The Science Fiction World of Xueba

When Zhang Deye said this, Pang Xuelin immediately stopped talking.

He understood what Zhang Deye meant. The things he wrote yesterday were like the manuscripts left by Grothendieck back then.

When future generations read the content of his writing on the blackboard, I am afraid that the state of mind he has today when he goes to the French Institute for Advanced Study to read Grothendieck’s manuscripts is probably the same.

After sending Zhang Deye and Qiu Chengtong away, Pang Xuelin called his parents again and learned that they had already flown to Northern Europe to continue their journey around the world, so he left them alone.

Afterwards, Pang Xuelin took the commercial vehicle provided by the hotel to the French Institute of Advanced Science in the suburbs of Paris. (The previous article was translated into the French Institute for Advanced Study, which is a more accurate translation. There is also an Institute for Advanced Practice in France, which is a comprehensive research institution and is not the same thing as the French Institute for Advanced Study)

At the gate of the hotel, many reporters set up long guns and short cannons, but were stopped by security guards.

Fortunately, Pang Xuelin was sitting in the car and was not discovered by the reporter.

Pang Xuelin made an appointment with Professor Barman of the French Institute of Advanced Science and Technology yesterday, and he will come to see it today.

The French Institute of Advanced Sciences, referred to as IHES, is a small research institute focusing on pure mathematics and theoretical physics. It was founded in 1958 and is located in Bures-sur-Yvette, a suburb of Paris.

Grothendieck's golden age was spent at IHES (1958-1970).

He and his colleagues during this period greatly developed modern algebraic geometry, making it a popular branch of modern mathematics.

The early international reputation of IHES is also largely derived from this.

From 1960 to 1969, IHES held the famous seminar on algebraic geometry.

The lectures of this seminar were later compiled and published, which is the famous SGA.

In addition, Grothendieck and Jean Dieudonne wrote "Principles of Algebraic Geometry" between 1960 and 1967, the famous EGA, which is regarded as the cornerstone of modern algebraic geometry.

However, because Grothendieck later did not allow some of his works to be translated and reprinted, although EGA was translated into many languages, these translations were not genuine.

The French version of EGA can only be bought at IHES at present, although it is very expensive, the full set costs 237 euros.

Pang Xuelin got off the car and followed Baman into the IHES.

The scale of IHES is very small. From its establishment to the present, there are only 18 official members, including Fields Medal winners Grothendieck, Rainer Thom, Deligne, and Sinkan Burgan. , Laurent Laforge, Maxim Kontsevich, Abel Prize winner Mikhail Gromov, Wolf Prize winner Sullivan and others.

In terms of the number of Fields Medal winners alone, IHES is second only to the Institute for Advanced Study in Princeton.

Professor Barman is actually just a visiting scholar of IHES, but he has been in IHES for two years as a visiting scholar, so he can be regarded as a member of IHES.

The arrival of Pang Xuelin did not cause much sensation in IHES.

At best, some doctoral students in IHES came to take a look. After all, it is not difficult to see the winner of the Philippine Award here. People are only curious about Pang Xuelin because he is younger.

Of course, this is also related to Pang Xuelin's report at the Four Seasons Hotel yesterday. Most of the IHES scholars are still studying Pang Xuelin's writing on the blackboard, and Pang Xuelin naturally has no intention of disturbing them.

IHES occupies a small area, only a few buildings, cafeteria, administrative building, library, scholar's office, lecture hall, surrounded by lush forests and a quiet environment.

Professor Barman brought Pang Xuelin to a small building and said: "This is the IHES library. Grothendieck's manuscripts have been in the storage room of the library. In order to prevent damage to the manuscripts,

At present, only the English translation is open to the public, and I will get it for you later. "

"Professor Barman, I will trouble you!"

"You're welcome."

Baman smiled slightly and helped Pang Xuelin find the manuscript of the English translation from the library.

It can be seen that this manuscript has been a few years old, the paper is slightly yellowed, and there are still many rough edges.

Baman said: "Pang, I won't bother you anymore, just call me after you finish watching, and I'll come pick you up when the time comes."

"Okay, then you go!"

Holding the yellowed paper in his hand, Pang Xuelin felt a little regretful.

Before his death, Grothendieck burned most of the manuscripts, and only a small part remained, which were respectively collected by the Institute for Advanced Study in Princeton and IHES.

Part of the IHES collection is some manuscripts describing the framework of Far Abelian geometry.

This manuscript perfectly presents Grothendieck's style of doing mathematics, that is, abstracting unnecessary details from mathematical objects as much as possible. Mathematicians with average abstraction would think that only "emptiness" is left, but he still Can grab something out of "the void" to build his theories and complete his proofs.

In Grothendieck's own words, if a mathematical problem is compared to a nut, what most mathematicians do is to use a hammer and chisel to chip open the nut, but his method is to soak the nut in water and slowly soften it The shell, or let it stand the wind and sun, and then wait for the right time, and the nut will naturally crack.

The same is true of this manuscript. In it, Pang Xuelin hardly sees specific examples. All descriptions start from the most abstract point of view, thinking about algebraic geometry and the grand mathematical structure behind number theory.

It was difficult for Pang Xuelin to read, but this was also the reason why he wanted to read Grothendieck's manuscript.

Although Pang Xuelin has long been familiar with the theoretical framework of Far Abelian geometry, through Grothendieck's manuscript, he can simulate as much as possible the way Grothendieck thought when he wrote this immortal masterpiece.

It took half an afternoon for Pang Xuelin to read all of Grothendieck's manuscripts.

Although Pang Xuelin didn't find anything new in it, Grothendieck's way of thinking about mathematics benefited him a lot.

Before leaving, Pang Xuelin bought a French version of "Principles of Algebraic Geometry" for 237 Euros as a souvenir of his trip to Paris.

After leaving the French Institute of Advanced Science, Pang Xuelin returned to the hotel by car.

The commercial vehicle was driving along the road along the Seine River. When approaching the Champs Elysees, looking at the Eiffel Tower in the distance, Pang Xuelin suddenly felt a whim, and asked the driver to park the car on the side of the road, ready to get off and walk.

He has only been to Paris twice. The last time, during his Ph.D. studies, he came to Paris with Tao Terence to attend an academic conference.

Pang Xuelin always passed by this romantic city, which is famous all over the world, and never took a good tour of the city.

It was only four o'clock in the afternoon, and there was nothing to do back at the hotel. It was a rare time to come out. Pang Xuelin was going to walk along the Seine River to relax.