# James Maynard awarded the Fields Medal

# Former CRM-ISM postdoctoral researcher awarded the Fields Medal

James Maynard today received a 2022 Fields Medal in Helsinki from the International Mathematical Union. The Fields medal is regarded as the top award in mathematical research. Up to four medals are presented every four years to researchers who are under 40 years old on January 1st of the year of the award, who have made the most important contributions in the world to mathematics.

Maynard received his PhD at Oxford in 2013 and then came to Montreal as a CRM-ISM postdoctoral researcher working under the guidance of Professor Granville, and established strong working relationships with Granville and Professor Koukoulopoulos of the Université de Montreal. After leaving Montreal he returned to Oxford where he soon became a full professor.

While at the CRM, Maynard proved two theorems that are cited as part of the reason he won his Fields medal; one developing a new method to show there are infinitely many pairs of primes differing by no more than 400 (and indeed there are patterns of m primes in bounded length intervals, for any m>1), another showing that there are far longer gaps between primes than had been known (and so winning a large monetary prize from the late Paul Erdos). Subsequently, he proved several spectacular theorems, including showing that there are infinitely many primes with no digit 7 in their decimal expansion (or any other given digit), and resolving the Duffin-Schaefer conjecture, jointly with Dimitris Koukoulopoulos, clarifying how well most real numbers can be approximated by fractions.

Maynard’s work is remarkable for the depth and importance of his breakthroughs coupled with a clarity of thought and reasoning, turning what had seemed impossibly hard, and long unresolved, questions into methods that, after the fact, seem “obvious” and will be included in every textbook.

Maynard will be back in Montreal as a plenary speaker at a CRM conference from September 5-9.

The CRM congratulates all four Fields medal laureates: Maryna Viazovska, Hugo Duminil-Copin, June Huh and James Maynard.

## Fields Medal short citation

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