Artificial Intelligence: New Revelations In Pure Mathematics By AI

December 6, 2021 | Artificial Intelligence, News

Maths pundits and AI experts have teamed up to use AI to suggest and prove hitherto unthought of theorems, and reveal new patterns in math.

Machine learning has assisted in the discovery of new fundamental results in pure mathematics. Researchers at DeepMind, London, University of Oxford, and University of Sydney have proposed a method by which machine learning can aid mathematicians in discovering new conjectures and theorems. (Science Alert)

Machine learning and AI technology can analyze massive amounts of data in miniscule amounts of time. They can discover potential patterns and relations between mathematical objects, and help scientists understand them with attribution techniques and use these observations to guide intuition and propose conjectures.

“While mathematicians have used machine learning to assist in the analysis of complex data sets, this is the first time we have used computers to help us formulate conjectures or suggest possible lines of attack for unproven ideas in mathematics,” says mathematician Geordie Williamson from the University of Sydney in Australia.

“We have demonstrated that, when guided by mathematical intuition, machine learning provides a powerful framework that can uncover interesting and provable conjectures in areas where a large amount of data is available, or where the objects are too large to study with classical methods,” says mathematician András Juhász from the University of Oxford in the UK.

Kazhdan-Lusztig polynomials and mathematical knots

The researchers used DeepMind’s AI to bring them close to proving an old conjecture about Kazhdan-Lusztig polynomials, which has been unsolved for 40 years.

The conjectures concern deep symmetry in higher dimensional algebra.

Furthermore, an entirely new theorem could be developed because a machine learning technique called a supervised learning model was able to spot a previously undiscovered relationship between two different types of mathematical knots.

This AI-led advance in knot theory will also be relevant in other scientific areas including genetics, fluid dynamics, and even the behavior of the Sun’s corona.

“AI is an extraordinary tool,” says Williamson. “This work is one of the first times it has demonstrated its usefulness for pure mathematicians, like me.”

Related Story: AI is Helping Itself to Get Smarter and Smarter

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