Fields medals in mathematics won by four under the age of 40

Credits…Ruth Frimson/The New York Times

Most of the great mathematicians discovered this topic when they were young, and they often excel in international competitions.

By contrast, mathematics was a weak point for June Huh, who was born in California and raised in South Korea. “I was good at most of the subjects except for math,” he said. “The math was remarkably mediocre, on average, which means that on some tests I performed reasonably well but on others, I almost failed.”

Teen, dr. Huo wanted to be a poet, and he spent a few years after high school chasing this creative pursuit. But none of his writings were ever published. When he attended 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 middle school in the ’90s, he was playing a computer game, “The 11th Hour”. The game featured a puzzle of four knights, two of them black and two white, placed on an oddly small chessboard.

The task was to exchange the positions of the black and white knights. He spent more than a week falling over before realizing that the key was to find the squares the knights could move to. The chess puzzle can be reformulated as a graph where each knight can move to an adjacent unoccupied space, and the solution can be seen more easily.

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

Mathematical thinking puzzle

Mathematical thinking puzzle

over here Puzzle beat Jun huh:

New York times

Objectives: The black and white knights exchange positions. →

Items 1 of 9

1 of 9

He only discovered mathematics again in his last year of college, when he was 23 years old. That year, Hisuki Hironaka, the Japanese mathematician who won the Fields Medal in 1970, was a visiting professor at Seoul National University.

Dr. Hironaka was teaching a class on algebraic geometry, and Dr. Huh, long before he got his Ph.D., he thought he could write an article on Dr. Hironaka, attend. “He’s like a star across much of East Asia,” Dr. Huh said about Dr. Hironaka.

The course initially attracted more than 100 students. Huh said. But soon most of the students found the material incomprehensible and dropped the class. Dr. Huh continue.

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

Dr. Hey, he started having lunch with Dr. Hironaka to discuss mathematics.

Dr. said. Huh said, “And my goal was to pretend to understand something and react in the right way so the conversation would go on. It was a tough job because I didn’t really know what was going on.”

Dr. Huh graduated and started working on a master’s degree with Dr. Hironaka. In 2009, when Dr. Huh has applied to about a dozen graduate schools in the United States for his Ph.D.

“I was fairly confident that despite all the failed math courses in my undergraduate transcript, I had received an enthusiastic letter from a Fields Medalist, so I would be accepted from 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 very pending few weeks,” Dr. Huh said.

In Illinois, he began work that brought him to the fore in the field of combinations, the field of mathematics that quantifies the number of ways things can be mixed. At first glance, it looks like playing with Tinker Toys.

Think of 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 given number of colours, how many ways are there to color the vertices since none of them can be the same colour? 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, d. Huh proved Reed’s conjecture, which described the mathematical properties of chromatic polynomials.

In 2015, Dr. Huh, with Eric Katz of The Ohio State University and Karim Adepracito of the Hebrew University of Jerusalem, proved Rota’s conjecture, which included more abstract combinatorial objects known as matroids rather than triangles and other graphs.

For matroids, there is another group of polynomials, which show behavior similar to chromatic polynomials.

Their proof was pulled into a mystical piece of algebraic geometry known as Hodge’s theorem, named after William Vallance Douglas Hodge, a British mathematician.

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

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