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A 50-year-old computer-assisted proof
5+ day, 1+ 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…...
AI is an intelligence multiplier
5+ day, 2+ 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…...
The part of Navier-Stokes no one is talking about
5+ day, 4+ 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…...
Navier-Stokes in the news
6+ day, 1+ hour ago (272+ words) There are rumors that a long-standing math problem, one of the Millennium Prize problems, has been solved. The problem concerns technical properties of solutions to the Navier-Stokes equations [1], an equation that describe the dynamics of fluid flow. Popular accounts of…...
Ngram error rate
6+ day, 22+ 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…...
Proof of the rank-trace theorem
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…...
Computing a lower bound on matrix rank
1+ week, 3+ day ago (487+ words) Suppose you want to know the rank of an n × n matrix A, the number of linearly independent rows of A, or equivalently the number of linearly independent columns. There are at least three difficulties. First of all, rank is…...
New RSA number factored
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…...
Patented application of linear algebra
1+ week, 6+ day ago (172+ words) I just found out Brian Beckman and I got a patent on work we did for GSI Technology [1]. Nearly all the work I do is under an NDA, so I don’t often get a chance to talk about my projects....
Making the unnecessary easier
2+ week, 3+ 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…...