Fields Medals in mathematics, won by four under 40s

Fields Medals in mathematics, won by four under 40s
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Recognition…Ruth Fremson/The New York Times

Most top mathematicians discovered the subject at a young age and often excel at international competitions.

Math, on the other hand, was a weakness for California-born and South Korean-raised June Huh. “I was pretty good at most subjects except math,” he said. “Math was remarkably mediocre on average, which means I did fairly well on some tests, but I almost failed other tests.”

As a teenager, Dr. Huh wanted to be a poet, and he spent a few years after high school chasing that creative pursuit. But none of his writings were ever published. Upon entering Seoul National University, he studied physics and astronomy and considered a career as a science journalist.

Looking back, he sees flashes of mathematical insight. He played a computer game, The 11th Hour, in middle school in the 1990s. The game involved 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 struggling before realizing that the key to the solution was figuring out which squares the knights could move to. The chess puzzle could be rearranged into a diagram where each knight can move to an adjacent unoccupied square, and a solution could be seen more easily.

Reformulating mathematical problems by simplifying 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,” says Dr. Ah said.

A riddle of mathematical thought

A riddle of mathematical thought

Here is the riddle that posed June Huh:

The New York Times

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

Point 1 of 9

1 out of 9

He only rediscovered mathematics in his final year at 23. That year, Heisuke Hironaka, a Japanese mathematician who won a Fields Medal in 1970, was a visiting professor at Seoul National.

Dr. Hironaka taught a class on algebraic geometry and Dr. Huh, long before he got his PhD he thought he could do an article on Dr. Hironaka, attended. “He’s like a superstar in almost all of East Asia,” said Dr. Huh said of Dr. Hironaka.

Initially, the course attracted more than 100 students, Dr. Ah said. However, most of the students quickly realized that the material was incomprehensible and dropped out of the class. DR Huh onward.

“After about three lectures, there were five of us,” he said.

Dr. Huh started talking to Dr. Hironaka to discuss math.

“Mostly he talked to me,” said Dr. Huh said, “And my goal was to pretend that I understood something and responded in the right way so that the conversation would continue.” It was a challenging task because I really didn’t know what was going on.”

Dr. Huh graduated and started working on a master’s degree with Dr. Huh. Hironaka. When in 2009 Dr. Huh applied to about a dozen graduate schools across the United States to earn his PhD.

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

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

“It’s been a very exciting few weeks,” said Dr. Ah said.

In Illinois, he began work that brought him exposure to combinatorics, a branch of mathematics that works out how many things can be mixed. At first glance it looks like playing with Tinker Toys.

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

One can then begin to ask questions such as: B. Given a number of colors, how many ways are there to color the vertices where none can be 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 implemented Read’s conjecture, which described the mathematical properties of these chromatic polynomials.

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

For the matroids, there is another set of polynomials that have behavior similar to chromatic polynomials.

Their proof drew on an esoteric piece 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, ubiquitous occurrence of the same pattern in all mathematical disciplines,” said Dr. Ah said. “The truth is that even the top experts in this field don’t know what it really is.”

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