Computers have already changed the way that humans do mathematics: they enable us to compute efficiently. But will they soon be helping us to reason? And will they one day start reasoning themselves? We give an overview of recent developments in neural networks, computer theorem provers and large language models.

We investigate the structure of Kazhdan-Lusztig polynomials of the symmetric group by leveraging computational approaches from big data, including exploratory and topological data analysis, applied to the polynomials for symmetric groups of up to 11 strands.

A personal and informal account of what a pure mathematician might expect when using tools from deep learning in their research.

One of the exciting directions regarding applications of computers in mathematics is to use them to experimentally form new conjectures. Google's DeepMind launched an endeavor for using machine learning (and deep learning in particular) for finding conjectures based on data. Two recent outcomes are toward the Dyer-Lusztig conjecture (Charles Blundell, Lars Buesing, Alex Davies, Petar Veličković, Geordie Williamson) and for certain new invariants in knot theory (Alex Davies, András Juhász, Marc Lackenby, Nenad Tomasev). There is also a Nature article Advancing mathematics by guiding human intuition with AI, on these developements. Here are also links to a new MO question and an old one on applications of computers to mathematics.

Research in mathematics is a deeply imaginative and intuitive process. This might come as a surprise for those who are still recovering from high-school algebra. What does the world look like at the quantum scale? What shape would our universe take if we were as large as a galaxy? What would it be like to live in six or even 60 dimensions?

Artificial intelligence is used across myriad disciplines to trawl through troves of data too complex for the human brain – and indeed the average computer – to process, as well as to solve seemingly unsolvable problems. It's posited that these technological super-brains could help us develop medicines and vaccines, solve economic problems, or engineer next-generation technology, among many other helpful applications. But in one of science's most difficult and often abstract fields, the power of the artificial mind is finally starting to prove itself. For the first time, scientists are using machine learning to come up with theories – rather than simply combing through the raw data – in some of the most confounding fields of mathematics. As described in a new study in the journal Nature, researchers from the universities of Sydney and Oxford have been working with AI lab DeepMind, based in London, to apply machine learning to suggest new avenues for inquiry, and to attempt to prove mathematical theorems. These technological super-brains could help us develop medicines and vaccines, solve economic problems, or engineer next-generation technology.