Author: Marianne Freiberger and Rachel Thomas
Martin Hairer's is being honoured for a major breakthrough that gives a way of attacking problems that had previously been impenetrable. 

Manjul Bhargava is being honoured as a number theorist of "extraordinary creativity," with "a taste for simple problems of timeless beauty." 
The early 1950s were an experimental gold mine for physicists, with new particles produced in accelerators almost every week. Yet the strong nuclear force that acted between them defied theoretical description, sending physicists on a long and arduous journey that culminated in several Nobel prizes and the exotic concept of "asymptotic freedom". 
By the 1970s physicists had successfully tamed three of the fundamental forces using a sophisticated construct called quantum field theory. The trouble was that the framework seemed to fall apart when you looked at very high or very low energy scales. So how could these be thought of as valid theories? It's a question physicists are still grappling with today. 

Is the Universe finite or infinite? Is there infinity inside a black hole? Is space infinitely divisible or is there a shortest length? We talk to philosophers and physicists to find out. 

You may have heard of quantum theory and you probably know what a field is. But what is quantum field theory? This article traces the development of quantum electrodynamics in the first half of the 20th century. Hair raising difficulties, heroic struggle and illustrious characters — this story has it all! 
This is the second article in our fourpart series exploring quantum electrodynamics. After successfully applying quantum mechanics to the electromagnetic field, physicists faced a problem of boundless proportions: every calculation they made returned infinity as the answer. 