Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao Subscribe to feed NOTE: these pages are no longer maintained. The updated version of these pages can be found here . Here I collect some links to some of my Mastodon posts , organized loosely by theme, together with some other miscellaneous posts outside of the Mastodon platform. Current events and personal thoughts: My personal traversal of Maslow’s hierarchy of needs after the election (Nov 7, 2024) An illustration of survivor bias during the Los Angeles fires (Jan 9, 2025) On the need to adopt complex solutions, and understand the limitations of simpler models, in a complex world (Jan 22, 2025) On the appropriate amount of reliance on metrics and quantitative reasoning in real world problems (Jan 28, 2025) On the complexities of mean field games, and the real-world impact of executive orders on fields such as mathematics (Jan 29, 2025) On the steep NSF spending cuts (May 25, 2025) On the precious nature of the consensus objective standard of mathematical truth, and the need to defend it (July 5, 2025) On how the modern world requires emerging forms of game theory that view the information space itself as a primary battleground (July 17, 2025) NSF and NIH suspend its funding to UCLA, and to IPAM in particular (Aug 1, 2025) On the compressed sensing work I did at IPAM (Aug 3, 2025) IPAM fundraising (Aug 7, 2025) A partial restoration of NSF funding by court order (Aug 13, 2025) On the compressed sensing work I did at IPAM (Aug 3, 2025) IPAM fundraising (Aug 7, 2025) A partial restoration of NSF funding by court order (Aug 13, 2025) On the decline of small grassroots organizations in society (Sep 29, 2025) Mathematical topics: An example of Simpsons paradox: the more failures an author has, the more likely the author is to be competent (Nov 20, 2022) Using symmetries to reduce a problem to special cases (Dec 3, 2022) Using Bayesian probability to measure bias (Jan 14, 2023) Viewing quantifier elimination and introduction of variables as a “wolf, goat, and cabbage” problem (Jun 13, 2024). On applying the laws of algebra strategically, by performing “gradient descent” on the complexity of the expression (Jul 1, 2024). My personal experience using kinesthetics (specifically, “rolling around on the floor”) to help me with a math problem (Nov 11, 2024). Using simplified probabilistic models to explore the interaction of personal risk and external risk in decision-making (Nov 13, 2024). An example of how numerics can be used to detect and fix errors in a paper (Mar 27, 2025). A short rule of thumb on when to use coordinates and concrete constructions, and when to use abstract, coordinate-free formalisms (May 5, 2025). Metamathematical or philosophical musings: On the role of speculation in mathematics (Nov 24, 2022) Memes as a means of communicating mathematical relationships (Nov 26, 2022) Mathematical critiques of real-world theories based on discontinuities (Dec 27, 2022) Mathematical collaboration requires both optimists and pessimists (Jan 4, 2023) Breaking up a difficult statement into statements of easier difficulty (Jul 15, 2023) Explaining mathematics to a non-mathematician (Jul 19, 2023) Opposition between technical meaning and colloquial meaning (Jul 30, 2023) On claimed superconductors and the notion of partial success (Aug 5, 2023) On the importance of incentive gradients (Feb 23, 2024) The implicit notational conventions of round numbers (Mar 18, 2024) On the conceptual and technical complexity of papers, and Berkson’s paradox (May 29, 2024) On the correct amount of mathematical analysis to use in a given situation (Nov 14, 2024) On the routine nature of rejection of submitted papers (Dec 26, 2024) On the uses and types of negative results in science and mathematics (Mar 15, 2025) The distinction between accuracy and inerrancy (Mar 21, 2025) AI, proof assistants, and other machine assistance: First encounter with ChatGPT (Dec 2, 2022) AI tools and homework assignments (Dec 19, 2022) On the lack of stylistic signals of importance in LLM-generated text (Feb 28, 2023) ChatGPT as a semantic search tool (Mar 5, 2023) AI tools as probability kernels (Mar 5, 2023) ChatGPT and bibliography formatting (Mar 13, 2023) Two minor use cases for ChatGPT (Mar 19, 2023) (see also this post ) 2000 “Visions in Mathematics” view of AI, compared with 2023 reality (Mar 25, 2023) AI and Cunningham’s law (Apr 4, 2023) ChatGPT saving me significant time on a data processing task (Apr 9, 2023) Comparative advantage between human experts and AI (Apr 23, 2023) Three different types of AI misinformation (Jun 2, 2023) Trying GPT-4 on a MathOverflow question (Jun 24, 2023) Automatic universal algebra proving as an AI project? (Jul 18, 2023) ChatGPT generating Python code (Sep 1, 2023) Installing VSCode (Sep 3, 2023) Using ChatGPT and Cocalc AI to write in SAGE (Sep 5, 2023) Github Copilot as a form letter writing tool (Sep 6, 2023) (see also this previous post ) Github Copilot as a mathematical blog post writing tool (Sep 30, 2023) Journaling my Lean learning process: Oct 9 2023 , Oct 10 2023 , Oct 11 2023 , Oct 12 2023 , Oct 14 2023 part 1, Oct 14 2023 part 2, Oct 14 2023 part 3, Oct 16 2023 , Oct 17 2023 . On the formalization of the symmetric polynomials paper (Nov 5, 2023) – see also previous updates here , here , here , here , here , here , here , and here . On the formalization of the PFR paper (Nov 18, 2023) On the need to address both false positives and false negatives in AI-generated deepfakes (Jan 30, 2024) On finding errors in an already formalized proof (Apr 25, 2024) Explaining a proof to ChatGPT, which then provides a LaTeX version (June 14, 2024) Using ChatGPT and Python to create graph illustrations of informal concepts (Jul 5, 2024) Initial impressions of GPT-o1 (Sep 13, 2024) Using LLM queries to augment understanding of a lecture in a different field (Feb 27, 2025) Comparing LLM queries with web searches for locating reasonably standard arguments (Mar 10, 2025) Large language models and proof assistants as a continuation of a millennia-long trend of increasing mathematics automation (Mar 26, 2025) On how the difficulty and acceptable failure rate of a task factors into considerations of suitability for AI-powered automation (Mar 29, 2025) On how one needs to consider metrics at multiple scales when measuring the efficiency of automation (in the context of autoformalization, at least). (May 13, 2025) On the crucial importance of standardized methodology when evaluating AI performance at mathematics competitions (July 20, 2025) As AI matures, one needs to transition from qualitative achievements to quantitative benchmarks (July 24, 2025) There is a stronger case for AI use in “red teaming” than “blue teaming” (July 25, 2025) AI tools need a clear “failure mode” in addition to a useful “success mode” (Aug 24, 2025) In the age of AI, project organizers need to state both explicit and implicit goals. (Sep 13, 2025) An example of how an extended conversation with AI, combined with external verification, can complete a solution to a MathOverflow problem (Oct 2, 2025) An update on a more definitive solution to that problem, obtained largely via crowdsourced effort (Oct 4, 2025) A second update, on an even more definitive solution (Oct 5, 2025) A third update, on the occasional non-monotonicity of mathematical research (Oct 6, 2025) An update on a more definitive solution to that problem, obtained largely via crowdsourced effort (Oct 4, 2025) A second update, on an even more definitive solution (Oct 5, 2025) A third update, on the occasional non-monotonicity of mathematical research (Oct 6, 2025) An experiment with using advanced AI on a problem outside of my area of expertise (Oct 10, 2025) The most productive near-term use cases of AI in mathematics will be on accelerating mundane tasks such as literature review (Oct 16, 2025) A complex story of how humans, numerics, ChatGPT, Lean, and the literature interacted to solve an Erdos problem (Oct 21, 2025) My experiment with “vibe coding” (Nov 4, 2025) AI assistance is becoming routine at the Erdos problem site (Nov 21, 2025) The space of cognitive tasks is very high-dimensional (Nov 26, 2025) AI is beginning to find success in the “long tail” of open mathematical problems (Nov 30, 2025) Artificial General Cleverness (Dec 14, 2025) An empirical correlation between AI-solvability of an Erdos problem, and the problem already being proved in the literature (Dec 26, 2025) AI tools permit the rapid creation of alternate (but still Lean-verified) writeups of an argument, both by the original author and