Schizoid trapezoid
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. On placehood Before talking about mathematics proper, I should specify what…
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. Context Unlike the previous time, where I took it upon myself to decorate a classroom without asking for permission, this time I made the proposal at a department meeting to make posters for our coffee room.…
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 theory 1 . Note: While I try to provide…
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…
During the holidays I worked on a small project to make posters for a computer room in my university. Since this was essentially an exercise in artistic creativity, I thought I’d document the process of making these, as I think this is often omitted despite being (for me, at least) the most interesting part of the creative process. Context The math department I work at moved to a new building a…
Mathematics is often seen by outsiders as an austere discipline of pure reason. The goal of this post is to present an interpretation of mathematics as literal magic. More precisely, the practice of mathematics bears striking similarities (vibes) to the magical tradition known as goetia , or sorcery . Goetia is a type of European sorcery, often referred to as witchcraft, that has been transmitted…
Most of modern mathematics, and as a consequence, science at large assume the existence of real numbers, pretty much as a postulate 1 . Given how successful both of these have been, it might seem odd to challenge it. However, when one takes a closer look at exactly how real numbers are defined, a couple of philosophical issues arise. In particular the fact that we (mere mortals) can only…
The Julia programming language currently holds the state of the art in terms of ODE solvers, and comes with a variety of ways of specifying ODEs. A common use case is to define modular dynamical systems, where the same pieces occur in multiple places with a bit of variation. Examples of this include running multiple copies of the same system with different parameters for each copy, or dynamical…
As someone who deeply enjoys mathematics, both on an intellectual and esthetic level, I have inevitably been confronted many times with some remark along the lines of > I never used any of the math I learned at school later in life . or > Mathematics is just intellectual masturbation, no better than philosophy . or even > Well this all nice and well, but what really matters are the practical…
I have had multiple encounters now with people interested or working in Machine Learning/AI Alignment, who wish they had more mathematical background. Most of them come from a Computer Science background, which is not surprising. Despite Machine Learning often being done in CS departments, the typical CS undergrad curriculum contains much less math than what one can find in some ML papers. In my…