An anonymous reader quotes a report from TechCrunch: Over the weekend, Neel Somani, who is a software engineer, former quant researcher, and a startup founder, was testing the math skills of OpenAI's new model when he made an unexpected discovery. After pasting the problem into ChatGPT and letting it think for 15 minutes, he came back to a full solution. He evaluated the proof and formalized it with a tool called Harmonic -- but it all checked out. "I was curious to establish a baseline for when LLMs are effectively able to solve open math problems compared to where they struggle," Somani said. The surprise was that, using the latest model, the frontier started to push forward a bit. ChatGPT's chain of thought is even more impressive, rattling off mathematical axioms like Legendre's formula, Bertrand's postulate, and the Star of David theorum. Eventually, the model found a Math Overflow post from 2013, where Harvard mathematician Noam Elkies had given an elegant solution to a similar problem. But ChatGPT's final proof differed from Elkies' work in important ways, and gave a more complete solution to a version of the problem posed by legendary mathematician Paul Erdos, whose vast collection of unsolved problems has become a proving ground for AI. For anyone skeptical of machine intelligence, it's a surprising result -- and it's not the only one. AI tools have become ubiquitous in mathematics, from formalization-oriented LLMs like Harmonic's Aristotle to literature review tools like OpenAI's deep research. But since the release of GPT 5.2 -- which Somani describes as "anecdotally more skilled at mathematical reasoning than previous iterations" -- the sheer volume of solved problems has become difficult to ignore, raising new questions about large language models' ability to push the frontiers of human knowledge. Somani examined the online archive of more than 1,000 Erdos conjectures. Since Christmas, 15 Erdos problems have shifted from "open" to "solved," with 11 solutions explicitly crediting AI involvement. On GitHub, mathematician Terence Tao identifies eight Erdos problems where AI made meaningful autonomous progress and six more where it advanced work by finding and extending prior research, noting on Mastodon that AI's scalability makes it well suited to tackling the long tail of obscure, often straightforward Erdos problems. Progress is also being accelerated by a push toward formalization, supported by tools like the open-source "proof assistant" Lean and newer AI systems such as Harmonic's Aristotle.

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An anonymous reader shares a report: For the past several years, America has been using its young people as lab rats in a sweeping, if not exactly thought-out, education experiment. Schools across the country have been lowering standards and removing penalties for failure. The results are coming into focus. Five years ago, about 30 incoming freshmen at UC San Diego arrived with math skills below high-school level. Now, according to a recent report from UC San Diego faculty and administrators, that number is more than 900 -- and most of those students don't fully meet middle-school math standards. Many students struggle with fractions and simple algebra problems. Last year, the university, which admits fewer than 30 percent of undergraduate applicants, launched a remedial-math course that focuses entirely on concepts taught in elementary and middle school. (According to the report, more than 60 percent of students who took the previous version of the course couldn't divide a fraction by two.) One of the course's tutors noted that students faced more issues with "logical thinking" than with math facts per se. They didn't know how to begin solving word problems. The university's problems are extreme, but they are not unique. Over the past five years, all of the other University of California campuses, including UC Berkeley and UCLA, have seen the number of first-years who are unprepared for precalculus double or triple. George Mason University, in Virginia, revamped its remedial-math summer program in 2023 after students began arriving at their calculus course unable to do algebra, the math-department chair, Maria Emelianenko, told me. "We call it quantitative literacy, just knowing which fraction is larger or smaller, that the slope is positive when it is going up," Janine Wilson, the chair of the undergraduate economics program at UC Davis, told me. "Things like that are just kind of in our bones when we are college ready. We are just seeing many folks without that capability." Part of what's happening here is that as more students choose STEM majors, more of them are being funneled into introductory math courses during their freshman year. But the national trend is very clear: America's students are getting much worse at math. The decline started about a decade ago and sharply accelerated during the coronavirus pandemic. The average eighth grader's math skills, which rose steadily from 1990 to 2013, are now a full school year behind where they were in 2013, according to the National Assessment of Educational Progress, the gold standard for tracking academic achievement. Students in the bottom tenth percentile have fallen even further behind. Only the top 10 percent have recovered to 2013 levels.

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