Fall 2026 · University of Colorado BoulderMath 5810: Special Topics in Mathematics — Math and AICourse page →The soundtrackA playlist on Spotify ↗ (suggestions appreciated!)Mathematician and Machine
- Proofs and Prompts (ongoing) — communal blog · some good ones: Duminil-Copin, “Care for a little more AI?” (Aug 2026) · Wang, “The AI-Assisted Mathematician's Dilemma” (Aug 2026) · Guo, “Evaluating mathematical merit” (Aug 2026)
- The AI & Mathematics Zulip (ongoing) — community chat; this channel is public, no login needed
- Matlas (ongoing) — semantic search over the theorems of 180 journals and 1,900 textbooks · the paper (Apr 2026)
- Math 2.0 — Terence Tao (Oct 2026) — AIM public lecture at Caltech, on video: how AI is changing mathematical research and where the field may go
- When A.I. Comes for Your Purpose in Life (Oct 2026) — The Daily (New York Times) podcast: Steven Strogatz on the excitement and grief of watching AI take on the work that gives mathematicians purpose, and what is lost when answers come without the human struggle
- The Enshittification of Mathematics (Sep 2026) — Fenner Tanswell in The Mathematical Intelligencer: what is happening to the discipline as it is sucked into the corporate vortex
- The Siren Call of Silicon Leviathan (Sep 2026) — Alexander Gamburd on the Navier-Stokes blowup proof no human has read: accepting it as a proof hands authority to Hobbes's Leviathan, so mathematicians should grant acceptance only to AI producers that practice legibility, disclosure and responsibility
- AI in Mathematical Research — panel at the Heidelberg Laureate Forum (Sep 2026) — Peter Scholze, Jacob Tsimerman, Michael Harris and Geordie Williamson, moderated by Tony Feng (video)
- Fast Math/Slow Math (Sep 2026) — Ben Antieau, guest posting on Tao's blog: contemplative and ambitious mathematics side by side, and nine community standards for working no faster than you can understand
- Priest, Monk, and Mathematician (Sep 2026) — Logan Graves, after the Navier-Stokes blowup: the human mathematical community as interpreters of revelation, then as monks
- The Next Unit of Science (Aug 2026) — Requarth on the future of scientific publishing, for humans and AI alike
- The Crisis of AI-Generated Mathematics (Aug 2026) — Max Weinreich's case for total opposition
- Organizing Mathematical Knowledge in the Age of AI and Formalization (Jul 2026) — National Academies workshop · full agenda (Jul 2026)
- Mathematics in the Age of AI — Terence Tao at ICM 2026 (Jul 2026) — public lecture on video · slides (Jul 2026)
- Why AI Needs Formal Mathematics (May 2026) — Edward Lockhart, on video: reward hacking and the case for formal proof · the full collection: Mathematics for and by Large Language Models, 3rd edition (IHES) (May 2026)
- The Fall of the Theorem Economy (Apr 2026) — David Bessis: how AI could destroy mathematics and barely touch it
- Will Machines Change Mathematics? (Apr 2024) — two special issues of the Bulletin: Venkatesh, Granville, Harris, Cheng, Davis, Williamson, … · part two (Jul 2024) · Venkatesh: some thoughts on automation and mathematical research (Apr 2024) · Bengio & Malkin: towards an AI mathematician (Jul 2024) · Poggio & Fraser: compositional sparsity of learnable functions (Jul 2024)
- The First Proof Project (ongoing) — testing AI with human research problems · the first ten questions (Feb 2026)
- The Leiden Declaration on AI and Mathematics (Jun 2026) — IMU-endorsed statement · the call for action, in the Notices (Sep 2026)
- The Association for Human Mathematics (ongoing) — mathematicians organizing working groups on AI's effects on teaching, research and publishing
