Google’s artificial intelligence helps prove or suggest new mathematical theorems

For the first time, computer scientists and mathematicians from Britain and Australia used artificial intelligence to help them prove or propose new mathematical theorems in the complex fields of node theory and representation theory. To the surprise of the mathematicians, artificial intelligence made propositions which they then considered and confirmed. This shows that machine learning can lend a helping hand even at the forefront of mathematical research.

Researchers at the Universities of Sydney and Oxford, as well as Google’s DeepMind artificial intelligence subsidiary, published in the journal Nature, expressed optimism that the way is now open for in-depth collaboration between the fields of “pure” mathematics and artificial intelligence, which is expected to bring impressive results. Artificial intelligence, as new research shows, has matured so much that it can now be used to aid mathematical research that – like art – is usually based on intuition and creativity.

As Professor Jordi Williamson of the Sydney Institute for Mathematical Research, one of the world’s leading mathematicians, puts it, “Mathematical problems are widely regarded as one of the most difficult in general. “This is the first time we’ve used computers to help us make mathematical conjectures or suggest possible ‘lines of attack’ on hitherto unproven mathematical ideas.”

Williamson, who is considered an international leader in representation theory, who explores higher dimensional spaces using linear algebra, used DeepMind’s artificial intelligence to come close to proving an old conjecture about Kazhdan-Lusztig polynomials. has remained unsolved for 40 years and which concerns the deep symmetry in algebra of higher dimensions.

With the help of artificial intelligence, Oxford professors Mark Lackby and Andras Jouchas discovered an unexpected connection between the algebraic and geometric constants of nodes, thus discovering a whole new mathematical theorem. Node theory has multiple applications in the physical and other sciences.

As Lackby said, “It is fascinating to use machine learning to discover new and unexpected connections between different areas of mathematics. The work done in Oxford and Sydney, in collaboration with DeepMind, shows that machine learning can to be a really useful tool in mathematical research “.

Source: ΑΠΕ-ΜΠΕ