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.
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.