The test ' part of a project called First Proof, which aims to evaluate the ability of AI to solve complex questions in mathematics ' posed ten research-level maths problems to four AI systems. A jury of anonymous human specialists in the relevant mathematical fields then assessed the models' answers. This test was the first of its kind to satisfy three key conditions simultaneously: first, it consisted of research-level maths questions; second, it involved problems that did not appear in the training data; and third, it was formally graded by mathematicians. The results were unveiled on the First Proof website on 10 June. These findings follow recent AI breakthroughs in solving maths problems. Last month, for example, a chatbot made by the technology firm OpenAI, in San Francisco, California, solved an 80-year-old maths challenge set by the late mathematician Paul Erdos. The First Proof team says that future iterations of the test could help researchers to judge how useful AI models could be for mathematicians; for example, in solving problems autonomously, checking proofs or acting as research assistants....

In a scene that could have easily featured in an episode of the US television sitcom The Big Bang Theory, the late US physicist Richard Feynman once turned a visit to a Thai restaurant he often dined at into a mathematical riddle: how adventurous should we be in trying new dishes' Feynman promptly solved this on a sheet of paper. Feynman's dilemma is one that will be familiar to any restaurant-goer. Do we keep ordering the best dish we've had so far, or do we explore the menu in the hope of finding something better' A study published in the Proceedings of the National Academy of Sciences on 1 June probes this question, and includes experimental findings that participants adopt meal-choosing strategies that closely approximate Feynman's mathematical solution1. Behavioural scientist Shoham Choshen-Hillel at the Hebrew University of Jerusalem says that the authors wrote a 'super creative article'. 'The restaurant example stands in for decisions in many settings,' she adds. Real-life examples include choosing a home to buy, deciding whom to partner up with and selecting a parking spot....

Paul Erdos, who published more than 1,500 papers during his lifetime, also left a legacy of more than 1,000 open research questions, some of which are now being solved with AI. Credit: George Csicsery The company has not revealed all the precise details and steps of how it did this, nor the name of the AI system that achieved the result, which it has published on its website. However, the finding has been verified independently by mathematicians not connected to the firm. OpenAI announced on 20 May that its chatbot software had disproved Paul Erdos (1913'1996) on what is called the unit-distance problem. In 1946, Erdos worked out what he suggested was the best arrangement of points on a plane so that as many pairs as possible are at a given distance from each other ' and he put down a challenge: no one could do better. Now, OpenAI says that its system has done precisely that. It did so by using techniques in algebraic number theory, which enabled it to choose points with coordinates that were the solutions of particular equations. And the finding has astonished mathematicians....

From his home in southwest England, Price got the popular artificial-intelligence tool to solve what is known as Erdos problem #1196, one of more than 1,000 puzzles that Hungarian mathematician Paul Erdos (1913'1996) collected throughout his life. Unlike other AI-generated solutions to mathematical problems, this one used a strategy that surprised specialists (B. Alexeev et al. Preprint at arXiv https://doi.org/q6p7; 2026). Posting on the social-media site X, mathematician Jared Duker Lichtman at Stanford University in California drew an analogy with chess. It was, he wrote, as if AI had discovered an opening no one had thought of before because of 'human aesthetics and convention'. This is one of the more remarkable examples in a string of successes for AI in mathematics. Researchers in academia and at AI companies have been making a major push to see how far the systems can go. Computers are now contributing not just brute-force calculations, but also the type of logically sound reasoning that has been the province of mathematicians since Euclid more than 2,300 years ago....