4+ day, 8+ 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…...

4+ day, 11+ 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…...

6+ day, 5+ hour ago   (282+ words) “understand empathically,” 1961, an arbitrary formation by U.S. science fiction writer Robert A. Heinlein (1907-1988) in his book “Stranger in a Strange Land.” In the book it is a transliteration of a Martian word and is said to mean etymologically “to…...

1+ week, 1+ day ago   (234+ words) The previous post discussed the motivation for and application of the rank-trace theorem. This post will give a proof. Suppose A is a real symmetric matrix. The rank-trace inequality says where tr is the trace operator, the sum of the…...

1+ week, 3+ day ago   (142+ words) NVIDIA has offered by buy Hugging Face for $12,930,300,000. 129303 is the Unicode code point for the Hugging Face emoj (U+1F917), which you can verify with the following Python code. >>> import unicodedata >>> 129303 == 0x1F917 True >>> unicodedata.name(chr(0x1F917)) 'HUGGING FACE' Related posts Prevent characters…...

1+ week, 3+ 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   (353+ words) I watched a few videos this morning, looking for ideas of what I could use AI to do. In one video, someone had an agent monitor tech news sites every 30 minutes to notify him of a variety of developments. No…...

2+ week, 3+ 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, 4+ day ago   (276+ words) AI-powered coding agents increase productivity for many developers. But do these agents produce good-quality code? Some say this doesn’t matter, we are heading toward dark software factories with source code never inspected, and maybe we should eliminate source code altogether…...

2+ week, 4+ day ago   (254+ words) When you’re interested in studying a family of functions, it can be useful to look at a differential equation that the functions solve. This is a theme I’ve written about several times, most recently here and here, but also three…...