Friday, February 17, 2017

Reporting on math

I followed a link to the Quanta article on "the fight to fix symplectic geometry. I didn't know what symplectic geometry was, but the link said this was about the foundations of one field of mathematics. So did the article itself:
The field continued to grow, even as the errors went largely unaddressed. Symplectic geometers simply tried to cordon off the errors and prove what they could without addressing the foundational flaws. Yet the situation eventually became untenable. This was partly because symplectic geometry began to run out of problems that could be solved independently of the foundational issues, but also because, in 2012, a pair of researchers — Dusa McDuff, a prominent symplectic geometer at Barnard College and author of a pair of canonical textbooks in the field, and Katrin Wehrheim, a mathematician now at the University of California, Berkeley — began publishing papers that called attention to the problems, including some in McDuff’s own previous work. Most notably, they raised pointed questions about the accuracy of a difficult, important paper by Kenji Fukaya, a mathematician now at Stony Brook University, and his co-author, Kaoru Ono of Kyoto University, that was first posted in 1996.

If, however, you go on to read the rest of the article, you find (executive summary) that they thought Fukaya's original paper hadn't quite proved what he set out to prove. After some back and forth, and 300 pages of explanation and elaboration by Fukaya, everybody thinks it's OK now.

Not foundational, except that a lot of people were using the techniques Fukaya said were OK. Nor errors, exactly. His proof wasn't complete, but the result looks like it was OK.

I guess writers have to try to make every story exciting. I was going to write more about this, but Lubos Motl already savaged the article, twice. Of course, he tries to make stories exciting in his own way. (If you want a less polemical essay by Motl, try one on Churchill as astrophysicist.)

Every now and then a story really is big news, but the constant overhype wears on me after a while. And that's just in the science section.

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