The Unapologetic Mathematician

Though most of the samples so far have been rock or pop, I’m really a great fan of electronica. Unfortunately, they tend not to have lyrics, which sort of disqualifies them for use here.

However, there are exceptions. And after pushing myself through the midterm and attendant annoyances, the graduate student seminar lecture, and trying to figure out this Kazhdan-Lusztig-Vogan business, there’s one that’s perfect. I’ve done the best I can with various sources and my own hearing to decipher some of the more shrouded phrases. If you see any errors, please help correct them.

From 1999’s Wide Angle, Hybrid’s “Sinequanon”, with lyrics provided by Soon E MC.
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It’s been a long day. I was grading the exams and trying to corral other graders through most of it, and ended up spending most of my time in the department.

Sometime in the late afternoon one of Kleiner’s students here was scribbling furiously on one of the blackboards in the lounge, and looking exasperated. She’d been looking over the expanded notes on Perelman’s papers and couldn’t seem to follow the argument in one of the more technical claims. Going back to Perelman’s paper to find the original reference didn’t much help, so she was trying over and over again to see how it worked. Having nothing else to do and being pretty handy with analysis myself, I decided to try to help.

And then it was 11 at night. We realized that not only doesn’t the argument work, the claim actually seems to be false.

How to explain.. basically we’re looking at a curved three-dimensional shape that we get from a certain method. We need to know that if the shape is curved just so much on a given point, then we can be sure it’s not curved too much at a nearby point. Perelman gives such an upper bound on the curvature, and says it follows from an earlier inequality. Except the earlier inequality goes the other way. In fact, you can show that at the other point the shape is more curved than the bound he gives.

So now I’m just getting home after midnight and I’m exhausted. I’ll not out the student here, but I just had to say something before it gets much later.

• Claim 1 from section 4 is actually labelled 4.2.
• Kleiner does have students, but no female students.
• I suck at analysis.
• There is no error.

Of course, I figured that more people would have the same sort of reaction I would: once I got it I’d let other readers figure it out on their own, and spread the link far and wide. Well, traffic did spike a bit, but I had to turn on comment moderation to hold off the spoilsports.

If you saw this somewhere else and decided to hang around, welcome. And remember: there’s nothing wrong with link-bait.