Notes from the common room
Axioms for Organizers by Fred Ross, Sr. | Fred Ross, Sr.
Simon on Twitter / X
Can AI help connect theorems humans write in papers to proofs computers can check?We just released TheoremGraph (https://t.co/PQ8FcFQGat), and I made a 3Blue1Brown style video overview of the idea.This project was my first real research experience, and it meant a lot. Start… pic.twitter.com/yMUA0QziXM— Simon (@waskaja) June 29, 2026
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
Bartosz Naskręcki on Twitter / X
Congrats to @LechMazur for the solution and to Terence Tao for the digestion and storytelling. You see the trend. Mathematicians are still needed if we want to make any sense of the formal proofs. For now... Maybe the next gen LLMs will simply read allthe blogs of Terry and… https://t.co/yXiISCrNAF— Bartosz Naskręcki (@nasqret) August 13, 2026
The Technological Turn in Mathematics
Quickly evolving technologies, such as Interactive Theorem Provers (ITPs), Automated Theorem Provers (ATPs), and Large Language Models (LLMs), all falling under the general heading 'AI for mathematics,' are transforming mathematical practice in profound ways. This chapter explores the implications of these innovations, focusing on their impact on how mathematical knowledge is created and shared. It also discusses how they are reshaping the social dimension of mathematics, altering collaboration dynamics, trust relationships, and the collective production of knowledge. For instance, tools like ITPs facilitate large-scale collaborations and make new types of teamwork possible, where trust is not a necessary ingredient. ITPs also help us mitigate our human fallibility, yet they raise questions about the nature of formalization and the relationship between traditional and formal mathematics. Technologies such as LLMs are reshaping the division of epistemic labour between humans and machines and urge philosophers of mathematics to ask questions about the value of their work.
. · openai/ten-proofs@d0e1ae7
Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@d0e1ae7
Too Big to Know
Too Big to Know: Rethinking Knowledge Now That the Facts Aren't the Facts, Experts Are Everywhere, and the Smartest Person in the Room Is the Room is a non-fiction book by the American technology writer David Weinberger published in 2012 by Basic Books.
Roomy Events, by OpenMeet
While Roomy is now quitely operational with a growing handful of pilot spaces, before we make a grander reveal about that particular milestone we have another exciting Report from the Atmosphere to share in the meantime. Events for organizing Events planning is an essential affordance in the world of organizing,
The Atmosphere, Explained - Erlend’s notes
people in the centre, platforms at the margins
Magic Paper
Working notes by Michael Nielsen, November 2017. Followup to (but doesn't require) my notes on Chalktalk.
. · openai/ten-proofs@5a102c1
Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@5a102c1
Writing design docs – Ceejbot's notes
How to figure out what to do and tell your colleagues at the same time
made some basic slides to organize my thoughts, even though there's no AV in the room! (may not make sense without me actually talking through what's on them though lol) docs.google.com/presentation/d/1VBGTPl6Jh4D_A…
This Talk Is Not About Bluesky: Building on the Atmosphere with ATproto, PDSes, and DIDs
docs.google.com
cyber professional
I've grabbed the Saturday 5 PM slot at @hope.net to give a talk: This Talk Is Not About @bsky.app - Building on the Atmosphere with ATproto, PDSes, and DIDs wiki.hope.net/index.php/Unscheduled_4th_Tra…