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 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 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)
Miscellaneous
- 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.
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.)
- “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.
- “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)
- “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.
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.
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