June Huh’s monochrome chess puzzle paved the way for chromatic geometry.

Credit...Ruth Fremson/The New York Times

When mathematicians were young, they excelled in international competition.

June Huh was born in California and grew up in South Korea. He said he was good at most subjects. On some tests, I did well, but on others, I almost failed.

Dr. Huh pursued a career as a poet after high school. His writing was never published. He wanted to be a science journalist when he entered the university.

He can see flashes of insight. He was playing a computer game when he was a kid. There was a puzzle of four knights, two black and two white, on a chess board.

The black and white knight's positions were to be swapped. The key to the solution was to find which squares the knights were able to move to. The chess puzzle could be made to look like a graph where each knight can move to a neighboring empty space.

Translating math problems into a solution that is more obvious has been the key to many breakthrough. Our intuition only works in one of the two formulas.

June Huh defeated the puzzle.

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The goal is to swap the positions of the knights.

There are many players looking for a pattern. He almost gave up after hundreds of attempts.

The odd-shape board and the L-shape movements of the knights aren't relevant to him. Relationships between the squares matter.

It's important tocasting a problem into something simpler to understand in order to make a breakthrough.

We can keep track of the squares by numbering them.

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Consider a knight on a piece of furniture. The knight on 5 can move to 1 or 7 if he chooses.

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Calculating a network diagram is called a graph. A knight can move between squares 1 and 5 and between squares 5 and 7.

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This graph was created when this analysis was extended to the chessboard.

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The knights are placed at spaces 1 and 5 and 7 and 9.

The black and white knights don't have the same position. A knight can move to an empty area.

It's easier to figure out the new version. One answer is given here.

The moves on the original board can be found using the graph with the numbered nodes as a ring.

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The solution was obvious after viewing the same puzzle in a new way. I thought about what it meant to understand something.

He discovered math in his final year of college. Heisuke Hironaka, a Japanese mathematician who had won a Fields medal in 1970, was a visiting professor at the time.

Dr. Huh thought he could write an article about Dr. Hironaka when he was a student. Dr. Huh said that Dr. Hironaka was a huge star in East Asia.

The course drew more than 100 students. Most of the students dropped the class after finding the materialincomprehensible. The doctor continued.

There were five of them after three lectures.

Dr. Huh and Dr. Hironaka were talking about math.

Dr. Huh said that his goal was to pretend to understand what he was saying so that the conversation wouldn't stop. I didn't know what was happening so it was a challenge.

Dr. Huh and Dr. Hironaka worked on a master's degree together. In 2009, Dr. Huh applied to a number of graduate schools in the US to pursue a PhD.

Despite all of my failed math courses in my undergrad transcript, I had an enthusiastic letter from a Fields Medalist so I would be accepted from many, many graduate schools.

He was put on a waiting list by the University of Illinois, which eventually accepted him.

Dr. Huh said it was a very tense time.

At Illinois, he started the work that made him famous in the field of combinatorics, which is about figuring out the number of ways things can be shuffled. It seems like it's playing with toys.

A triangle is a simple geometric object with three edges and three vertices.

Given a certain number of colors, one can start asking questions such as, how many ways are there to make a color different from another color? The answer is given by a mathematical expression.

For more complex geometric objects, more complex coefficients can be written.

Dr. Huh used tools from his work with Dr. Hironaka to prove Read's hypothesis.

The Rota Conjecture, which involved more abstract objects known as matroids instead of triangles and other graphs, was demonstrated in 2015.

The matroids have another set of polynomials, which are similar to the ones shown in the picture.

Their proof was based on a piece of geometry called the Hodge theory.

It was just one example of the same pattern across all of the mathematical disciplines. Even the top experts in the field don't know what it is