James A. Maynard, Ph.D., is a professor of number theory at the Mathematical Institute in Oxford University in Oxford, England. He is being recognized with the 2025 Carrier Medal for transformative discoveries in analytical number theory and the structure of prime numbers, advancing both foundational science and practical application. He will accept the Rev. Carrier Medal on September 15, 2025.
Maynard won the Fields Medal, a prestigious honor awarded every four years by the International Mathematical Union, which chooses two to four medalists during each award cycle for outstanding advancements in mathematics. His early work was on sieve methods, a technique used to estimate the size of a set of numbers by "sifting out" numbers that are divisible by specific primes. He settled an established conjecture by Paul Erdös — a prolific mathematician who spent a year on the faculty of the University of Notre Dame during the 1950s — on large gaps between prime numbers.
Recently, Maynard has improved upon previous work on questions about the Diophantine approximation, the process of finding successively better rational approximations to irrational numbers. In 2024 he and Larry Guth, of the Massachusetts Institute of Technology, developed a new proof that better estimates how many primes exist in short intervals on the number line. The proof also provides more insights into the behavior of prime numbers.
You are invited to join the College of Science as Maynard accepts the Carrier Medal. A reception will follow Maynard's lecture.
The Rev. Joseph Carrier C.S.C. Science Medal is the most prestigious award presented by the College of Science, and is given for sustained, outstanding achievements in any field of science. It is awarded annually, alternating between the mathematical, physical, chemical, and biological sciences.
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