The mathematician Martin Hairer has been awarded the 2021 Breakthrough Prize for Mathematics which, apart from the accolade, comes with $3 million in prize money.

Hairer received the prize for "transformative contributions to the theory of stochastic analysis, particularly the theory of regularity structures in stochastic partial differential equations". You can find out more about what this means in the following article and podcast, which we produced after interviewing Hairer about receiving the Fields Medal, one of the highest honours in maths, in 2014.

Martin Hairer: At the interface — A brief look at Hairer's groundbreaking work, which involves the maths of change and chance.

Interview with Martin Hairer: The podcast — Listen to Hairer talk about his research in this podcast, recorded a day before he received the Fields Medal in 2014.

Hairer has also written us a series of articles about the maths of randomness. These are based on a lecture he gave at the Heidelberg Laureate Forum 2017, where we also recorded a video of Hairer talking about issue surrounding randomness. The video is shown below.

The maths of randomness — Randomness is surprisingly hard to define. But as Hairer explains in this article, the mathematical language we use to describe it is beautifully succinct.

The maths of randomness: Symmetry — In this article Hairer explains why symmetry is one of the two guiding principles in understanding probabilities.

The maths of randomness: Universality — The second guiding principle of the maths of randomness is *universality*, which Hairer explains in this article.

The two envelopes problem — Here's a brain teaser Hairer presented at the Heidelberg Laureate Forum 2018. See if you can crack it!