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Hardcore math at the speed of the Net

From its inception, the Internet has been about connecting researchers and research institutions to each other (and, of course, about national defense). As the Web continues to explode, though, it's interesting to see how new generations of researchers work, collaborate, and criticize online.
Written by Christopher Dawson on

From its inception, the Internet has been about connecting researchers and research institutions to each other (and, of course, about national defense). As the Web continues to explode, though, it's interesting to see how new generations of researchers work, collaborate, and criticize online.

A particular example comes from a poor sod of a professor at Brigham Young University. Xian-Jin Li preprinted a proposed proof of the Riemann Hypothesis, a lovely little bit of math that was, according to Wikipedia,

...first formulated by Bernhard Riemann in 1859, is one of the most famous and important unsolved problems in mathematics. In 2009, it will have been an open question for 150 years, despite attracting concentrated efforts from many outstanding mathematicians.

My reference to Xian-Jin Li as a poor sod is not a judgment. Rather, it's a reflection on the way in which the mathematical elite gave his proof the smackdown in very short order via the blogosphere. One of the foremost experts on noncommutative geometry (that just sounds fun, doesn't it?), Alain Connes, pointed out on his own blog:

I dont like to be too negative in my comments. Li's paper is an attempt to prove a variant of the global trace formula of my paper in Selecta. The "proof" is that of Theorem 7.3 page 29 in Li's paper, but I stopped reading it when I saw that he is extending the test function h from ideles to adeles by 0 outside ideles and then using Fourier transform (see page 31). This cannot work and ideles form a set of measure 0 inside adeles (unlike what happens when one only deals with finitely many places).

Well of course. Silly Xian-Jin and his unworkable Fourier transform. Other leading mathematicians dug in further within days of his posting the proof on arXiv.org; it's only July 7th now and the paper has been withdrawn.

It's easy for us to get caught up in YouTube and MySpace as the ultimate expressions of Web 2.0 goodness. However, the ability to communicate and exchange ideas quickly and transparently remains the killer app for education.

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