A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture. One morning last November, the ...

Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says ...

The verdict, it seems, is in: artificial intelligence is not about to replace mathematicians. That is the immediate takeaway from the “First Proof” challenge—perhaps the most robust test yet of the ...