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For the first time, mathematicians have partnered with artificial intelligence to suggest and prove new mathematical theorems.

The work was done in a 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 has relied mainly on the intuition of the mathematicians themselves. However, it’s now possible to generate more data than any mathematician can reasonably expect to study in a lifetime. Which is where machine learning comes in.

A paper, published today in Nature, describes how DeepMind was set the task of discerning patterns and connections in the fields of knot theory and representation theory. To the surprise of the mathematicians, new connections were suggested; the mathematicians were then able to examine these connections and prove the conjecture suggested by the AI. These results suggest that machine learning can complement mathematical research, guiding intuition about a problem.

Using the patterns identified by machine learning, mathematicians from the University of Oxford discovered a surprising connection between algebraic and geometric invariants of knots, establishing a completely new theorem in the field. The University of Sydney, meanwhile, used the connections made by the AI to bring them close to proving an old conjecture about Kazhdan-Lusztig polynomials, which has been unsolved for 40 years.”

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