mathematics

Scientists have developed a new mathematical theorem using artificial intelligence (AI) and machine learning. This finding has revealed for the first time that artificial intelligence can assist in pure mathematics. Mathematicians from the universities of Oxford and Sydney teamed up with DeepMind, a Google-owned company based in London, to investigate knot theory and representation theory. Both of these are considered pure mathematics and rely heavily on human intuition for progress. DeepMind was able to find patterns and…

as the atoms of arithmetic, prime numbers have always occupied a special place on the number line. Now, Jared Duker Lichtman, a 26-year-old graduate student at the University of Oxford, has resolved a well-known conjecture, establishing another facet of what makes the primes special—and, in some sense, even optimal. “It gives you a larger context to see in what ways the primes are unique, and in what ways they relate to the larger universe of sets of numbers,” he said.The conjecture deals with primitive sets—sequences in…

“ homology theory depends only on the topology of your manifold. is Floer’s incredible insight,” said Agustin Moreno of the Institute for Advanced Study.Dividing by ZeroFloer theory ended up being wildly useful in many areas of geometry and topology, including mirror symmetry and the study of knots.“It’s the central tool in the subject,” said Manolescu.But Floer theory did not completely resolve the Arnold conjecture because Floer’s method only worked on one type of manifold. Over the next two decades, symplectic…