Slashdot Mirror
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!"
There is a saying that goes something like "for every new discovery in math, a new field of science begins".
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.
I don't know, but it works for me.
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.
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.
Backups are for wimps. Real men post their data in comments and have slashdot mirror it
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
I like the math articles on here. Usually I'm reduced to a "eh??" (I've ~30 credits of college math but most of the interesting stuff is well beyond that) but when someone here takes a significant discovery and breaks it down so I can understand it ... that's one of the things I most love about /.