3+ day, 14+ hour ago   (254+ words) The idea of using computers to assist with proofs is not new. The first major computer-assisted proof was published in 1976, the proof of the four color theorem by Kenneth Appel and Wolfgang Haken. The authors reduced the proof of the…...

3+ day, 15+ hour ago   (257+ words) A rising tide may lift all boats, but the AI tide lifts some boats much more than others. By all accounts, the best programmers have had the biggest productivity boost from AI. And top tier mathematicians are using AI to…...

3+ day, 16+ hour ago   (289+ words) Yesterday OpenAI announced a proof that settled a long-standing question about the Navier-Stokes equations from fluid dynamics. The announcement has created a lot of buzz, as one would expect. But there’s an aspect of OpenAI’s work that I haven’t seen…...

1+ week, 2+ day ago   (244+ words) Eric Lu announced on X today that he has factored RSA-260, a number N with 260 digits (862 bits) that is the product of two large primes [1]. RSA numbers are challenge problems posed to gauge the security of RSA encryption, which rests…...

2+ week, 2+ day ago   (239+ words) This post provides a couple examples to go along with two earlier posts. The pattern we’re illustrating is families of polynomials pn(x) that each satisfy a differential equation and a three-term recurrence. The differential equations have a second solution…...

2+ week, 5+ day ago   (259+ words) Probability density function must integrate to 1, and so if you know a density function up to a constant, the constant is determined. This post will do the opposite of the advice above and focus on normalization constants because this ties…...

2+ week, 6+ day ago   (509+ words) Special functions often have arcane names that not very helpful without some context. The previous post goes into some reasons for this. This post will expand on a point at the end of the post about “modified” functions. Things are…...

3+ week, 6+ day ago   (181+ words) The first post in the recent series of posts on Hadamard matrices describes a way of constructing new Hadamard matrices from two other Hadamard matrices by taking their Kronecker product. Starting with a Hadamard matrix H0 and a Hadamard matrix G,…...

4+ week, 13+ hour ago   (469+ words) Hadamard matrices are in the news following the recent announcement of a newly discovered Hadamard matrix. I’ve written three posts on Hadamard matrices recently, one as a sort of introduction and two on applications: the error correcting code used in…...