"I've known you for a long time. In the past two years, your name has been circulating in the mathematics community."

When Zhao Xiancai came to the University of California and saw the Chinese mathematician born in Adelaide, Australia, Terence Tao spoke first before he could say anything.

The reason why Tao Zhexuan is called the "mathematical prodigy" and is so well-known is related to his rocket-like progress in school when he was a child.

He was born on July 17, 1975. When he was only two years old, his parents discovered his talent in mathematics, and he was sent to a private primary school when he was three and a half years old.

However, during the year and a half in kindergarten, due to his mother's guidance, he taught himself almost all the elementary school mathematics courses.

When he was 5 years old, when his parents sent him to a public school two miles away from home, he entered the second grade as soon as he entered the school. Moreover, as a second grader at that time, his math class was still in the fifth grade.

Two years later, the 7-year-old Tao Zhexuan began to teach himself calculus, and the principal of his elementary school, with the consent of his parents, took the initiative to persuade the principal of a nearby middle school to let him go to the school every day to listen to middle school mathematics classes.

When little Terence Tao entered middle school at the age of 8 and a half, and after a year of adjustment, he spent one-third of his time studying mathematics and physics at Flinders University, not far from home.

It was also during this period that Tao Zhexuan, who was 10, 11 and 12 years old, participated in the International Mathematical Olympiad and won bronze, silver and gold medals respectively.

When he reached the age of 14, he officially entered Flinders University where he attended classes in middle school.

At the age of 16, he received an honorary science degree from Flinders University.

At the age of 17, he received a master's degree from Flinders University and entered Princeton University in the same year, where he studied under Wolf Prize winner Elias Stein.

Earned a PhD from Princeton University at the age of 21.

At the age of 24, he was hired as a full professor at the University of California, Los Angeles.

Such a rapid progress in school, and he is not a Fang Zhongyong-type figure. He even won the Fields Medal, known as the "Nobel Prize in mathematics" at the age of 31. When he was a child, he was called a "mathematical prodigy".

There is absolutely nothing wrong with it.

However, after listening to Tao Zhexuan's words, Zhao Xiancai did not expect that this Chinese-American who had not been in the country for a long time would actually say such polite words.

In fact, in his own opinion, what Terence Tao said was not really polite.

Because the international mathematics community in the past two years is indeed what he just said. Whether it is China, the United States, or Europe, Zhao Xiancai's name is being circulated everywhere.

And compared with the exaggerated speed of his "mathematical prodigy", although Zhao Xiancai's childhood was ordinary, it only took him three or four years to go from a freshman in a Chinese ordinary high school to a millionaire at Princeton University.

Full professors hired with an annual salary.

This experience is much more legendary than his.

Another point is that a few months before Zhao Xiancai solved Erdös's arithmetic sequence conjecture, Tao Zhexuan also solved a conjecture raised by Erdós.

On September 17, 2015, Terence Tao announced that he had proved the existence of the Erdos difference problem raised by Paul Erdos in 1932. This is also a problem that has troubled academic circles for more than 80 years.

The so-called Erdős difference problem is discussed around the properties of infinite sequences containing only 1 and -1. Models in such sequences can be measured by creating finite subsequences.

To use the popular explanation of British mathematician Enrico Scaras, if you have a sequence consisting of 1 and -1 and a constant c, you need to find a finite sequence long enough to make the sequence

The sum is greater than the constant c.

The answer to this question is actually very simple for some sequence. In a sequence with only 1, adding up the terms will definitely yield an arbitrarily large number, which will naturally make the sum of this sequence greater than the constant c.

For an infinite sequence such as (-1,1,-1,1,-1,1,...), if you want to find a subsequence with a sum greater than 2 and a fixed interval, you only need to take

The second and fourth digits are enough; if you want to find a subarray whose sum is greater than 4, just take the second, fourth, sixth, and eighth digits.

So no matter how big the number is, you can find a subsequence in this sequence that adds up to this number, and naturally you can find a subsequence that is greater than the constant c.

However, Erdesh's conjecture is that no matter how these positive and negative ones are arranged, the conclusion "can find a long enough but finite sub-sequence such that the sum of the sub-sequence is greater than the constant c" is true.

Although like many number theory problems, the Erdös difference problem is very simple to describe. As long as you know the concept of a sequence, even a primary school student can probably understand the description of this problem.

However, it is very difficult to prove this conjecture.

From the time Erdos raised this question in 1932 until his death in 1996, no proof of this question was seen.

However, both Tao Zhexuan and Zhao Xiancai solved the different conjectures raised by Erdez.

But one of them was already forty when he solved the conjecture of Erdős' difference problem, and the other was not even twenty when he solved the conjecture of Erdós's arithmetic sequence.

It's no wonder that Terence Tao would say such things.

"No, I have admired your name for a long time. When I was in high school, you were my idol."

Zhao Xiancai also started to be confused. When he was in high school, before he obtained the system and started mathematics-related competitions, he had never even heard of the name Terence Tao.

Even after participating in mathematics competitions and getting to know young mathematics experts from all over the world, and getting to know mathematical geniuses such as Terence Tao and Peter Schultz, Zhao Xiancai actually had no feelings of admiration for them, let alone idols.

When Zhao Xiancai heard about what happened to them, his thoughts in his mind were similar to "He can take his place", and he felt that he would definitely become such a person in the future.

However, the two of them did not exchange too many polite words, and soon they started chatting about their respective research.

Because both Zhao Xiancai and Tao Zhexuan have studied some of Erdez's conjectures, and Tao Zhexuan's interests are very broad, spanning multiple fields of mathematics, including harmonic analysis, nonlinear partial differential equations, combinatorial theory, etc., and even

Involves the field of applied mathematics.

The same is true for Zhao Xiancai, but he doesn't do much research on applied mathematics, and he dabbled in it when he helped Professor Gong and others do data analysis.

Therefore, Zhao Xiancai and Tao Zhexuan can chat very well.

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