Alongside three mathematicians under the age of 40, James Maynard received the Fields Medal in mathematics during a ceremony in Helsinki on Tuesday.
The Fields Medal, a prize awarded to two, three, or four mathematicians under 40 years of age every four years, is an Olympic-like honor for budding mathematicians. The medals, depicting the Greek mathematician Archimedes in 14-karat glory, were presented to Hugo Duminil-Copin, 36, of the Institut des Hautes Études Scientifiques just south of Paris and the University of Geneva in Switzerland; June Huh, 39, of Princeton University; James Maynard, 35, of the University of Oxford in England; and Maryna Viazovska, 37, of the Swiss Federal Institute of Technology in Lausanne.
While other mathematicians focused on more abstract areas of math such as chromatic geometry or stacking equally sized spheres, James Maynard dialed in on a topic anyone who remembers high school math can understand: prime numbers. A prime number is a whole number whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into the original number. 2, 3, and 5 are prime, but 4 is not since 2 is a factor.
“I personally find them just totally fascinating,” said Maynard. On his way to the top of his field, Maynard cut through simple-sounding questions about prime numbers that have stumped mathematicians for centuries. More than 2,000 years ago, Euclid proved there are an infinite number of prime numbers, but many more unsolved problems about prime numbers remain. One such problem is the Twin Prime Conjecture.
A prime gap is the difference between two consecutive primes, and a twin prime is a prime number with a prime gap of 2 — for example, 3 and 5 or 11 and 13 are twin primes. As numbers get larger, primes become sparser and twin primes scarcer still; a theorem proved by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann. The Twin Primes Conjecture asserts that there are infinitely many twin primes.
Maynard suspected that he could further understand twin primes using a method described in a paper from about a decade earlier. While the method had already been scrutinized by other mathematicians, Maynard surmised that he could still extract more juice from it. “I kept doing calculations and computations, and I kept on getting these sort of small signals that there was something there to be understood and discovered.”
In 2013, a seismic event occurred in the world of number theory. A little-known mathematician Yitang Zhang of the University of New Hampshire proved, not quite the Twin Primes Conjecture, but the next best thing: he showed that there exist infinitely many pairs of primes with a gap of at most 70 million. The finding catapulted Zhang to fame in the form of lectures, news stories, and even a documentary.
Six months later, Maynard reproduced Zhang’s findings using his own approach. He also narrowed the size of the gap to 600. A group of mathematicians have since collaborated to push the size of the prime gap down to 246. (That group includes Terence Tao of UCLA, one of the most influential mathematicians of today. Tao came up with the same result as Maynard, but delayed publishing his result to avoid eclipsing Maynard.)
Maynard also proved that there are an infinite number of primes not containing the digit 7, and the same proof works for any other digit as well. “Although this sounds like a bit of a curiosity, the key point is that it overcame various sorts of technical mathematical hurdles for studying the prime numbers,” Maynard said. He said that he is fond of problems involving primes because despite taking little math knowledge to understand, “you have to really go deeply into very complicated and very modern math to actually prove these results.”
The Fields Medal, a prize awarded to two, three, or four mathematicians under 40 years of age every four years, is an Olympic-like honor for budding mathematicians. The medals, depicting the Greek mathematician Archimedes in 14-karat glory, were presented to Hugo Duminil-Copin, 36, of the Institut des Hautes Études Scientifiques just south of Paris and the University of Geneva in Switzerland; June Huh, 39, of Princeton University; James Maynard, 35, of the University of Oxford in England; and Maryna Viazovska, 37, of the Swiss Federal Institute of Technology in Lausanne.
While other mathematicians focused on more abstract areas of math such as chromatic geometry or stacking equally sized spheres, James Maynard dialed in on a topic anyone who remembers high school math can understand: prime numbers. A prime number is a whole number whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into the original number. 2, 3, and 5 are prime, but 4 is not since 2 is a factor.
“I personally find them just totally fascinating,” said Maynard. On his way to the top of his field, Maynard cut through simple-sounding questions about prime numbers that have stumped mathematicians for centuries. More than 2,000 years ago, Euclid proved there are an infinite number of prime numbers, but many more unsolved problems about prime numbers remain. One such problem is the Twin Prime Conjecture.
A prime gap is the difference between two consecutive primes, and a twin prime is a prime number with a prime gap of 2 — for example, 3 and 5 or 11 and 13 are twin primes. As numbers get larger, primes become sparser and twin primes scarcer still; a theorem proved by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann. The Twin Primes Conjecture asserts that there are infinitely many twin primes.
Maynard suspected that he could further understand twin primes using a method described in a paper from about a decade earlier. While the method had already been scrutinized by other mathematicians, Maynard surmised that he could still extract more juice from it. “I kept doing calculations and computations, and I kept on getting these sort of small signals that there was something there to be understood and discovered.”
In 2013, a seismic event occurred in the world of number theory. A little-known mathematician Yitang Zhang of the University of New Hampshire proved, not quite the Twin Primes Conjecture, but the next best thing: he showed that there exist infinitely many pairs of primes with a gap of at most 70 million. The finding catapulted Zhang to fame in the form of lectures, news stories, and even a documentary.
Six months later, Maynard reproduced Zhang’s findings using his own approach. He also narrowed the size of the gap to 600. A group of mathematicians have since collaborated to push the size of the prime gap down to 246. (That group includes Terence Tao of UCLA, one of the most influential mathematicians of today. Tao came up with the same result as Maynard, but delayed publishing his result to avoid eclipsing Maynard.)
Maynard also proved that there are an infinite number of primes not containing the digit 7, and the same proof works for any other digit as well. “Although this sounds like a bit of a curiosity, the key point is that it overcame various sorts of technical mathematical hurdles for studying the prime numbers,” Maynard said. He said that he is fond of problems involving primes because despite taking little math knowledge to understand, “you have to really go deeply into very complicated and very modern math to actually prove these results.”
