Machine learning helps mathematicians make new connections

Date:
December 1, 2021
Source:
University of Oxford
Summary:
Mathematicians have partnered with artificial intelligence to
suggest and prove new mathematical theorems.



FULL STORY ==========================================================================
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.

Professor Andras Juhasz, of the Mathematical Institute at the University
of Oxford and co-author on the paper, said: 'Pure mathematicians work by formulating conjectures and proving these, resulting in theorems. But
where do the conjectures come from? '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.' Professor Marc Lackeby, of the Mathematical Institute at the University of Oxford and co-author, said:
'It has been fascinating to use machine learning to discover new and
unexpected connections between different areas of mathematics.

I believe that the work that we have done in Oxford and in Sydney in collaboration with DeepMind demonstrates that machine learning can be
a genuinely useful tool in mathematical research.' Professor Geordie Williamson, Professor of Mathematics at the University of Sydney and
director of the Sydney Mathematical Research Institute and co- author,
said: 'AI is an extraordinary tool. This work is one of the first times
it has demonstrated its usefulness for pure mathematicians, like me.

'Intuition can take us a long way, but AI can help us
find connections the human mind might not always easily spot.' ========================================================================== Story Source: Materials provided by University_of_Oxford. Note: Content
may be edited for style and length.


========================================================================== Journal Reference:
1. Alex Davies, Petar Veličković, Lars Buesing, Sam
Blackwell,
Daniel Zheng, Nenad Tomasev, Richard Tanburn, Peter Battaglia,
Charles Blundell, Andra's Juha'sz, Marc Lackenby, Geordie
Williamson, Demis Hassabis, Pushmeet Kohli. Advancing mathematics
by guiding human intuition with AI. Nature, 2021; 600 (7887):
70 DOI: 10.1038/s41586-021- 04086-x ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2021/12/211201111925.htm

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