by third parties (Jan 7, 2026) An empirical tradeoff between the amount of AI used in a solution, and the depth of that solution (Jan 13, 2026) On the reporting bias against negative results for AI attacks on open math problems (Jan 17, 2026) Modern machine assistance is, paradoxically, reviving some archaic mathematical practices (Feb 8, 2026) On the value of selective friction in AI assistance in mathematics (and other idea-powered activities) (Feb 22, 2026) An analogy between AI and the automobile, and the need for “AI planning” (Mar 18, 2026) A casual experiment on using AI chatbots with fictional personalities as a “splash of vanilla” in education (Apr 11, 2026) Douglas Adams’ three phases of galactic civilization (Survival, Inquiry, and Sophistication) in the age of AI (Apr 20, 2026) The three components of problem solving: proof generation, proof verification, and proof digestion (Apr 22, 2026) The transfer of prestige between these components as one enters an era of proof abundance (Apr 27, 2026) Why overoptimizing on metrics of “proof digestibility” may undermine the net appeal of a proof (May 10, 2026) The transfer of prestige between these components as one enters an era of proof abundance (Apr 27, 2026) Why overoptimizing on metrics of “proof digestibility” may undermine the net appeal of a proof (May 10, 2026) Using Claude Code to implement minor corrections from a referee report (May 4, 2026) My new, and significantly more restrictive, policy on commenting on new proofs in my field (May 12, 2026) My endorsement of the Leiden declaration (June 2, 2026) In my formalization projects, the bottleneck has shifted from formalization to review, refactoring to Mathlib quality, and issue design (June 21, 2026) My experiences at an IPAM workshop on Machine Assisted Proof (Feb 13, 2023) Viewing historical mathematical documents at the French Academy of Sciences (Mar 22, 2023) Visually seeing the curvature of the Earth while on vacation (Jul 7, 2023) My experiences at a Warsaw/Kyiv math conference (Aug 7, 2023) Update #1 , Update #2 , Update #3 An unusual optical phenomenon arising from a solar eclipse (Apr 11, 2024) I have found that answering MathOverflow questions sometimes provide an opportunity to make a broader point beyond the narrow scope of the original question. Here are some selected answers of mine in this vein: Using physical intuition to buttress mathematical intuition (Nov 18, 2009) How to think about Sobolev spaces (Mar 11, 2010) Thinking about higher dimensions (May 27, 2010) On what it means to be unprovable (Jun 11, 2010) On the preference for minimalism in mathematical foundations (Jul 1, 2010) Some of my conceptual frameworks for thinking about mathematics (Sep 15, 2010) On the desirable features of different types of mathematical notation (Jul 20, 2020) How to justify a complicated looking step in a paper one is reading (Oct 4, 2023) (see also this followup ) A description of my problem solving process for a specific MO question (Jun 3, 2024) How to think about functional inequalities such as the Sobolev inequality (Jun 26, 2024) Finding the right balance between “optimism” and “pessimism” when solving mathematical problems (Feb 2, 2025) In some cases, the text medium is not ideal for a demonstration (particularly if it involves interactive code), so I have made a few videos for some concepts that are best illustrated in that medium: Formalizing a proof in Lean using Github Copilot and canonical , May 11, 2025. Formalizing a proof in Lean using Claude and o4 , May 13, 2025. Formalizing a proof in Lean using Github Copilot only , May 17, 2025 Formalizing a proof in Lean by hand , May 25, 2025. Formalizing a proof in Lean using Claude Code , Mar 7, 2026. Golfing and stylistically aligning a proof using Claude Code , May 23, 2026. Also, here are some links to some of my articles, talks and interviews outside of Mastodon: 2015 Math Panel with Donaldson, Kontsevich, Lurie, Tao, Taylor, Milner , Breakthrough Prize Symposium, Nov 14, 2014. (Contains some speculation about machine-assisted proof and AI which has become increasingly relevant in recent years.) The World’s Best Mathematician (*), Numberphile, Mar 14, 2017. Interview at CIRM , Oct 2-6, 2017. Four Minutes with Terence Tao , Simons Foundation, Feb 23, 2018. Terence Tao