3+ day, 13+ 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, 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…...

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,…...

1+ mon, 2+ day ago   (237+ words) In science and engineering classes, you might describe a system using Newton’s laws and end up with a differential equation. You then solve the differential equation, analytically or numerically, to see how the solutions behave. You might also do the…...

1+ mon, 5+ day ago   (474+ words) Calculus professors with no experience in numerical computing will tell students that computers calculate trig functions with power series. They don’t. I worked on the implementation of trig functions in hardware, and I can assure you we didn’t just use…...

1+ mon, 5+ day ago   (398+ words) In a footnote to the previous post, I said that Python’s math library can calculate the logarithm of extremely large numbers but not the cosine. This post will expand on that comment. In this post I’ll use n = 200! as my…...

1+ mon, 2+ week ago   (215+ words) It’s well known that you can convert the base 16 (hex) representation of an integer to the base 2 (binary) representation by simply converting each digit from hex to binary. For example, CAFEhex = 1100 1010 1111 1110two I imagine it’s less well known that you can…...

1+ mon, 2+ week ago   (175+ words) This post takes a more abstract view of the previous post. That post looked at the concrete question of whether a number ever has the same sine in radians as in degrees. The relation between radians and degrees is irrelevant…...

2+ mon, 1+ day ago   (162+ words) Years ago I wrote about Gilbreath’s conjecture. It’s a simple conjecture; you could explain it to anyone who understands what prime numbers are. See the linked post for a description of the problem. Gilbreath’s conjecture is simple, but it’s also…...