David Savitt retweeted
the inimitable David Harvey wrote about his experience understanding the o(n log n) integer multiplication result: web.maths.unsw.edu.au/~david…
it's absolutely worth a read, both for the technical content and especially for the reflections on math and AI at the start
David Savitt retweeted
No relation.
David Savitt retweeted
"the most significant moment in mathematical history" like "being bombed was the most significant moment in the history of Hiroshima"
Big, big, big, big props for quasiriemann and no Siegel zeroes (with many other beauties in there), I’m kicking myself for talking all over about it being within reach but not actually having pushed.
There are some sad stories related to their users getting scooped / conflicts of interest (kakeya maximal comes to mind), and obviously we had some of the problems (without commenting on precise rumours).
We should put that aside for today though. It’s obviously the most significant moment in mathematical history.
David Savitt retweeted
My dream had always been to prove beautiful theorems as the AI agents unloaded my dishwasher. Well, it went the wrong way... 😂
David Savitt retweeted
My blog post giving a lot more details about Hexagon is up on Terry Tao's blog. One big reason is that we wanted mathematical results in a forum maintained by the mathematical and TCS communities.
terrytao.wordpress.com/2026/…
David Savitt retweeted
We all know that AI is a highly divisive issue. A working group convened at the Simons Institute earlier this month, to formulate concrete action items for TCS academia to take in response to AI. Remarkably, despite the wide range of opinions, participants were able to arrive at broad consensus on the list of recommendations here: simons.berkeley.edu/AITCSrep…. Many apply more broadly to mathematics, and beyond.
This document is NOT a declaration or essay. It is a list of concrete proposals, fleshed out all the way from motivation to implementation. Its purpose is to provide a common reference point and shared baseline for the community to discuss and enact change.
The actions are intentionally designated to be taken in the short term (specifically, this academic year); they are not meant to represent a stable vision of the future. You do not have to like them; you just have to like them MORE than what will happen if nobody takes action. Not everybody at the workshop agreed with every action, but they ultimately came together through discussion and compromise.
For transparency, I was involved in this event in a purely organizational capacity. I did not come up with any of these actions, but I recognize their importance and I will support them however I can. I hope you do too.
In September, we hosted a working group to think about how the TCS community should respond to AI progress. Their report, released yesterday, highlights 12 near-term actions that received broad support among the participants.
simons.berkeley.edu/news-pub…
David Savitt retweeted
I was part of a group that met last week to try to propose recommended changes to the structure of math PhD programs in an age of AI. Our report, together with a collection of related resources, is now available here:
cmsa.fas.harvard.edu/aimathp…
David Savitt retweeted
I'm optimistic that the Advisory Group on Mathematics and Artificial Intelligence (agmai.org/) will help improve the communication and conduct of AI companies around mathematics. The initial board members are stellar mathematicians. Any honest frontier lab or Math/AI startup should be expected to engage with them in good faith.
David Savitt retweeted
Mikhail Khovanov, @JohnsHopkins, will give an Invited Address, “Problems and advances in categorification and link homology,” at the AMS Eastern Sectional Meeting at @GWtweets on Sunday, October 4.
Learn more. Link in comments.
David Savitt retweeted
worrying about recursive self-improvement on australian TV (lateline) in 1996.
David Savitt retweeted
I think the attacks on Levent @__alpoge__ are unfair. He is in an impossible position: if he doesn't drop a writeup immediately, people complain; if he does, people complain; if he withholds everything, people complain. Cynical accusations of "advertising for IPO" are clouding the main point: powerful and dangerous capabilities are here, while more powerful and more dangerous ones are on the way.
My vote is for AI companies to immediately drop all slop breakthroughs into a common repository, where people can see and process them soberly. Thoughtful individuals (not me) are donating their time to build an appropriate such repository, and when it arrives I hope it will be appreciated and adopted.
David Savitt retweeted
I've seen several posts listing the Fields medalists who didn't sign the declaration and trying to ascribe motives, and I'd like to say: don't become a mob. People can have nuanced opinions, and can speak for themselves.
David Savitt retweeted
The resolution of Navier-Stokes is an amazing accomplishment. Some comments …
First, a brief mathematical postmortem. Millennium problems are important, but when you confront an unsolved problem, it is always unclear how far the solution is out of reach. The initial opinion of at least some experts (not myself – I have no expertise on this problem) seems to be that, in retrospect, the conceptual program underlying this solution happened to already be in place*, and the contribution of AI was a very intricate technical execution. Technical execution is one of the axes on which we've already seen AI become superhuman, though never before with such a dramatic demonstration.
This is not to diminish the solution or OpenAI’s achievement. But there are many problems which are out of reach of current models, no matter how much inference-time compute one invests. I’m still convinced that human mathematicians are laying indispensable groundwork for future progress.
