With the recent results from OpenAI, Deepmind and others it is now undeniable by anyone except the terminal copium addicts that Frontier LLMs are capable of doing research-level mathematics. With this observation comes an important discussion about what the future of mathematics (and scientific research at large) as a discipline looks like. The meme answer is to say that all mathematical research will eventually be carried out by AI with little (if any) human input, and with many mathematicians quitting mathematics since they cannot compete with AI. More precisely, there are two closely related answers,

I have long been trying to express a particular idea with respect to how I experience mathematics. Namely, Mathematics feels like a place, which I poetically like to call The Garden. This post is an attempt at articulating that thought, along with some recent reflections on what the future of mathematics might look like.

After making the computer room posters last year, I suggested to my department to make some for our coffee room. Just like the first time, this post is to document the creative choices made.

Turing Machines are the classic formalization of computation, later followed by many others. In this post, I will show how to represent any Turing Machine as a nonlinear operator on an appropriate Banach space. Along the way, we’ll find interesting interpretations of things like the Halting Problem as well as connections to a cool part of Dynamical Systems theory¹.

The purpose of this post is to provide a somewhat opinionated guide to doing scientific research (mostly in machine learning) for people outside traditional research institutions. There are already several excellent guides on writing papers and how to work on research projects (see below), so I aim for it to be a complement to those that can still serve as a standalone guide. Specifically, this guide covers “basic” concepts that I’ve often seen people confused about. The last section also contains links to various tools and resources.