Link exchange

Fields Medals in Mathematics won by four under 40

Credit…Ruth Fremson/The New York Times

Most top mathematicians discovered the subject when they were young, often excelling in international competitions.

In contrast, math was a soft spot for June Huh, who was born in California and raised in South Korea. “I was pretty good in most subjects except math,” he said. “Mathematics was particularly poor, on average, meaning on some tests I did reasonably well. But other tests I almost failed.

As a teenager, Dr. Huh wanted to be a poet, and he spent a few years after high school pursuing that creative quest. But none of his writings have ever been published. When he entered Seoul National University, he studied physics and astronomy and considered a career as a science journalist.

Looking back, he recognizes flashes of mathematical insight. In college in the 1990s, he played a video game, “The 11th Hour.” The game included a puzzle of four knights, two black and two white, placed on a small, oddly shaped chessboard.

The task was to swap the positions of the black and white knights. He spent more than a week fidgeting before realizing that the key to the solution was figuring out which squares the knights could move to. The chess puzzle could be recast as a graphic where each knight can move to a neighboring unoccupied space, and a solution could be seen more easily.

Redesigning mathematical problems by simplifying them and translating them in a way that makes a solution more obvious has been the key to many breakthroughs. “The two formulations are logically indistinguishable, but our intuition only works in one of them,” Dr. Huh said.

A mathematical thought puzzle

A mathematical thought puzzle

Here is the puzzle june huh beat:

The New York Times

Objective: Swap the positions of the black and white knights. →

Item 1 of 9

1 of 9

It was only during his last year of college, at the age of 23, that he rediscovered mathematics. That year, Heisuke Hironaka, a Japanese mathematician who had won a Fields Medal in 1970, was a visiting professor at Seoul National.

Dr. Hironaka was teaching a class on algebraic geometry, and Dr. Huh, long before receiving a doctorate, thinking he could write a paper on Dr. Hironaka, attended. “He’s like a superstar in most of East Asia,” Dr Huh said of Dr Hironaka.

Initially, the course attracted more than 100 students, Dr. Huh said. But most students quickly found the material incomprehensible and dropped out of the course. Dr. Huh continued.

“After about three lectures, we were about five,” he said.

Dr. Huh started having lunch with Dr. Hironaka to discuss math.

“It was mostly him talking to me,” Dr. Huh said, “and my goal was to pretend to understand something and react in the right way to keep the conversation going. It was a difficult task because I really didn’t know what was going on.

Dr. Huh graduated and began working on a master’s degree with Dr. Hironaka. In 2009, Dr. Huh applied to a dozen graduate schools in the United States to earn a Ph.D.

“I was pretty confident that despite all my failed math classes in my undergraduate transcript, I had an enthusiastic letter from a Fields Medalist, so I would be accepted into many, many graduate schools.”

All but one rejected him – the University of Illinois Urbana-Champaign put him on a waiting list before finally accepting him.

“It’s been a suspenseful few weeks,” Dr. Huh said.

In Illinois, he began the work that brought him fame in the field of combinatorics, an area of ​​mathematics that determines the number of ways things can be mixed. At first glance, it looks like playing with Tinker Toys.

Consider a triangle, a simple geometric object – what mathematicians call a graph – with three edges and three vertices where the edges meet.

One can then start asking questions like, given a number of colors, how many ways are there to color the vertices with the rule that the vertices at each end of an edge cannot be of the same color? The mathematical expression that gives the answer is called a chromatic polynomial.

More complex chromatic polynomials can be written for more complex geometric objects.

Using tools from his work with Dr. Hironaka, Dr. Huh proved Read’s conjecture, which described the mathematical properties of these chromatic polynomials.

In 2015, Dr. Huh, along with Eric Katz of Ohio State University and Karim Adiprasito of Hebrew University of Jerusalem, proved Rota’s conjecture, which involved more abstract combinatorial objects known as matroids instead of triangles and other graphics.

For matroids, there is another set of polynomials, which exhibit similar behavior to chromatic polynomials.

Their proof drew from an esoteric element of algebraic geometry known as Hodge’s theory, named after William Vallance Douglas Hodge, a British mathematician.

But what Hodge had developed “was just one example of this mysterious and ubiquitous appearance of the same pattern in all mathematical disciplines,” Dr Huh said. “The truth is that we, even the top experts in the field, don’t know what it really is.”


July 5, 2022

Due to an editing error, this article has distorted the way chromatic polynomials are calculated. The two vertices at the end of an edge in a graph must be different colors, not that all vertices in the graph must be different colors.