Machine learning helps mathematicians make new connections — ScienceDaily

For the first time, mathematicians have partnered with artificial intelligence to propose and prove new mathematical theories. The work was carried out in collaboration between the University of Oxford, the University of Sydney in Australia, and DeepMind, Google’s artificial intelligence sister company.

While computers have long been used to generate data for mathematicians, the task of identifying interesting patterns relied primarily on the intuition of the mathematicians themselves. However, it is now possible to generate more data than any mathematician would reasonably expect to study in his lifetime. This is where machine learning comes in.

Paper published today in temper nature, describes how DeepMind has been assigned the task of distinguishing patterns and connections in the areas of knot theory and representation theory. To the astonishment of mathematicians, new connections have been proposed; Then the mathematicians were able to examine these connections and prove the conjecture suggested by the artificial intelligence. These results suggest that machine learning can complement mathematical research, directing intuition about a problem.

Using patterns identified by machine learning, mathematicians from Oxford University have discovered a surprising relationship between the algebraic and geometric constants of knots, creating an entirely new theory in the field. Meanwhile, the University of Sydney has used artificial intelligence communication to bring it closer to proving an old conjecture about Kazhdan-Lusztig polynomials, which have not been resolved for 40 years.

Professor Andras Juhas, from the University of Oxford Institute of Mathematics and co-author of the paper said: “Pure mathematicians work by formulating and proving conjectures, which results in theorems. But where do the guesses come from?

We have shown that when guided by mathematical intuition, machine learning provides a powerful framework that can detect interesting and provable guesses in areas where a large amount of data is available, or where objects are too large to be studied by classical methods.

Professor Mark Lackebe, from Oxford University’s Institute of Mathematics and co-author said: “It has been fascinating to use machine learning to discover new and unexpected connections between different areas of mathematics. I think the work we’ve done in Oxford and Sydney in collaboration with DeepMind shows that machine learning can be a really useful tool in mathematical research.

Professor Jordi Williamson, Professor of Mathematics at the University of Sydney and Director of the Sydney Institute for Mathematics Research and co-author, said: “Artificial intelligence is an extraordinary tool. This work is one of the first times it has demonstrated its usefulness to pure mathematicians, like myself.

Intuition can take us a long way, but AI can help us find connections that the human brain might not always easily detect.

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