Paata Ivanisvili

@PI010101

Professor of Mathematics @ UC Irvine | Former postdoc @ Princeton | Exploring what AI can (and can’t) do in math.

Irvine, CA

sites.google.com/view/paata

Joined October 2019

Paata Ivanisvili
@PI010101
13h
The preimage of every line under a conformal map of the unit disk has total length at most π², and this is best possible arxiv.org/pdf/2608.12844 I first learned about this problem from John Garnett and Donald Marshall’s wonderful book Harmonic Measure. Chapter I gives the
Paata Ivanisvili
@PI010101
Aug 14
AI’s ranking of open problems solved in today’s arXiv list. AI put problems connected to Gromov’s work in the top two spots. For #3, I remember attending a talk by one of the authors. #4 is, to me, one of the cutest problems in complex analysis, I first learned about it in
Paata Ivanisvili
@PI010101
Aug 13
A small episode from the AI–math battlefield: Aug 4: a paper appears on arXiv arxiv.org/pdf/2608.04237 claiming partial progress on the Bourgain–Brezis Sobolev conjecture. Same day: I ask AI, “can you try solving the full conjecture?” Aug 6: AI says, “done.” (The proof attempt
Paata Ivanisvili
@PI010101
Aug 13
Before giving a talk on an open problem, there is now one final item on the checklist: “Make sure it is still open.” Preferably, test it with AI the night before.
Paata Ivanisvili
@PI010101
Aug 12
This is a pretty cool result, congratulations. These are not just random orderings of pluses and minuses, this is a very important ordering something humans have never seen before.
levent
@__alpoge__
Aug 12
+++-+-+-+-+--+--+++-++----++--+----+-----+++---++-+---+++++++-+--+-+-+--++-+--+--+----+-+-+-+-++-++---+--++++--++-++++-+++++--+---++-+---+++++++++--+-+-+--++-+--+--+-----+++-+++-++-+-++++-++-+--+--+------++--+-++-+-+---+--+-+-+-+--++---+++++-----+++++++---+---+--+-+--+-+--+-++-++