Blogs about Mathematics

I have another new arXiv preprint: “Computational geometry with probabilistically noisy primitive operations”, arXiv:2501.07707, with Mike Goodrich and his student Vinesh Sridhar. Many computational geometry algorithms are designed around the use of primitives, subroutines that …

All of Richard Feynman’s books, is Feynman himself. This introduction sets the stage for a deep exploration of how his works have reshaped the way we approach and appreciate the art of understanding physics.

You may remember the Weight Today shortcut I wrote about last month. I run it from my iPhone every morning to record my weight in both the Health app and a CSV file I use …

Blocking sets are one of the central topics in finite geometry, which were originally introduced in the context of game theory under the name of `blocking coalitions’: On Finite Projective Games. I first learned about …

DMFT is significantly less perplexing than HMRC Hello! My name is Colin and I am a mathematician on a mission to spread mathematical joy. This week, I’ve made another contribution to the OEIS (currently in …

This is a piece of advice that I found myself giving to many early career researchers, students, and colleagues supervising and advising those as well. For years, actually. A mathematician, the joke says, is a …

The fourth in the series about every year of Numberphile. Videos about Klein bottles, infinity, and coin flips.

The piranha problem is both a metaphor and a set of theorems coming out of Andrew Gelman’s research group. The metaphor is of large intervention effects as piranhas that can’t be kept together in the …

I just filled out an online survey after a positive interaction with an online chat representative (a human) because I wanted to give him a thumbs up. The survey was (to my relief) relatively short, …

Roll up, roll up, roll up and welcome to the two hundred and twenty ninth Carnival of Mathematics! 229 is a prime number, and that in itself is interesting. Its the “elder” of a set …

$\newcommand\C{\mathbb{C}}$ I came up with the proof below while preparing a lecture for my complex analysis course. I learned from Sinan Gunturk that Peter Lax showed him the same proof back in 2007. Let \(O\subset\C\) …

A central problem in combinatorics, probability theory, and analysis is to understand the spectrum of random d-regular graphs G with vertices. The following paper marks a huge leap in our understanding of this problem. Ramanujan …

Slide in Lev Reyzin's JMM talk "Problems in AI and ML for Mathematicians" Reyzin is paraphrasing Telgarsky. Posted with permission.Last week I attended the Joint Mathematics Meeting in Seattle with a theme ofWe Decide Our …

2024-2025 Cruise Our first stop in 2025 on the leisurely tour of SIST is Excursion 4 Tour I which you can read here. I hope that this will give you the chutzpah to push back …

Acknowledgements The code in this post is indebted (and in some cases wholly ripped off from) work by the glorious Finn Lindgren, who emailed me some code to do this probably a decade ago. Yes …

Principal Component Analysis, or PCA, is a fundamental dimensionality reduction technique using in Machine Learning. The general goal is to transform a -dimensional problem into a -dimensional one, where is smaller than . This can …

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website. For this issue, we have a very special interview with Erica Klarreich. Erica earned her doctoral degree …

new theory

Just in time for the holidays, Colleen Robichaux and I wrote this paper on positivity of Schubert coefficients. This paper is unlike any other paper I had written, both in the content and the way …

I had an enjoyable little discussion with Joe Murray of The Human Podcast, part of his new series, called 10 questions in 10 minutes, in which he asks his interview subjects for short answers to …