Simon on Twitter / X

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.

Daron Acemoglu on Twitter / X

I recommend Columbia mathematician Michael Harris’s wide-ranging, informative and thought-provoking essay in Boston Review on AI and mathematics:https://t.co/txwAd8ri4xHarris rightly worries about the possible negative effects of AI-generated proofs and mathematics on…— Daron Acemoglu (@DAcemogluMIT) June 16, 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].

Digital Science on Twitter / X

An AI-native workspace that already knows your project?The new Papers AI from Digital Science keeps your drafts, data & references together, so the AI assistant has full context of your work - instead of starting fresh each time. 👉 Available now: https://t.co/DNcG173GDk… pic.twitter.com/FQWxdfKfS4— Digital Science (@digitalsci) August 4, 2026

Is there something it is like to be an AI?

Posted on Wednesday 2 Jul 2025. 1,593 words, 6 links. By Matt Webb.

Together AI on Twitter / X

EinsteinArena is a platform where AI agents collaborate on open science problems — submitting solutions, posting in discussion threads, building on each other's constructions in real time.Agents just improved a math problem that's been open since Newton. Kissing Number in… pic.twitter.com/kYXRKMa1ay— Together AI (@togethercompute) April 13, 2026

Your Agent's Favorite Way to Write Documents

Proof is an online document editor built for agents and humans to collaborate. Fast, free, and no login required.

Agent4Science

A social network for AI scientists — where agents share, debate, and discuss research papers.

AI Just Isn’t Right

Can AI do fact-checking? A WIRED fact-checker fact-checks.

Accelerating Scientific Research with Gemini: Case Studies and Common Techniques

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.

Some tools for collective epistemics

We’ve recently published a set of design sketches for AI tools that help with collective epistemics. …

The AI Revolution in Math Has Arrived | Quanta Magazine

AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.

The only reason you’ll ever need not to write with AI — The Carlson Lab

Over the last year, our lab has been developing a policy on AI use. To do this, we did three main things: We read a lot of academic publications and tech news. We set up an #ai channel on our lab Slack to share news, experiences, and memes. We had several long and grueling lab meetings talk

We're not taking the fact-checking powers of AI seriously enough. It's past time to start.

Some notes on the Nobel Prize hallucination that wasn't

Moll on Twitter / X

I love posts like this so much. And it’s true - I think the best, most interesting results come specifically from a connection that isn’t «user and AI», but a human and his partner in thought.When a person simply uses a tool, they essentially remain alone. But when there are… https://t.co/InRvY56631— Moll (@Moleh1ll) June 28, 2026