On July 5, Princeton mathematician June Huh received the Fields Medal — often referred to as the “Nobel Prize in Mathematics” — at the International Mathematical Union (IMU) awards ceremony. The ceremony took place this year in Helsinki, Finland, as part of the virtual International Congress of Mathematicians 2022 (ICM). Huh is the first Korean-born mathematician to win the medal.
The Fields Medal is awarded 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 awarded to a research mathematician.
With this honor, Huh became the 13th Princeton-affiliated individual to win the medal. Previous winners are 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 awards ceremony – dating back to 2006 – in which a Princeton-affiliated mathematician has received the medal.
Although he won the most prestigious prize in mathematics, Huh’s relationship with the subject was not always good. 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 he “was pretty good in most subjects except math.”
Huh eventually attended college, enrolling at Seoul National University in 2002, where he majored in physics and astronomy.
Huh’s outlook on mathematics changed, however, after an encounter with 1970 Fields Medal recipient Heisuke Hironaka in a mathematics course Huh took during his final year of undergraduate studies. The class was on algebraic geometry, and Huh had decided to attend in hopes of writing an article on Hironaka.
After earning a master’s degree in mathematics at Seoul National University, where he spent more time with Hironaka, Huh applied to graduate schools across the United States to pursue a doctorate. With a letter of recommendation 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 began his studies there in 2009 before eventually transferring to the University of Michigan in 2011.
In an interview with Quanta magazine, Huh described his life during his doctoral studies as “almost monastic”, as he “just wanted to do math” and only really interacted with his adviser, Mircea Mustaţă.
“June is a mathematician with amazing intuition, who sees beautiful connections between different areas of mathematics and has the technical power to exploit those connections in order to prove major theorems,” Mustaţă wrote in an email to ” Prince”. “I’m certainly very happy to see that he’s getting the recognition he deserves.”
Huh did not respond to a request for comment.
Huh received the award for applying “the ideas of Hodge’s theory to combinatorics” and his “proof of the Dowling-Wilson conjecture for geometric networks”, among other reasons.
“Using methods from Hodge theory, tropical geometry and singularity theory, June Huh, along with his collaborators, transformed the field of geometric combinatorics,” the IMU statement reads.
In algebraic geometry, the algebraic variety refers to a geometric shape, such as a parabola or the surface of a sphere, which can be described using certain algebraic equations.
Named after British mathematician Sir William Vallance Douglas Hodge, Hodge’s theory deals with understanding complex algebraic varieties using Hodge’s structure, a much simpler algebraic structure.
Using purely combinatorial techniques in his groundbreaking work, Huh applied ideas from Hodge’s theory to combinatorics, which deals with the study of countable discrete structures, to solve problems that mathematicians had struggled to solve for nearly 40 years old.
A simplified way to look at Huh’s work is to imagine having a sequence of numbers containing some sort 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 the dimensions of a space. This space must satisfy certain properties, which in turn imply the pattern in the sequence of numbers.
Huh’s contributions also involve Read’s conjecture. This conjecture involves simple geometric objects, which mathematicians call graphs. A triangle, for example, which has 3 edges and 3 vertices, is a simple graph.
One of the questions mathematicians have asked about such graphs is that, given a number of colors, how many distinct ways are there to color the vertices of the graph without any of the adjacent vertices have 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 on this proof, Huh also proved Rota’s 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 doctorate. in 2014, Huh joined the Institute for Advanced Study (IAS) at Princeton, where he was Oswald Veblen Fellow until 2017, and Visiting Professor from 2017 to 2020.
“I’m very happy that Huh won this award because I think he’s the kind of role model who should be at the top of mathematics,” said Jacob Matherne, Huh’s postdoctoral advisor at IAS in 2018.
Matherne described Huh as an “optimistic” and “intrepid” person, saying that “in addition to being a great mathematician, [Huh] is just a great human being.
Matherne also pointed to Huh’s signature “walk-and-talk” style.
“Sometimes I wanted to discuss a topic with June,” Matherne said, “and as soon as I approached him, he was like, ‘Let’s go think about it now. “”
“And then we would just start walking and talking and we’d end up in front of a blackboard or something,” he added.
Among most of his work, especially the groundbreaking connections he made between algebraic geometry and combinatorics, Huh deeply connected fields seemingly unrelated to mathematics.
“If you think of mathematics as a kind of continent divided into countries, I think in June’s case nobody really told her that there were all these borders,” Matherne said, quoting what Robbert Dijkgraaf, former director of IAS, said about Huh. “It is certainly not limited by demarcations,” Matherne added.
Huh received the medal alongside three other mathematicians: Hugo Duminil-Copin, James Maynard and Maryna Viazovska. Viazovska, a Ukrainian mathematician and the second woman to receive the medal since it was first presented in 1936, was Minerva’s guest emeritus at the University in 2017.
Senior News Editor Allan Shen contributed reporting for this article.
Mahya Fazel-Zarandi is editor for the “Prince”. She can be contacted by email at [email protected] or on Twitter @MahyaFazel.