Fields Medals in Mathematics were won by four people under the age of 40

Fields Medals in Mathematics were won by four people under the age of 40
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credit…Ruth Fremson/The New York Times

Most of the best mathematicians discovered this subject when they were young and often excelled in international competitions.

In contrast, math was a weakness for June Huh, who was born in California and raised in South Korea. “I was good at most subjects except math,” he said. “Maths was particularly average, meaning I was pretty good on some tests but almost failed on others.”

As a teenager, Dr. Huh wanted to be a poet, and he spent several years pursuing this creative pursuit after high school. But none of his writings were published. When he entered Seoul National University, he studied physics and astronomy and considered a career as a science journalist.

In retrospect, he recognizes flashes of mathematical understanding. In the 1990s, he played a computer game called “11th Hour” in high school. The game included four knight puzzles, two black and two white, placed on a small, oddly shaped chessboard.

The task was to change the positions of black and white knights. It took him more than a week before he realized that the key to the solution was to find out which squares the Knights could move to. A chess puzzle can be transformed into a graph where each knight can move to the adjacent space, and the solution can appear easier.

Simplifying math problems and translating them into clearer solutions has been the key to many breakthroughs. “The two forms are logically indistinguishable, but our intuition works on only one of them,” said Dr. Huh he said.

The puzzle of mathematical thinking

The puzzle of mathematical thinking

that’s it A puzzle beaten by June Huh:

The New York Times

Purpose: Switch the positions of the black and white knights. →

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It wasn’t until his senior year of college, when he was 23, that he rediscovered mathematics. That year, Japanese mathematician Heisuke Hironaka, who won the Fields Medal in 1970, was a visiting professor at Seoul National University.

Dr. Hironaka taught algebraic geometry and Dr. Well, long before he got his Ph.D., he thought he could write an article about Ph.D. Hironaka attended. “He’s like a superstar in most of East Asia,” said Dr. Huh said about Dr. Hironaka.

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

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

Dr. Huh began to dine with Dr. Hironaka to discuss the math.

“He was the one who talked to me the most,” said Dr. Huh said: “My goal was to understand something and react in the right way so that the conversation could continue. It was difficult because I didn’t really know what was going on.”

Dr. Huh graduated and Dr. Hironaka. In 2009, Dr. Huh applied to nearly a dozen graduate schools in the United States to pursue a Ph.D.

“I was pretty confident that I had an enthusiastic letter from a Fields Medalist on my undergraduate transcript, despite all the math courses I failed, so I would be accepted by many, many colleges.”

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

“It’s been a very suspicious few weeks,” said Dr. Huh he said.

In Illinois, he began work that made him famous in combinatorics, the branch of mathematics that counts the number of ways to mix things up. 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 intersect.

You can then start asking questions such as, given a given number of colors, how many ways are there to color the vertices, none of which 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.

Dr. using tools from his work. Hironaka, Dr. Huh proved Read’s conjecture describing the mathematical properties of these chromatic polynomials.

In 2015, Dr. Huh, along with Eric Katz of Ohio State University and Karim Adiprasito of the Hebrew University of Jerusalem, proved the Rota Connection, which involves more abstract combinatorial objects known as matroids instead of triangles and other graphs.

There is another set of polynomials for matroids that exhibit similar behavior to chromatic polynomials.

Their proof is an esoteric algebraic geometry known as Hodge theorem, named after the English mathematician William Vallance Douglas Hodge.

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

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