On July 5, Princeton mathematician June Huh was awarded the Fields Medal — often referred to as the “Nobel Prize of Mathematics” — at the International Mathematical Union (IMU) Award Ceremony. The ceremony was held this year in Helsinki, Finland, as part of the virtual 2022 International Congress of Mathematicians (ICM). Huh is the first mathematician of Korean descent to win the medal.
The Fields Medal is presented every four years by the IMU to two to four mathematicians under the age of 40 in recognition of “outstanding mathematical achievement for existing work and for the promise of future achievement.” The Fields Medal is one of the highest distinctions that can be conferred upon a research mathematician.
With this honor, Huh became the 13th Princeton-affiliated individual to win the medal. Previous winners include current faculty members Charles Fefferman and Manjul Bhargava GS ’01, who received the award in 1978 and 2014, respectively.
This year also marks the fifth consecutive IMU Award Ceremony — dating back to 2006 — at which a Princeton-affiliated mathematician has received the medal.
Despite having won the most prestigious award in mathematics, Huh’s relationship with the subject has not always been a good one. He had no interest in being a mathematician at a young age, and later even dropped out of high school to become a poet. In an interview with The New York Times, Huh said that he “was pretty good at most subjects except math.”
Huh did eventually attend college, enrolling at Seoul National University (SNU) in 2002, where he majored in physics and astronomy.
Huh’s outlook on mathematics changed, however, after an encounter with Heisuke Hironaka, a recipient of the Fields Medal in 1970, in a math class Huh took during the last year of his undergraduate study. The class was on algebraic geometry, and Huh had decided to attend in the hopes of writing an article about Hironaka.
After receiving a master’s degree in mathematics at SNU, where he spent more time with Hironaka, Huh applied to graduate schools across the United States to pursue a doctoral degree. With a recommendation letter from a Fields medalist, Huh expected to be accepted by many.
Instead, every school he applied to except the University of Illinois Urbana-Champaign rejected him. Huh started his studies there in 2009 before eventually transferring to the University of Michigan in 2011.
In an interview with the Quanta Magazine, Huh described his life during his doctoral studies as “almost monastic,” as he “just wanted to do math” and really only interacted with his advisor, Mircea Mustaţă.
“June is a mathematician with an amazing intuition, who sees beautiful connections between different fields of mathematics and has the technical power to exploit these connections in order to prove major theorems,” Mustaţă wrote in an email to the ‘Prince.’ “I am certainly very happy to see that he is getting the recognition he deserves.”
Huh did not respond to a request for comment.
Huh was awarded the prize for applying “the ideas of Hodge theory to combinatorics” and his “proof of the Dowling–Wilson conjecture for geometric lattices,” among other reasons.
“Using methods of Hodge theory, tropical geometry, and singularity theory, June Huh, with his collaborators, has transformed the field of geometric combinatorics,” the IMU statement read.
In algebraic geometry, algebraic variety refers to a geometric shape, like a parabola or the surface of a sphere, that can be described using certain algebraic equations.
Named after British mathematician Sir William Vallance Douglas Hodge, the Hodge theory deals with the understanding of complex algebraic varieties using the Hodge structure, a much simpler algebraic structure.
Using purely combinatorial techniques in his groundbreaking work, Huh applied the ideas of Hodge theory to combinatorics, which deals with the study of countable discrete structures, to solve problems that mathematicians had struggled to solve for almost 40 years.
A simplified way of looking at Huh’s work is to imagine having a sequence of numbers containing some kind of hidden pattern. For example, in the sequence 2, 4, 8, 16, the pattern is that each consecutive number is multiplied by 2. To find the hidden pattern, Huh sees the numbers in this sequence instead as dimensions of some space. This space should satisfy certain properties, which in turn imply the pattern in the number sequence.
Huh’s contributions also involve Read’s conjecture. This conjecture involves simple geometric objects, which mathematicians refer to as graphs. A triangle, for example, which has 3 edges and 3 vertices, is a simple graph.
One of the questions mathematicians have dealt with regarding such graphs is that given a certain number of colors, how many distinct ways are there to color the vertices of the graph without any of the adjacent vertices having the same color? A chromatic polynomial is the mathematical equation that represents the answer to this question.
Huh was able to prove Read’s conjecture, which concerns the mathematical properties of complex chromatic polynomials. Building upon this proof, Huh also proved the Rota Conjecture, which focuses on a more abstract class of structures called matriods.
Huh’s other contributions include proofs of the Dowling–Wilson and Mason conjectures.
After receiving his Ph.D. in 2014, Huh joined the Institute for Advanced Study (IAS) in Princeton, where he was an Oswald Veblen Fellow until 2017, and a visiting professor from 2017 to 2020.
“I’m very happy Huh won this award because I think he is the kind of role model that should be at the top of mathematics,” said Jacob Matherne, a postdoctoral advisee of Huh at the IAS in 2018.
Matherne described Huh as an “optimistic” and “fearless” person, saying that “in addition to being a great mathematician, [Huh] is just a great human being.”
Matherne also pointed out Huh’s characteristic “walk-and-talk” style.
“Sometimes I wanted to discuss a topic with June,” Matherne said, “and as soon as I walked up to him, he would say, ‘Let’s go think about it right now.’”
“And then we would just start walking and talking and end up at a blackboard or something,” he added.
Among most of his works, especially the groundbreaking connections he has established between algebraic geometry and combinatorics, Huh has profoundly linked seemingly unrelated areas of mathematics.
“If you look at mathematics as a kind of continent divided into countries, I think in June’s case nobody really told him there were all these borders,” Matherne quoted what Robbert Dijkgraaf, former director of the IAS, said about Huh. “He’s definitely not constrained by any demarcations,” Matherne added
Huh was awarded the medal alongside three other mathematicians: Hugo Duminil-Copin, James Maynard, and Maryna Viazovska. Viazovska, a Ukrainian mathematician and the second woman to ever receive the medal since it was first given in 1936, was a Minerva Distinguished Visitor at the University in 2017.
Senior News Writer Allan Shen contributed reporting to this piece.
Mahya Fazel-Zarandi is a staff writer for the ‘Prince.’ She can be reached by email at mahyaf@princeton.edu or on Twitter @MahyaFazel.
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