Do Androids Dream of
Electric Sheaves?
Mathematics as it navigates the brave new AI world
Producing Mathematics With AI
Mathematicians using the machines: recent advances, with the popular account and the paper side by side.
- Proofs and Prompts (Aug 2026) — a communal blog — mathematicians on how AI is changing mathematical practice, launched with Martin Hairer's “Writing mathematics in the age of AI”
- Organizing Mathematical Knowledge in the Age of AI and Formalization (Jul 2026) — National Academies workshop (Washington, DC, July 20–21), opened by Terence Tao and featuring Ken Ono's “Formally Verified Knowledge as Infrastructure for Math, Science, and Technology” · full agenda (Jul 2026)
- Mathematics in the Age of AI — Terence Tao at ICM 2026 (Jul 2026) — Tao's public lecture at the International Congress of Mathematicians, Philadelphia, July 24 — on video · slides (Jul 2026)
- Why the Legendary Erdős Problems Are Falling to AI (Aug 2026) — Quanta Magazine, on the disproof of Erdős's 1946 unit distance conjecture by an OpenAI model, and the systematic AI assault on the Erdős problems database · verification paper (Alon–Bloom–Gowers–Litt–Sawin) (May 2026)
- How Terry Tao Became an Evangelist for AI in Math (Jun 2026) — Quanta Magazine, on Tao's machine-assisted mathematics, from the PFR formalization to the Equational Theories Project · Equational Theories Project paper (Dec 2025)
- The AI Revolution in Math Has Arrived (Apr 2026) — Quanta Magazine's state-of-the-field survey: AlphaEvolve on 67 research problems, Nesterov's 42-year-old conjecture settled with ChatGPT's help, the First Proof challenge · Mathematical exploration and discovery at scale (Nov 2025)
- The Erdős Problems database (2023–) — Thomas Bloom's catalogue of 1000+ Erdős problems, now tracking Lean formalization and AI-assisted solutions · the AI-contributions ledger (2025–)
- Semi-Autonomous Mathematics Discovery with Gemini (Jan 2026) — DeepMind's case study on the Erdős problems: five open problems resolved autonomously, eight lost solutions recovered from the literature
- Using AI, Mathematicians Find Hidden Glitches in Fluid Equations (Jan 2026) — Quanta Magazine, on unstable singularities in Euler and porous-media flows found by physics-informed neural networks — a step toward Navier–Stokes · Discovery of Unstable Singularities (Sep 2025)
- Early science acceleration experiments with GPT-5 (Nov 2025) — Bubeck, Gowers, Eldan et al. document new results found with GPT-5, including an improved convex-optimization bound
- AlphaProof: Olympiad-level formal reasoning, in Nature (Nov 2025) — DeepMind's silver-medal IMO 2024 system, its proofs formally verified in Lean; gold-medal performance (in natural language) followed at IMO 2025 · the IMO gold announcement (Jul 2025)
- AlphaEvolve: a coding agent for scientific and algorithmic discovery (Jun 2025) — the first improvement to Strassen-style 4×4 matrix multiplication in 56 years, among other records
The Mathematics That Builds AI
What is inside the machines: the linear algebra, probability, and optimization that make them go.
- The Mathematics of Large Language Models (2026) — an eight-lecture mini-course with a build-your-own-LLM project, by Agnès Beaudry and Katherine E. Stange
- Neural Networks (3Blue1Brown) (2017–2024) — Grant Sanderson's animated series, from gradient descent to attention and transformers
- Understanding Deep Learning (2023) — Simon J. D. Prince's textbook (MIT Press), free to read online
- A Mathematical Framework for Transformer Circuits (Dec 2021) — Anthropic's foundational interpretability paper: transformers by hand, one attention head at a time
Wrestling with the Future
Forecasts, benchmarks, and arguments about where this is all going.
- AI 2040: Plan A (Jul 2026) — the AI Futures Project's follow-up to AI 2027 — not a prediction but a plan: how coordinated action could delay superintelligence to 2040
- AI 2027 (Apr 2025) — Kokotajlo, Alexander, Larsen, Lifland, and Dean's month-by-month forecast scenario of an intelligence explosion
- AI Is Acing Math Exams Faster Than Scientists Write Them (Feb 2026) — IEEE Spectrum on the benchmark treadmill, from FrontierMath's launch (under 2% solved) to its open-problems tier · FrontierMath benchmark paper (Nov 2024)
- Machine-Assisted Proof (Jan 2025) — Terence Tao in the Notices of the AMS, on what proof assistants and machine learning will do to the working mathematician
Human Understanding
What mathematics is for, and what remains ours to understand.
- Catching Crumbs from the Table (Jun 2000) — Ted Chiang in Nature — human scientists interpreting the output of metahuman science; republished as “The Evolution of Human Science”
- Why A.I. Isn't Going to Make Art (Aug 2024) — Ted Chiang in The New Yorker, on choices, intention, and effort
- ChatGPT Is a Blurry JPEG of the Web (Feb 2023) — Ted Chiang in The New Yorker — the lossy-compression view of language models
- On Proof and Progress in Mathematics (1994) — William Thurston's essay: mathematics is about human understanding, not just theorems
- What is Good Mathematics? (2007) — Terence Tao on the many axes of mathematical quality
- Mathematics for Human Flourishing (Jan 2017) — Francis Su's farewell address as MAA president, later a book (Yale, 2020)