teaches mathematical thinking , Masterclass, 2022. “ The value in “Dumb” questions “, interview with Dr. Berger, September 14, 2022. “ Embracing change and resetting expectations “, T. Tao, Microsoft Anthology, June 12, 2023. “ What makes for ‘Good’ Mathematics “, interview with Steven Strogatz, Feb 1, 2024. “ Supercharging Research: Harnessing Artificial Intelligence to Meet Global Challenges “, PCAST report, April 2024. “ AI Will Become Mathematicians’ ‘Co-Pilot’ “, Christoph Dresser, Scientific American, June 8, 2024 “ KI wird ein großartiger Kopilot für Mathematiker sein “, Christian Dresser, Spektrum, Mar 7, 2024. (Original version of the above article.) “ KI wird ein großartiger Kopilot für Mathematiker sein “, Christian Dresser, Spektrum, Mar 7, 2024. (Original version of the above article.) “ Machine assisted proof “, T. Tao, Notices Amer. Math. Soc., Vol. 72 (1), January 2025. ( Video version ) “ Terence Tao on the cosmic distance ladder “, 3Blue1Brown, Feb 8, 2025. “ Terence Tao continuing history’s cleverest cosmological measurements “, 3Blue1Brown, Feb 23, 2025. “ Terence Tao continuing history’s cleverest cosmological measurements “, 3Blue1Brown, Feb 23, 2025. “ The Potential for AI in Science and Mathematics “, Oxford Mathematics Public Lecture, July 17, 2024. “ The Future of Math with o1 Reasoning “, OpenAI Forum, December 3, 2024. With Mark Chen and James Donovan. “ Machine-Assisted Proofs “, Simons Presidential Lecture, Feb 19 2025. “ Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI “, Lex Friedman podcast, June 14, 2025 “ He’s the ‘Mozart’ of Math and Trump killed his funding “, Jonathan Cohn, The Bulwark, Aug 6, 2025. “ I’m an award-winning mathematician. Trump just cut my funding. “, Home of the Brave, Aug 18, 2025. “ Great Immigrant: Terence Tao “, Carnegie Corporation of New York, Aug 21, 2025. “ The ‘Mozart of Math’ rarely speaks on politics. The wide-ranging cuts to science funding made him change that. “, Evan Bush, NBC News, Aug 26, 2025. “ The world’s greatest mathematician avoided politics. Then Trump cut science funding “, Carolyn Johnson, Washington Post, Sep 7, 2025. “ Losing support for research means losing our best and brightest “, UCLA interview, Sep 9, 2025. “ Terence Tao: Research powers progress “, UCLA, Sep 9 2025. “ Is Math the Next AI Frontier? A Conversation with Terence Tao “, Tom Kalil, Renaissance Philanthropy, Sep 29 2025. “ The mathematicians teaching AI to reason “, Sascha Brodsky, IBM Think, Oct 13 2025. “ Best practices for incorporating AI etc. in papers “, AI-math discussion, Oct 22, 2025. “ Top researchers consider leaving U.S. amid funding cuts: ‘The science world is ending’ “, Stephanie Sy, Mike Fritz, Sam Weber, PBS News Hour, Oct 29, 2025. “ Terence Tao Explains How AI Fits Into Scientific Research “, SAIR, Nov 11, 2025. “ Terry Tao: “Trump CUT My Funding.” Here’s how I am going to react. “, Brian Keating, Nov 17, 2025. “ Mathematicians say Google’s AI tools are supercharging their research “, Alex Wilkins, New Scientist, Nov 18, 2025. “ Terence Tao & Riley Tao: Turning AI’s Firehose Into Usable Science “, SAIR, Dec 10, 2025 “ AI is solving ‘impossible’ math problems. Can it best the world’s top mathematicians? “, Kit Yates, LiveScience, Dec 19, 2025. “ Can AI help us solve the hardest problems in Mathematics? (ft. Terry Tao) “, Brian Keating, Dec 30, 2025. “ Terry Tao on the future of mathematics “, Math, Inc., Dec 30, 2025. “ Terence Tao, inaugural Veritas Fellow — autoformalizing number theory “, Math Inc., Jan 7, 2026. “ Can AI Prove It? Terence Tao on “Big Math” and Our Theoretical Future “, The Futurology Podcast, Jan 20, 2026. “ Math maestro Terence Tao *96 is solving the world’s puzzles “, Don Steinberg, Princeton University Alumni, Feb 9, 2026. “ Why I co-founded SAIR “, Feb 10, 2026. “ Machine Assistance and the Future of Research Mathematics “, AI for Science Kickoff, Feb 10, 2026. Madison Medal Lecture , Princeton University’s Alumni Day, Feb 21, 2026 Daily Princetonian article (Aitana Camponovo, Mar 16, 2026) Daily Princetonian article (Aitana Camponovo, Mar 16, 2026) “ The Edge of Mathematics “, Matteo Wong, The Atlantic, Feb 24, 2026. “ Is the Universe a Math Problem? With Terence Tao “, StarTalk with Neil DeGrasse Tyson, Feb 24, 2026. [ Youtube version ] “ Terence Tao and