*Terry Tao describes one possible program at mathstodon.xyz/@tao/11720785…. As I understand, the one Tao describes is NOT the Cordoba--Martınez-Zoroa program that OpenAI (and Alpoge/Buckmaster) followed. However, the successful approach was not as esoteric as Buckmaster’s statement might make it seem – there were certainly other people (not me) also prompting that approach; it just isn’t the kind of thing that one goes around saying publicly.
As far as I know, Navier–Stokes is the only one among all Millenium problems with a well-defined program towards a solution. Concretely, for the Birch and Swinnerton-Dyer Conjecture (over number fields) I am not aware of even a vague proposal of what a proof might look like, so I doubt that current AI models will get anywhere close to a resolution. (My opinion is that this conjecture cannot be resolved in the negative; perhaps the most refined formulation is false, but then the real problem would be to correct the formulation and then prove it.) I'd be curious to see what progress was made on it!
David Savitt retweeted
Poured my heart and soul into advocating for formal proof with AI assistance in a mathematical setting because of the large collaborations I thought it could empower. (1/3)
David Savitt retweeted
About Mathathon: undergrads at Caltech are organizing a 40 hour event where participants can use $2M API credits, sponsored mostly by AI companies, to work on open math problems. Recently this event received strong pushback, and below I share my thoughts.
mathathonchallenge.com/
David Savitt retweeted
There is a super shady data control setting on everyone's ChatGPT which makes it seem like your data can be used for training even if you explicitly say to *NOT* improve the model for everyone (1/9)
Readers added context they thought people might want to know
This claim is false. OpenAI has clarified that the in-app toggle and the privacy portal are independent ways to opt out of data training. You only need to use one method, and OpenAI respects the opt-out choice regardless of where it is set.
x.com/thsottiaux/sta…
help.openai.com/articles/77308…
David Savitt retweeted
unfortunately i contacted them on the night of wednesday, september 2nd making the following points
1. i had intel they had information about math work i was doing and a few days before they had spun up a group to try to compete.
2. i emphasized and reemphasized mine was a strictly personal mathematical collaboration
3. that this was a collaboration that had been going on for a year
4. that in my personal collaboration we were happy users of codex as well as obviously claude (and i later complimented astra explicitly after it came out for its help, and reassured i would obviously be sprinkling acknowledgments for it, previous models, and codex liberally in the writeups)
5. that it would look terrible if openai were competing against mathematician consumers, and my collaborator (Tristan) wanted to email about this explicitly
6. that i expected none but in the worst case intended to refuse marketing around the result we were working towards, being the fruit of a personal external academic collaboration, and wanted to express this because i figured worries about such marketing by their leadership was why a team was spun up to extraordinarily directly compete.
sebastien and i have in the past months had our fun pushing each other on twitter, but as i process it all i keep feeling bad about Tristan.
1. neither of us could sleep Sunday night, so we went on a walk around the city. i finally asked him why fluids, and he told me it was the navier-stokes problem. he told me parts of the story about his classic nonuniqueness result with Vicol i hadn’t heard yet, and also about how he too grew up writing shaders as a kid and then switched to math
2. tristan is a mathematician’s mathematician. he kept rock solid to his principles during the tense calls and negotiations, immediately turning down a career dream and million dollar prize for me, the sort of strange excited unclear-quasiuseful confused idiot in our collaboration. fifteen minutes later, his feet were up on his desk with three toes per foot peeking out of ripped socks
3. our periodic call after i’d texted him euler blowup was just laughing for an hour or two. just laughing. i’d seen fable deal correctly with monge ampere in the equality case of ehrhart’s conjecture, so in some call before that i’d really pushed him for the craziest shit he could think of that i might try. i texted him the pdf as an update on that “diego luis 3” line, in which following his incredible expression of intuition i hodgepodge slapped together a bunch of our recent work, in particular correcting a bunch of better and lesser known papers in the literature, as well as on diego and luis’ ipm paper, and hoped an analogous construction for boussinesq (thus axisym euler) might work out. i managed to wade through enough confusion to insist to the model it stop telling me stupid regularity stuff about kelvin waves, and a rayleigh-taylor ansatz stuck. like i said, just laughing. when i texted him the pdf, the worst thing either of us had seen so far, i didn’t even comment on the euler blowup claim, only explaining why skepticism should remain for boussinesq, because i found it so shocking. i mean what the hell did i know, i must’ve confused myself by misunderstanding one adjective like i was used to with algebraic geometry. im so lucky to have been able to live that
4. he managed all this this entire time with unclear sleep, timestamps continue to amaze me, due to just recently having a kid
it is obvious he deserves the same sort of praise he heaped upon luis, perhaps mutatis mutandis:)
Replying to @__alpoge__
nothing at all was locked we were just willing to talk but you didn't talk to us ... sorry but that's just untrue, we were willing to go above and beyond and have as many discussions as you would have liked to reach resolution.
RT @amermathsoc: The news today of progress on resolving the Navier–Stokes problem, one of mathematics’ great longstanding challenges conce…


























