne]

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

[pclminion]

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

[moderatorrater]

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

[ceoyoyo]

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

[ceoyoyo]

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.

Not quite a breakthrough

[l2718]

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:Design

[ceoyoyo]

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

[Bananatree3]

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

[Bloodoflethe]

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

[Joe Snipe]

Tell that to the dragonfly