#OnThisDay #Balfour #Declaration proclaims support for a Jewish state in #Palestine (1917).

Birth Anniversary of George Boole (1815) - best known as the author of The Laws of Thought (1854) which contains #Boolean #Algebra.

Today is International Day to End Impunity for #CrimesAgainstJournalists.

https://knowledgezone.co.in/news

I've found a citation of my own work on Wikipedia for the first time!

https://en.wikipedia.org/wiki/Commutative_magma

Naturally, I read this page before I wrote my rock-paper-scissors paper. It's neat to see that my own work is now the citation for something that was unsourced "original research" on Wikipedia.

The notion of epimorphism can be quite different from surjection, e.g. in Rings.

Though I recently learned epimorphisms can be characterized in terms of Isbell's zig-zags: https://en.wikipedia.org/wiki/Isbell%27s_zigzag_theorem.

Whereas monic seems to capture the notion of "injective" quite well in a categorical def. And indeed the two agree on any variety of algebras in the sense of universal algebra.

There are different translations for al-Khwarizmi’s book title “Al-Jabr wa’l muqabalah” from which the name algebra is derived, but my favorite is “The Compendious Book on Calculation by Completion and Balancing”

My fourteenth Math Research Livestream is now available on YouTube:

https://www.youtube.com/watch?v=pVoFfZAyXzk

I talked about some topics related to my recent preprint (https://arxiv.org/abs/2409.12923) about topological lattices.

I decided to skip streaming today because I wanted to talk about polyhedral products, but I haven't found the old calculation that I wanted to talk about yet. Shocking I couldn't find something I did like six years ago in the ten minutes before I would start streaming. I'll look for it now, so hopefully I'll be ready next week.

#Mathober #Mathober2024

The prompt for day 4 was 'Form'. In algebra, a multilinear map is a function from several vector spaces to another vector space which is linear in each argument. Just as a linear map can be represented by a grid of numbers in a matrix, a multilinear map can be represented by a multidimensional grid of numbers: a tensor. A 'form' is the function you get by taking a multilinear map from V×...×V to the scalars and evaluating it with each of its arguments the same. In this way you get a *non*linear map from V to the scalars.

The image shows a degree 50 form on ℝ³ evaluated on the unit sphere. The form was randomly chosen with each of the 3⁵⁰ entries in its tensor having a standard normal distribution.