- Advisory Group on Mathematics and Artificial Intelligence (ongoing) — independent group of mathematicians (Gowers, Hairer, Vakil, Witten, Wood, and others) advising AI companies on the responsible release of AI-generated mathematics · general guidelines for AI labs (Sep 2026)
- AIAL Statement on Generative AI and Scientific Integrity (Oct 2026) — the AI Accountability Lab (Trinity College Dublin) asks researchers to treat generative AI use as a choice to be justified and disclosed, not a default
- Axplorer (Mar 2026) — tool for exploration
- Agentic Coding in Practice (2026) — MIT seminar series · “Slop Is a Skill Issue” (video) (May 2026) · slides (May 2026)
- How to Tame Your LLM: Harnesses for Rigorous Work (Sep 2026) — Edgar Costa's slides from his Math 5810 guest lecture at CU Boulder: skills, standing instructions, project records, fresh contexts, independent checks, and budgets
- Open-weight models, compared (ongoing) — 300+ models
- The NAIRR Pilot (ongoing) — NSF compute
AI-Assisted Mathematics
- IMProofBench (ongoing) — ETH's research-level proof benchmark: private problems, public leaderboard · the paper (Sep 2025)
- mathcity (ongoing) — a Gas City pack for doing mathematics research: agents file briefs, humans adjudicate
- The Ramanujan Challenge (Jul 2026) — can AI prove formulas for π, e, and ζ? a month-long open test
- Benchmarks in Leipzig (May 2026) — 100 research-level problems from 49 mathematicians, at MPI MiS · the paper (Jun 2026)
- VibeMathed, the stats (ongoing) — a running tally of AI-resolved open problems
- The Erdős Problems database (ongoing) — 1000+ problems, Lean and AI progress tracked · the AI-contributions ledger (ongoing)
- More Than Two Thirds of the Zeta Zeros on the Critical Line (Aug 2026) — an experimental Claude improves the bound of record · the paper (Aug 2026) · Lean formalization (Aug 2026)
- The Jacobian counterexample, explained (Jul 2026) — the conjecture falls in dimension three, interactively · the Secret Blogging Seminar writeup (Jul 2026)
- Remarks on the disproof of the unit distance conjecture (May 2026) — nine mathematicians verify
- Semi-Autonomous Mathematics Discovery with Gemini (Jan 2026) — DeepMind loose on the Erdős problems
- Discovery of Unstable Singularities (Sep 2025) — neural nets find singularities in fluid flow
- Early science acceleration experiments with GPT-5 (Nov 2025) — Bubeck, Gowers, Eldan et al. with GPT-5
- AlphaEvolve: a coding agent for scientific and algorithmic discovery (Jun 2025) — new records, incl. 4×4 matrix multiplication
- Mathematical discoveries from program search with large language models (Dec 2023) — FunSearch evolves programs to a record cap set
The Mathematics of AI
- The Mathematics of Large Language Models (2026) — eight lectures, build your own LLM
- Neural Networks (3Blue1Brown) (2017–2024) — animated explainers
- Will AI Outsmart Human Intelligence? (Jul 2025) — Geoffrey Hinton's Royal Institution lecture, on video
- Andrej Karpathy (ongoing) — on YouTube: build GPT from scratch, and more
- Build Your Own Reasoning Model (Oct 2026) — Sebastian Raschka's video course, eight coding videos (about 11 hours) in Python and PyTorch: take a pre-trained Qwen3 0.6B and add evaluation, inference-time scaling, reinforcement learning with verifiable rewards, and distillation
- Who needs verifiable rewards? (Oct 2026) — Aashish Reddy and Harry Law at the Cosmos Institute: reinforcement learning on checkable math and code teaches conjecture-and-refutation habits that travel to domains without answer keys, with Popper and a Greenwich Personal Equation Machine
- The Bitter Lesson (Mar 2019) — Rich Sutton's two-page essay: seventy years of AI say that general methods that scale with computation beat built-in human knowledge · original essay (Mar 2019)
- Understanding Deep Learning (2023) — Prince's textbook, free online
