A tour of some of the current features of CatColab, as of the recent release of version 0.2: Wren.

via: https://johncarlosbaez.wordpress.com/2025/10/05/negative-mass-part-2/

I’ve been studying the physics of negative mass. Basically it doesn’t exist.

“Correct” doesn’t mean “correct” when correctly using “correct”

via: https://buttondown.com/hillelwayne/archive/three-ways-formally-verified-code-can-go-wrong-in/

We programmers need all the help we can get, and we should never assume otherwise. Careful design is great. Testing is great. Formal methods are great. Code reviews are great. Static analysis is great. But none of these things alone are sufficient to eliminate bugs: They will always be with us. A bug can exist for half a century despite our best efforts to exterminate it. We must program carefully, defensively, and remain ever vigilant.

via: https://lukeplant.me.uk/blog/posts/breaking-provably-correct-leftpad/ via: https://buttondown.com/hillelwayne/archive/three-ways-formally-verified-code-can-go-wrong-in/

Acsets are a novel infrastructure for handling data of different shapes, based on category theory and implemented in Catlab.jl. Acsets generalize both graphs and dataframes, and allow a much more general approach to data manipulation than was previously available. We will discuss both the mathematics of acsets and some of the metaprogramming techniques we used to implement them in Julia. Finally, we will give examples of how acsets have been key in developing many projects in AlgebraicJulia.

Probably the best AlgebraicJulia tutorial on the planet LOL.

One often hears it said that “absence of evidence is not evidence of absence”. For example, if you excavate some fossil sauropods and they don’t have preserved feathers, that not evidence that sauropods didn’t have feathers. Oh yes it is.

I am a PhD student in Sam Staton’s group at Oxford University and a research software engineer at Topos Research UK. My current aim in research is to build domain specific languages for categorical systems theory.

Categorical systems theory is the study of the design and analysis of systems using category theory. Category theory is a hopelessly abstract branch of pure mathematics, so abstract that even the other mathematicians refer to it as “abstract nonsense”. Why would anyone want to study such complex and concrete situations as general systems with a branch of mathematics so divorced from reality? In this blog post, I hope to answer that question. I want to say what the point of doing systems theory categorically is; what the main take-away lesson is, beyond the technicalities. I also want to show that category theory isn’t divorced from reality at all; it’s just general purpose.

via: https://ncatlab.org/nlab/show/category+theory+for+dynamical+systems

We introduce a versatile method for finding prime numbers that display surprisingly intricate visual patterns— hypothetically, any desired pattern is possible, with only mild distortion. We use this method to locate several examples of large prime numbers that are, in and of themselves, self-referential works of art.

How to be taken seriously

Great pair of talks.

via: https://golem.ph.utexas.edu/category/2025/10/a_complex_qutrit_inside_an_oct.html

Mathematicians cannot determine whether multiplying pi by itself repeatedly might produce a whole number

My research focuses on “homotopical physics”: the interplay between mathematical physics (particularly quantum field theory) and higher (aka categorical) algebra. Other buzzwords that describe my work: higher symmetries, topological field theory, phases of condensed matter, “moonshine” phenomena, perturbative quantization, categories, representation theory, and algebraic topology.

via: https://golem.ph.utexas.edu/category/2025/10/a_complex_qutrit_inside_an_oct.html#c069081

The writer Ta-Nehisi Coates joins Ezra Klein on the show to discuss how the left should think about the work of politics and persuasion in this moment.

In which Ezra Klein partly redeems himself.