Mastodon

Here I collect some links to some of my Mastodon posts, organized loosely by theme.

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 (Jul 13, 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)

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)

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.