- Deep Learning: Foundations and Concepts (2024) — Bishop & Bishop's textbook, free online
- A Mathematical Perspective on Transformers (Jul 2025) — Geshkovski, Letrouit, Polyanskiy & Rigollet in the Bulletin: attention as interacting particles · arXiv version (Dec 2023)
- On the Geometry of Deep Learning (Apr 2025) — Balestriero, Humayun & Baraniuk in the Notices: networks as piecewise-affine splines · arXiv version (Aug 2024)
- Differential Equations for Continuous-Time Deep Learning (May 2024) — Ruthotto in the Notices: residual networks as ODEs · arXiv version (Jan 2024)
- What is… an Equivariant Neural Network? (Apr 2023) — Lim & Nelson in the Notices · arXiv version (May 2022)
- Is Deep Learning a Useful Tool for the Pure Mathematician? (Apr 2024) — Williamson in the Bulletin, starting from what a neural network is · arXiv version (Apr 2023)
- Large Language Models: A Mathematical Formulation (Jan 2026) — Baptista, Stuart & Tran: tokenization, next-token architecture, training and deployment, from information theory, probability and optimization
- Large Language Models for Mathematicians (Dec 2023) — Frieder, Berner, Petersen & Lukasiewicz: a mathematical description of the transformer, and what LLMs can do
- Statistical Mechanical Approaches to Deep Learning (Oct 2026) — Zohar Ringel's mini-course at the Fields Institute, on video: infinite-width networks and kernels, feature learning and grokking, scaling laws, and a renormalization-group look at RLVR · the full playlist (Oct–Nov 2026) · the course page (Oct–Nov 2026)
- Neural Networks Are Already Clean (2026) — Nick Cammarata (Goodfire), an interactive essay with neuron viewers: much apparent polysemanticity and superposition is an artifact of weak architectures and tools, so interpretability may be more tractable than feared
- Sparks of Weight-Space Programming (Nov 2026) — Rikiya Takehi, Jayden Teoh, Alex Zhang, and Omar Khattab (MIT CSAIL): frontier LLMs reading and editing neural network weights directly in natural language, no gradient descent, from fixing a game-playing policy by hand to a 0.016% weight edit that lifts a small Qwen's MATH-500 score from 8% to 48%; early and limited, by the authors' own account
- Transformer Explainer (2024) — a live GPT-2 in your browser: embeddings, attention, and next-token probabilities as you type
- MicroGPT Visualizer (ongoing) — Karpathy's microgpt.py, step by step
- Tiktokenizer (ongoing) — watch text break into tokens
- Neural Network Playground (2016) — train a network in your browser
- Neural Canvas (2026) — David Bachman's browser workbench for teaching neural networks: build a network from individual operations, group them into neurons, layers, attention heads, and transformer blocks, train it, and inspect every value and gradient; comes with nineteen course assignments
- Neural Function Playground (2026) — my own: hand-wire a tiny network, drag the weights, and watch each neuron's function change
- Neural n-gram Explorer (2026) — my own: a tiny neural language model over Shakespeare, every parameter editable, training stepped one example at a time, its whole probability table compared with the corpus
Wrestling with the Future
- The AI Futures Project (ongoing) — Kokotajlo's forecasting shop · AI 2027 (Apr 2025) · AI 2040: Plan A (Jul 2026)
- AI Digest (ongoing) — interactive explainers and demos
- The AI Village (ongoing) — frontier agents on real computers, all day · a good starting point: Gemini's compounding misalignment (Aug 2026)
- Emergence World: Adversarial Stress-Testing of Long-Horizon Multi-Agent Systems (Sep 2026) — eight towns of ten agents, 16 days, then phishing, misinformation, and a memory leak: alignment is not compositional · the worlds themselves (ongoing)
