A mathematical historian once described Henry Poincare, who was born in 1854, as follows: "Some people seem to be born for.

As if to prove the existence of genius, every time I see Henry, I hear this annoying voice ringing in my ear. "Poincare as a mathematician.

His greatness lies not entirely in how many problems he solved, but in that he raised many groundbreaking and fundamental big problems. huge

Calais conjecture is one of them.

1904, poincare put forward a seemingly simple topological conjecture in a paper: in three-dimensional space, if every line is closed,

The curve can be contracted to a point, then this space must be a three-dimensional sphere. After putting forward this conjecture, Poincare once thought that he

It has been proved. But soon, the mistakes in the proof were exposed. Therefore, topologists began to prove it.

Before 1930s, there was little research on Poincare conjecture. But suddenly, the British mathematician Whitehead became interested in it.

This question aroused great interest. He once claimed that he had finished the proof, but he quickly withdrew his paper. Sang Yu's loss and East Corner's gain are,

In this process, he found some interesting special cases of three-dimensional manifold, which are now collectively called Whitehead manifold.

During the 1950s and 1960s, some famous mathematicians claimed to have solved the Poincare conjecture, such as R.Bing and Harken (

Haken), Maeuser and Papa-kyriakopoulos are all among them. Pappa Cirac Pross is.

1964 Van Buren Prize winner, Greek mathematician. Because his name is too long and difficult to pronounce, everyone calls him "Dad".

Before 1948, Papa kept a certain distance from the mathematical circle until he was invited by Princeton University to be a guest. Dad proved the famous

"Deen Lemma" is famous all over the world. john milnor, a mathematician who likes dancing and writing ink, once.

Write a limerick for this: "The ruthless Dean Lema/the natural enemy of every topologist/until Papa Cirac Pross/actually proved this."

Effortless. "However, the clever Greek topologist, but folded in the proof of poincare conjecture. There is a legend in Princeton University.

A story. Until 1976 died, my father was still trying to prove Poincare's conjecture. On his deathbed, he gave a thick stack of manuscripts to a man.

However, mathematician friend, just turned over a few pages, the mathematician found the mistake, but in order to let dad leave quietly, he finally chose Yin.

Shut up.

During this period, topologists' research on Poincare conjecture failed to produce the expected results, but they developed a low-dimensional extension.

Learn this subject.

The failure of repeated attempts makes Poincare conjecture one of the most famous mathematical problems. However, because it studies geometric topology.

Mathematicians can't put it aside. At this time, things have changed.

1966 fields prize winner smer put forward a genius idea in the early 1960s: if the three-dimensional poincare conjecture is difficult to solve,

Sure, is it easier to have high dimensions? From 1960 to 196 1, a man was often seen on the beach in Rio de Janeiro, holding a draft paper in his hand.

And pencils, thinking about the sea. He's Smale. 196 1 In the summer of, Smale gave a self-report at the conference on nonlinear vibration in Kiev.

The proof of Poincare conjecture in five dimensions and above immediately caused a sensation.

10 years later, in 1983, American mathematician Freeman will be proved to be a progress. The key person who works in Donaldson

On this basis, he proved the Poincare conjecture in four-dimensional space and won the Fields Prize for it. However, the work ahead has once again stagnated.

There is no progress in the study of three-dimensional Poincare conjecture by topological method, and some people begin to think of other tools. Thrush is one of them.

One. He introduced the geometric structure method to cut three-dimensional manifolds, and thus won the Fields Prize of 1983.

However, Poincare conjecture has not been proved.

People are looking forward to the emergence of new tools.

"Just like Fermat's last theorem, when Taniyama Zhicun's conjecture is proved, although people still can't see the specific prospect, everyone knows it.

. Because, a tool that can solve the problem has appeared. Wen Zhiying, director of the Department of Mathematics in Tsinghua University, said.

But where are the tools to solve Poincare conjecture?

I have tools.

Richard Hamilton was born in 1943, six years older than Qiu Chengtong. Although when joking, Qiu Chengtong would jokingly call this one over 30.

Playboy, an old friend for many years, likes surfing, traveling and making girlfriends, but only praises and appreciates each other in math.

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1972, Qiu Chengtong and Li Weiguang jointly developed a set of theories to study geometric structures by using nonlinear differential equations. Qiu Chengtong used this.

This method proved Calabi's conjecture and won the Fields Prize. 1979, in the discussion class at Cornell University, and then Stanford.

Qiu Chengtong, a professor of mathematics at the university, met Hamilton. "At that time, Hamilton was just doing Matteo Ricci, and others didn't know. Tell me.

Speaking of which. I don't think this thing is easy to make. Unexpectedly, at 1980, he made the first important result. "Qiu Chengtong said," in.

Yes, I told him that this result can be used to prove Poincare conjecture and the big problem of three-dimensional space. "

Ricci flow, an equation named after Italian mathematician gregorio Ricci. It can be used to complete a series of topological operations and construct geometry.

Structure, changing irregular manifold into regular manifold, thus solving the three-dimensional Poincare conjecture. After seeing the importance of this equation, Qiu Chengtong

Immediately let several students who followed them follow Hamilton to study Matteo Ricci flow. Among them, including his first student, Cao.

Huai Dong.

The first time I met Cao Huaidong was in Qiu Chengtong's report on Poincare conjecture at the superstring conference. Although during that time, almost all the media

Looking for Cao Huaidong, but wearing a big T-shirt with bright colors, he walked around the venue several times and no one recognized him. No wonder. vast

Most mathematicians are still people in ivory towers far from the public's sight, even if they are world-famous like Witten and sit in the back row, just like

Is also a big faint in the city.

1982, Cao Huaidong received his doctorate in Qiu Chengtong. 1984, when Qiu Chengtong was transferred to teach at the University of California, San Diego, Cao Huaidong followed.

Let's go However, he spent most of his time with Hamilton, who also transferred from Cornell University to San Diego. At this moment

Four doctoral students in Qiu Chengtong are following Hamilton's research direction. Among them, Shi Wanxiong is the best. He wrote a lot.

Beautiful paper, put forward a lot of good ideas, but because of personality and environmental reasons, I didn't get tenure at the university.

Wan Xiong actually gave up doing math. Speaking of Shi Wanxiong, today, Qiu Chengtong still regrets what he said. It's not helpful, but it's profound

The hypothesis is that if Shi Wanxiong at that time persisted, would the story about Poincare's conjecture be rewritten today?

There are always uncontrollable points when using Ricci stream for spatial transformation. These points are called singularities. How to master it

The movement of scientists is the key to prove the three-dimensional Poincare conjecture. 1993 after studying the work of Qiu Chengtong and Li Weiguang on nonlinear differential equations.

In 1998, Hamilton published an important paper on understanding singularities. At this time, Qiu Chengtong vaguely felt that solving Poincare conjecture.

After a while, it came.