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On Some Problems from the Kourovka Notebook

With Wouter van Doorn, Pietro Monticone, and Daniel Morrison, I released a preprint presenting solutions to eight problems from the Kourovka Notebook.

Paper and Lean source · arXiv

Sharing ChatGPT’s skill files

I shared copies of the files in ChatGPT’s /home/oai/skills directory: instructions and resources for working with documents, PDFs, and spreadsheets. The archive was obtained by asking ChatGPT to zip the directory.

In his December 12 write-up, Simon Willison credited me with bringing these skills to his attention and linked to the repository. He then tried the same export and explored how ChatGPT used the files.

Simon Willison’s write-up · Repository

Links saved with the December 2025 entry about OpenAI skills.

Write-up, discussion, and repository

Guillaume Brümmer’s 90th conference

Guillaume C. L. Brümmer’s 90th conference took place at the University of Cape Town on December 12–13, 2024. It was organised by George Janelidze with assistance from Jacob Lund.

Speakers and programme

Tarski on logical notions

we call a notion “logical” if it is invariant under all possible one-one transformations of the world onto itself.

Alfred Tarski, What are logical notions?, 1986, p. 149. The passage asks what remains invariant under the widest class of transformations: every one-to-one transformation of the universe of discourse onto itself.

Full passage saved with the November notes

Finitely complete co-pretoposes are ideally exact

James R. A. Gray’s category theory seminar, November 6: Finitely complete co-pretoposes are ideally exact.

Seminar abstract and references

Began attending the weekly seminars held by George Janelidze at UCT with Stellenbosch University in August 2024, with research talks by members of the category theory group.

Yvonne Lundie from SAOTA’s resource centre contacted me to consult on archiving architectural materials with a view towards the right use of artificial intelligence.

Ording, Oulipo, and mathematical style

I’ve been working through Philip Ording’s 99 Variations on a Proof. Its attention to mathematical style has helped clarify some ideas about my own writing.

Ording’s introduction mentions Oulipo, particularly Raymond Queneau’s Exercises in Style. I had encountered Oulipo before and was interested in its use of mathematics in literature and its structural constraints. I started reading the Oulipo Compendium and All That Is Evident Is Suspect: Readings from the Oulipo: 1963 - 2018 to learn more.

Reading geometry visually

Jeffrey R. Weeks’s The Shape of Space stretched my imagination: I had to work at visualising the spaces it describes.

I used it as a visual complement to differential geometry, alongside Tristan Needham’s Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts. Needham’s visual exposition complemented the more rigorous, algebraic course notes.

I came to this book through his Visual Complex Analysis. Its approach was quite different from my complex analysis course, and I found its visual intuition beautiful.

Reading Einstein and Gödel

I started Abraham Pais’s Subtle is the Lord: The Science and the Life of Albert Einstein to learn more about general relativity and Einstein’s work. Much of the book explains the work itself and how Einstein arrived at his ideas.

I’ve also been reading Stephen Budiansky’s Journey to the Edge of Reason: The Life of Kurt Gödel. Alongside Gödel’s life and work, it describes early twentieth-century Vienna and the beginnings of the Vienna Circle.

Other reading from January 2022

Badiou on mathematics

I finished Alain Badiou’s In Praise of Mathematics as part of my interest in modern continental philosophy. Through a dialogue, it explores mathematics’ influence on philosophy and Badiou’s fascination with the subject, although he says little about contemporary mathematics.

Reading Zalamea

I’ve read most of Fernando Zalamea’s Synthetic Philosophy of Contemporary Mathematics, jumping between sections. Much of it went over my head.

The sections on Albert Lautman and Michael Atiyah were particularly illuminating; Lautman’s work on structuralism was new to me. I found the bibliographic survey and biographical sketches the most accessible, and expect to return to the book.