Shulou(Shulou.com)11/24 Report--

Eugenio Calabi, a mathematician hailed as "one of the most influential in the 20th century", has died at the age of 100.

In his life, he made many important contributions to the progress of human geometry.

Among them, the most famous conjecture is the Calabi conjecture about a kind of special manifolds put forward by Karabi in 1954.

In 1976, 22 years later, S.T. Yau, then 27, became famous by proving this conjecture.

As a result, S.T. Yau won the Fields Award, the highest prize in mathematics, in 1982, becoming the first Chinese winner of this award.

△ Karabi (left) and S.T. Yau (right) were shot in 1999, but more importantly, it was the confirmation of the Calabi conjecture that led to the Calabi-Qiu manifold later named after them.

Under the attention of physicists, Karabi-mound manifold has also become an important bridge between mathematics and physics, and opened a new door for physics.

In short, in the words of physicist Brian Greene:

The code of the universe may be engraved in the geometry of Karabi-Qiu space.

Even now, every year, many mathematicians and physicists publish thousands of articles to explore its properties.

And the beginning of all these stories comes from the conjecture put forward by Karabi at that time.

As a result, many people use this description when referring to Karabi:

A creative, revolutionary and original mathematician.

Now that this mathematical superstar has fallen, we would like to use this article to commemorate the legendary and admirable life of Karabi.

Laying the foundation for superstring theory in 1923, Calabi was born into a family in Milan, Italy, and the family moved to the United States in 1938.

He was a talented teenager who entered the MIT at the age of 16, but he didn't graduate until seven years after entering the campus.

Of course, the problem is not Karabi himself, but fate played a little joke on him.

Karabi, who enrolled in 1939, spent almost all his undergraduate career during World War II, and the first three years went well.

The turning point came in 1943, when Karabi, who was about to graduate, was drafted into the army, and school had to be postponed.

It took two years to go, and after the victory in World War II, Calabi finally received his bachelor's degree in 1946 with the help of veterans' organizations.

But geniuses are geniuses after all-only a year after graduation, Calabi earned a master's degree in mathematics from the University of Illinois at Urbana-Champaign.

After graduating with a master's degree, Karabi went to Princeton University to study for his doctorate under the guidance of Salomon Bochner, an academician of the National Academy of Sciences.

When △ Bohener was a doctoral student, Calabi developed a deep interest in Keller manifolds, which was also related to his thesis, which laid the groundwork for the proposal of Calabi's conjecture.

In 1950, Calabi received his doctorate and began his career as an assistant professor at Louisiana State University the following year.

In 1953, Calabi began to think about a shape that had never been imagined before.

It was not until 1954 that the International Mathematical Congress was held in Amsterdam, at which Calabi wrote his famous conjecture on a page in the invitation report of the conference.

Let M be a compact Kahler manifold, then there exists a unique Cahler metric for any form R of the first Chen class (1 ~ (1)), whose Ricci form happens to be R.

If described in physics, this conjecture can be expressed as whether there is a gravitational field without material distribution in a closed space.

Calabi also roughly described a proof of his conjecture and proved that if the solution exists, it must be unique.

But for more than 20 years, this conjecture was never proved, during which Calabi taught at the University of Minnesota and the University of Pennsylvania and was promoted to professor.

Although Karabi put forward the conjecture and gave the idea of proof at the same time, in 1957, he found that this road may not work.

According to Karabi's idea, a very difficult and complex partial differential equation, called Monge-Ampere equation, needs to be solved in the process of proof.

Karabi consulted Professor Andre Weil, a famous mathematician, and Weil said there was nothing he could do.

(in fact, by 2021, the breakthrough on the equation will still be at the top level. )

It wasn't until 1970 that S.T. Yau, who was studying at Berkeley, met Karabi on the recommendation of his mentor, Blaine Lawson.

However, after a conversation between Karabi and S.T. Yau, S.T. Yau thought his conjecture was not valid, and then began a three-year career in searching for counterexamples.

In 1973, S.T. Yau told the news to several friends while attending the International Geometry Conference, which caused an uproar and was invited to report.

At the meeting, S.T. Yau explained in detail how to find the counterexample of Calabi's conjecture, and Calabi himself attended the report meeting.

Shiing-Shen Chern told S.T. Yau after the meeting that this counterexample may be the best outcome of the conference.

The "Chen category" involved in the Shiing-Shen Chern conjecture is named after Calabi, and Shiing-Shen Chern's comment seems to announce the end of the Calabi conjecture.

△ Shiing-Shen Chern

But that didn't make Karabi give up his idea.

Two months later, Karabi wrote to S.T. Yau, asking him to explain to himself some of the problems that were not clear in the counterexample.