- Open-ended and AI-generating Algorithms in the Era of Foundation Models (Sep 2025) — Jeff Clune's SRI seminar, on video · his essay: why work on self-improving AI despite the risks (May 2026) · The AI Scientist (Sakana AI) (Aug 2024) · its first peer-reviewed paper (Mar 2025) · Darwin Gödel Machine (May 2025)
- The ‘Breaking’ News: The OpenAI–Hugging Face Incident (Aug 2026) — Black Hat talk, on video: an evaluation agent escapes its sandbox · Dwarkesh Patel: The Rise and Fall of Agent Civilizations (Aug 2026)
- AI Models May Be Capable of Self-Replicating Without Access to a Datacenter (Oct 2026) — Zhou & Freeman (Anthropic Frontier Red Team): a 9B-parameter model runs on 8 of 9 kinds of cheap, poorly secured devices, and stronger models complete simplified end-to-end replication
- The Machine Consumes Itself (Jun 2026) — Manabu on AI and the end of publish-or-perish
- Pessimists Archive (ongoing) — “fears about old things when they were new”
- Shaping the Future of Mathematics in the Age of AI (Jun 2026) — Commelin, Jamnik, Ochigame, Taelman & Venkatesh in the Notices
- Machine-Assisted Proof (Jan 2025) — Tao in the Notices
AI Safety
- AI-Safety for Mathematicians (ongoing) — research directions, from Tsimerman et al. · Tsimerman in the Notices: getting to the fun faster, and worrying about the future (Aug 2026)
- Why Should Mathematicians Work on AI Safety? (Sep 2026) — Yevgeny Liokumovich at the Columbia Geometric Analysis Seminar, on video: capability growth, catastrophic risk, and reading an LLM's thoughts in the geometry of its activations
- Mathematics for AI Safety (Fall 2026) — Liokumovich's graduate course at the Fields Institute (Toronto MAT1510), lectures on video: capability forecasting, theory of deep learning, interpretability, scalable oversight, multi-agent interactions, formal methods · the course page (Fall 2026)
- From Academia to Alignment (Sep 2026) — Mike Winer's story of leaving physics for the Alignment Research Center: the dread, the worry hour, and the mistakes along the way · his view of ARC's research agenda: mechanistic estimators, the Matching Sampling Principle, and problems to hand to mathematicians (Jun 2026)
- RESI, the Institute for Responsible Superintelligence (ongoing) — Goldwasser, Vaikuntanathan and Kalai's nonprofit: cryptography and formal methods for safety by design
- The Feasibility of a Hardwired Pause of Frontier AI Training (2026) — a Berkeley-led working group (Fithian, Holliday, Russell, Krueger, and others) on a verifiable international pause: stop making training-capable chips, phase out the stock, switch to inference-only hardware · executive summary (2026) · full report (2026)
- Addressing Broader AI Risks as Mathematicians (2026) — Xiaoyu He and Francis Su, for MAA Focus: why X-risk is a credible possibility, and concrete steps mathematicians can take, from advocacy to rethinking teaching and assessment
- Existential Risk from AI: An Exposition for Mathematicians (Aug 2026) — an essay by Xiaoyu He
- A Taxonomy of Omnicidal Futures Involving Artificial Intelligence (Jul 2025) — Critch & Tsimerman classify the ways it could end, so as to prevent them
Substacks
- Silicon Reckoner (ongoing) — Michael Harris on what computers will do for, or to, mathematics
- Entropy Bonus (ongoing) — David Bachman navigating the chaotic terrain of AI
- David Bessis (ongoing) — the author of Mathematica, on mathematical cognition and AI
- Ahead of AI (ongoing) — Sebastian Raschka on machine learning research
- Deep (Learning) Focus (ongoing) — Cameron Wolfe explains AI research topics
- Gradient Ascent (ongoing) — Sairam Sundaresan's weekly guide to AI
- AI Futures Project (ongoing) — Kokotajlo et al., preparing for a world with AGI
- The Third Hemisphere (ongoing) — Tim Requarth, a neuroscientist's field notes on AI and our brains