Two prominent and very well-regarded mathematicians have isolated a specific and serious error in Mochizuki’s proof of the abc conjecture. They are preparing a detailed writeup explaining the issue, which should be available publicly in the next month(s).
(I heard this from good friend X, who heard it directly from one of the two people involved.)
Whether or not their writeup is widely read, I am certain that for most in the community, the verdict of these two persons will instantly settle the matter.
Just back from the 2017 Arizona Winter School on perfectoid spaces. First of all, I should say that everything was impressively well-organized, and that the lecturers did a fantastic job, especially considering the technical weight of this material. (Watch the videos if you don’t believe me.) Jared Weinstein, in particular, has an almost supernatural ability to make a lecture on some technical thing feel comforting.
Now to the jokes.
- In his opening lecture, Scholze called perfectoid spaces a “failed theory”, on account of his inability to completely settle weight-monodromy. “You see, I’m Prussian, and when a Prussian says he wants to do something, he really feels responsible for doing it.”
- Audience member: “Why are they called diamonds?”
Scholze: “[oral explanation of the picture on p. 63 of the Berkeley notes]”
Weinstein: “Also, diamonds are hard.”
- Anon.: “When you’re organizing a conference, the important thing is not to give in and be the first one who actually does stuff. Because then you’ll end up doing everything! Don’t do that! Don’t be the dumb one!”
Me: “Didn’t you organize [redacted] a couple of years ago?”
Anon.: “Yeah… It turned out that Guido Kings was the dumb one.”
- Mazur: “It just feels like the foundations of this area aren’t yet… hmm…”
Mazur: “Yes, exactly. I mean, if Grothendieck were here, he would be screaming.”
- “Do you ever need more than two legs?”
- During the hike, someone sat on a cactus.
- Finally, here is a late night cartoon of what a universal cohomology theory over might look like (no prizes for guessing who drew this):
Just attended a week-long meeting at Oberwolfach on arithmetic geometry.
- “So did you do this computation like Gauss, or did you use a computer?” – Gabber to Katz
- “Let the indices work it out themselves!” – Janssen
- “Shouwu, either you’re going to answer my question, or I’m going to hand you over to Ofer!” – Kisin
- Katz (telling a story at the beginning of his talk): “… So anyway, after Spencer returned to Princeton, this is how he described the math department at Stanford [where he had just been a professor for a couple years]: ‘At Stanford, they’re still studying the topology of the unit disk!’ ”
Conrad (from the audience): “Those days are over.”
- “We use what I wrote.” – Janssen reassuring Gabber
- “So Peter, why did you turn down the breakthrough prize? [pause] I’m only asking because I’m drunk!”
- Anon.: “So Ofer, do you come here much?”
Gabber: [looks down at table, silently moves his finger across it in stepwise motion for 30 seconds] “Seventeen times.”
- Two common referees for technical papers on Shimura varieties: Frobenius and Verschiebung.
- Me (after writing down the “new” definition of a diamond): “Is that OK, Peter?”
Scholze (from the back row): “Looks good!”
- Zhang: “So Mochizuki is like the Buddha. He writes his ideas. He is satisfied. If you want to understand them, you visit him, you ask him questions, he gives you a little idea, you go away and study. You have to be a monk. Have a monk’s approach.”
Anon.: “Unfortunately, there aren’t very many good monks.”
- A “symplectic lifting whatever shit”. Apparently they’re defined in Kai-Wen Lan’s thesis?
- Gabber was NOT happy when he heard about Mochizuki’s Gaussian integral analogy.
- While eating the horrible bread casserole thing, which Kedlaya, Lieblich and I had mangled pretty badly while serving ourselves:
Lieblich:”What is this supposed to BE?”
Kedlaya: “Some kind of croque madame?”
Nizioł: “Yes, a croque madame. But I think you guys croqued it.”
The autocorrect feature in Gmail has the unfortunate but hilarious habit of vigorously changing standard math terms into free-associative nonsense. Here are some highlights (and I might add to this list from time to time):
- “Igusa varieties” -> “Iguana varieties”
- “Zariski topology” -> “Czarist topology”
- “Gelfand spectrum” -> “Gelatin spectrum”
- “cokernel” -> “cockerel” (my favorite so far)