Developments in number theory in the last two weeks illustrate how artificial intelligence is helping advance the frontiers of mathematics, but also raising questions about what mathematics means vis-à-vis humans.The first development is about the Riemann zeta function, a mathematical idea connected to the distribution of prime numbers.The prime numbers, 2, 3, 5, 7, 11, and so on, are divisible only by 1 and themselves. Scientists have used this property to secure communications and financial transactions, putting prime numbers at the heart of contemporary digital security.Stepping stonesThe Riemann zeta function has many solutions called non-trivial zeroes. The Riemann hypothesis states that all of these solutions lie on a vertical line in the complex plane (on a graph) called the critical line. This remains unproved.Proving it would enhance experts’ ability to predict the distribution of prime numbers, potentially exposing weaknesses in some cryptographic systems.Mathematicians have been able to show that 41.6% of the solutions lie on this line. On August 10, an internal version of Anthropic’s AI model Claude showed that at least 67.2% of the non-trivial zeroes lie on the critical line.