MixedMath - explorations in math and programing

Typesetting tables in latex is annoying. In practice, I usually have the tabular data in some programming-friendly format and need to put it in latex. I forget how to do this nicely, but it's extremely simple using the tabulate package in python. import tabulate from itertools import batched # Data A = [ 1, 2, 3, 4, 5, 6, 7, 10, 11, 14, 15, 17, 19, 21, 23, 26, 31, 34, 35, 39, 41, 47, 51, 55, 59, 71, 79, 87, 95, 111, 119, 131, 143, 159

There is no reason why amateurs can't make worthwhile contributions to research mathematics. But there is also no reason why every mathematician must listen to any particular amateur.1 1This is much more true now that it's easier to write mathlike documents with help from an LLM. I don't have time to offer personal advice or guidance to everyone who contacts me.2 2If I have sent you to this page, it likely means that I have also given you a boilerplate response. You've probably asked me for…

I write most professional correspondence in either plaintext (markdown) or latex+pdf. I recently had to make two versions of the same document in latex and Google Docs.1 1This is unnatural. The medium of communication affects both the reading and writing experience. But I don't explain why, and instead merely comment on how. Eventually the latex+pdf version will be made public, so I write the initial draft in latex. The Venting Part Latex is a more powerful and easier drafting language than…

I've heard it said that reading LLM prose is a bit like remembering a dream. It can be ok if you were the one who had the dream, but all details are fuzzy and unhelpful if you try to describe it to others. Nonetheless, I think it can be useful to share LLM-generated or LLM-assisted writing with explicit AI content warnings. For now, I will give AI content warnings in approximately the following shape: AI Written (and implicitly I think you need a very good reason to share unedited AI output) AI…

You know what's great? Writing things down and sharing them. I want to do that more here. To make this happen more, I'm going to intentionally, deliberately lower the bar for what I think is suitable to put here. I might get lucky and have a quantity-breeds-quality aspect. But I also know that I've been emailing and zuliping a manner of notes that I've written over the last few years that aren't available here. Why not? Because the bar is too high! So I'm going to lower it.

At today's Paper Talk session cohosted by IDI, I'm giving a talk today on the paper "The Free Transformer" by Fleuret (preprint available here). This paper describes a modification of the standard decoder-only transformer that learns to condition token generation on random latent variables learned without supervision. We describe some of the intuition and background for the new architecture. My talk is a RevealJS presentation, and is available here. This architecture is very straightforward t...