Mark Chen – Fireside Chat with James Donovan ” – IPAM at UCLA, Mar 4, 2026. “ What does it mean to think like a mathematician? “, Curtis Center Pi Day event, Mar 14, 2026. [ Youtube version ] “ Terence Tao – How the world’s top mathematician uses AI “, Dwarkesh Patel, Mar 20, 2026. “ Terence Tao and Tanya Klowden: Mathematical Methods and Human Thought in the Age of AI “, SAIR, Apr 7, 2026. “ The music of the spheres “, Terence Tao and Zach Wienersmith, Saturday Morning Breakfast Cereal, Apr 9, 2026. [ Part 1 ] [ Part 2 ] [ Part 3 ] [ Part 4 ] [ Part 5 ] “ Qué hace a Terence Tao “el mejor matemático vivo del mundo” “, Margarita Rodríguez, BBC News Mundo, Apr 18, 2026. “ ‘The job description is changing’: mathematician Terence Tao on the rise of AI “, Davide Castelvecchi, Nature, Apr 27, 2026. “ New Mathematical Workflows “, Future of Mathematics Symposium, Stanford, May 2, 2026. ( slides ) “ The Integrated Explicit Analytic Number Theory Network: a progress report “, ICERM talk, May 15, 2026. ( slides ) “ How Terry Tao Became an Evangelist for AI in Math “, Kevin Hartnett, Quanta, June 6, 2026. “ Award-winning maths prodigy Terence Tao on the importance of making mistakes “, ABC Radio, June 7, 2026. “ How should university students control their AI diet? “, 2026 EMS Lecture Series on Mathematics Education. Lecture 6, June 12, 2026. ( slides ) “ What it means to be a mathematician when AI does the Math “, Ben Skuse, IEEE Spectrum, June 25, 2026. Finally, my instagram account on “Climbing the Cosmic Distance Ladder” , with Tanya Klowden, has a number of additional astronomy-themed essays. I also collect here some selected talks, essays, or articles by others on the interaction between math, AI, and proof assistants. Jeremy Avigad, “ Mathematicians in the age of AI “, Mar 2026. David Bessis, “ The fall of the theorem economy “, Apr 21, 2026. Johan Commelin, Mateja Jamnik, Rodrigo Ochigame, Lenny Taelman, Akshay Venkatesh, “ Shaping the Future of Mathematics in the Age of AI “, Mar 2026. David Donoho, “ Data science at the Singularity “, Oct 2023. Timothy Gowers, “ Rough strcuture and classification “, GAFA 2000 Special Volume “Visions in Mathematics”, 79-117 (see in particular the section “Will Mathematics Exist in 2009?”). Martin Hairer, “ Does Mathematicians need computers? “, Simons Foundation, Dec 5, 2025. Minas Karimanis, “ The machines are fine. I’m worried about us. “, Mar 30, 2026. Daniel Litt, “ Mathematics in the Library of Babel “, Feb 21, 2026. Heather Macbeth, “ Algorithm and abstraction in formal mathematics “, May 2024.

Emily Riehl, “ A New Paradigm for Mathematical Proof? “, Hopkins Natural Philosophy Forum, Nov 7, 2025. Talia Ringer, “ Proofs and Conversations “, AMS Early Career Notices, May 2024. Akshay Venkatesh, “ What do we tell our students about AI? “, Mathematics in the age of automated proofs, Oct 1, 2025. The Bulletin of the AMS published two issues devoted to mathematics and AI, featuring articles by Fraser-Granville-Harris-McLarty-Riehl-Venkatesh, Venkatesh, Buzzard, Avigad, Commelin-Topaz, Shulman, Williamson, Davis, Cheng, Granville, Harris, Romeo, DeDeo, Davies, De Toffoli, McLarty, Ochigame, Poggio-Fraser, and Bengio-Malkin. The Feb 2023 IPAM workshop on Machine Assisted Proofs has a number of interesting talks recorded on these topics. Recent Comments Why I didn't sign the Fields medallists' letter A Severe Misalignment of AI in Mathematics A CERN for AI-assisted science? 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Polymath 13 – a success! Non-transitive Dice over Gowers’s Blog To enter in LaTeX in comments, use $latex <Your LaTeX code> $ (without the < and > signs, of course; in fact, these signs should be avoided as they can cause formatting errors). Also, backslashes \ need to be doubled as \\. See the about page for details and for other commenting policy. Blog at WordPress.com. Ben Eastaugh and Chris Sternal-Johnson. Subscribe to feed. Subscribe Subscribed What's new Already have a WordPress.com account? Log in now. Already have a WordPress.com account? Log in now. What's new Subscribe Subscribed Sign up Log in Copy shortlink Report this content View post in Reader Manage subscriptions Collapse this bar Subscribe Subscribed Report this content View post in Reader Manage subscriptions Collapse this bar