Seeing the letter, S.T. Yau knew at once that he had made a mistake.

After many failed attempts to cite counterexamples, S.T. Yau decided to change the direction of his research-- to prove that the Calabi conjecture was valid.

It took S.T. Yau four years to prove it, but the first three years were trying to find a smooth solution to the Monge-Ampere equation.

But the difficulty can be imagined. In the end, S.T. Yau decided to change the way of thinking, construct a series of approximate solutions and finally converge to the Monge-Ampere equation.

Finally, in 1976, S.T. Yau successfully proved the Karabi conjecture by using the concept of curvature in Carlerian geometry and sent a copy of the proof process to Calabi.

After more than 20 years of speculation, the dust has finally settled. Based on this conjecture, Karabi-Qiu manifold has been constructed, which has become an important foundation of superstring theory in the field of physics.

After that, Calabi still had a deep passion for mathematics, and he continued to study mathematics until he was in his 90s.

However, Karabi was not determined to become a mathematician from the beginning.

The father of Karabi, who switched from chemical engineer to math, is a lawyer and a sister who is a journalist.

Although Karabi had a strong interest in mathematics when he was a child, he majored in chemical engineering at MIT.

During his enlistment in World War II, he worked as an interpreter for the United States Army in France and Germany.

After returning to the United States, he worked briefly as a chemical engineer before studying for a master's degree and a doctorate in mathematics.

But from the beginning of his master's degree in mathematics, Calabi's love of mathematics continued to the end of his life.

As for his favorite math, Karabi described it as follows:

Being able to treat my hobby as a profession is an extraordinary luck in my life.

Karabi is very fond of communicating with people about math problems, and talking to students may last for hours.

Chen Xiuxiong, his student, recalled that Professor Karabi always played the role of the opener of the topic.

Whether in the mailroom or in the corridor, Chen Xiuxiong is often "stopped" by Karabi to discuss math problems.

Whenever △ Chen Xiuxiong is inspired, Karabi takes paper and writes down formulas on envelopes, napkins and other pieces of paper.

S.T. Yau encountered the same situation when communicating with Calabi, and he kept some of the napkins he used at the time.

I always learn from these formulas, which convey Calabi's incredible geometric intuition.

He shares his ideas generously and doesn't care if he gets honors for it.

He just thinks it's interesting to do math.

The 100th birthday is congratulated by many mathematicians. It is not common in the field of mathematics to celebrate the 100th birthday of a legend.

The last time this happened was in 1991, when Leopold Vietoris celebrated his 100th birthday.

So on May 11 this year, on the occasion of Karabi's 100th birthday, many mathematicians around the world congratulated him.

From these congratulatory words, we can also see the human and academic light emitted by Karabi.

The most noteworthy is S.T. Yau, who wrote for Karabi:

I regard Shiing-Shen Chern, Morri, Nilenberg, Singh and Karabi as teachers, but ideologically they are closest to Carrabee and communicate most freely. So every time I see him, I will go to the world and talk about everything.

We haven't seen each other much in the past twenty years, but I always think about my teacher and my friend Mr. Karabi. He pursued learning all his life, did not admire fame and wealth, was willing to teach, and was respected by his peers and looked up by the younger generation. His remarkable achievements in mathematics have long been engraved on the monument in the history of science.

Jerry Kazdan of the University of Pennsylvania recalls his academic exchanges with Calabi.

He believes that Calabi's amazing insight into geometry is his talent, he has a deep intuition about what is important and interesting, and always generously shares his ideas:

He often came to my office and began to explain some of his recent ideas on the blackboard.

So much so that sometimes undergraduates who happen to be in the office are confused about their discussions.

In his congratulatory message, Chen Hsiu-hsiung mentioned a good habit taught by Calabi:

Professor Calabi will ask me to repeat what he said or what I heard at the next meeting without referring to any notes.

As he explained, "it won't be yours until it's imprinted on your memory."

Now I am a big fan of this sentence, and I have been passing it on to my own students.

Throughout the congratulatory messages of other mathematicians, a very intuitive feeling is that many people are recalling the academic topics they exchanged with Calabi and impressed them.

From this, it can be seen that Calabi is full of enthusiasm in geometry.

What is more commendable is that he is not only feverish by himself, but also spreads the remaining temperature to others: either the academic habits or the spiritual strength emitted are all inspiring and inspiring the "back waves".

R.I.P

Reference link:

[1] https://www.quantamagazine.org/the-mathematician-who-shaped-string-theory-20231016/

[2] https://euromathsoc.org/magazine/articles/144#S0.SS0.SSSx9

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