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.
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).
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)
AI, proof assistants, and other machine assistants:
- 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)
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)
- 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)
Also, here are some links to some of my articles and interviews outside of Mastodon:
- “Embracing change and resetting expectations“, T. Tao, Microsoft Anthology, June 12, 2023.
- “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
- “Machine assisted proof“, T. Tao, to appear, Notices AMS.
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