Faltins returned to the editorial office upstairs in the café and looked up the paper in the Annals of Mathematics submission system for the problem of concave points and strongly smooth spaces in Barnach spaces.

The paper was in the first review of the editor, so it did not flow to the editor-in-chief.

Faltins went straight to "reviewer review" and sent Mill and Shen Qi's paper to the mathematics department of the Institute for Advanced Study in Princeton.

Muller and Shen Qi belong to the same school and department as Faltins, and in principle, Faltins should avoid becoming a reviewer for Muller and Shen Qi's papers.

The Institute for Advanced Study (IAS) in Princeton is an independent, private research institution, and although they are close to each other, IAS and the University are not the same institution.

Faltins felt that the paper by Mill and Shen Qi was well written, in-depth, and promotable.

Faltins approached two reviewers for Mill and Shen Qi's paper on the problem of concave and strongly smooth spaces in Barach space, both senior fellows at the Institute for Advanced Study in Princeton.

The two reviewers are Fields Medalist Drigne and Wolf Prize-winner Sanders.

Including the editor-in-chief Faltins, who has the final decision, the joint jury composed of two Filipino Award winners and one Wolf Award winner is very luxurious.

After the paper on the problem of concave points and strong smooth spaces in Banach space was delivered, Shen Qi was still very concerned.

Within a week, Shen Qi met Faltings three times in the mathematics department building.

"Hey, Professor Faltins, hello. ”

"Strange, hello. ”

"The paper I and Professor Müller is still 'under review'. ”

"Wait for news, young man, don't be in a hurry. ”

"Okay, Professor Faltins, goodbye. ”

The conversation between the two is roughly like this, and Shen Qi doesn't know who the reviewer is and what the review progress is.

"But think about it, the recognition of a new theorem will have to be reviewed for ten days and half a month, or even a few months. If it's a week to finish, I can't believe it. ”

Today is the eighth day of the paper "under review", and Shen Qi habitually logs in to the Mathematics Yearbook submission system and brushes it every day.

This brush frightened Shen Qi for a moment, and "in the review" was brushed by him as "passed the review".

Shen Qi hurriedly entered the e-mail box, but did not receive a new email from the editor of the Annals of Mathematics.

What does this mean?

"This means that my paper and Professor Müller's paper passed the reviewer's review within 8 days, and we don't even need to change it?"

"This is the 'Muller-Shen theorem', which reviewer is so perfunctory?"

Shen Qi ran to the editorial office of the Mathematics Yearbook on the fourth floor of the Department of Mathematics Building, found Faltins, and asked, "Professor Faltins, the paper between me and Professor Mueller was passed?"

"After that, the status can be changed to 'Recorded' immediately. Faltins said with certainty, and held out his hand: "Congratulations on joining the 'Naming Club', Odd!"

Shen Qi hesitated a little, did not immediately shake hands with Faltins, and asked, "Since it has been passed, can I know who the reviewer is now?"

Faltins: "Andrew Saunders. ”

"It turned out to be Mr. Sanders!" Shen Qi was very excited, Sanders was last year's Wolf Award winner and a big bull in the industry.

"Then I'm relieved. Shen Qi shook hands with Faltins enthusiastically, and I said, which big bull can complete the verification of the "Muller-Shen theorem" within 8 days? It turned out to be the Wolf Award boss!

Faltins added: "Sanders was one of the reviewers, the other being Pierre Deligne. ”

"Mr. Deligne!" Shen Qi was completely relieved at this time, Deligne is the winner of the F++A plus Crawford Award Golden Slam, a super bull.

So the two reviewers of this paper are both gods of the Institute for Advanced Study, what else is Shen Qi worried about?

"It doesn't count if the journal passes, but it doesn't count if it passes Princeton. Shen Qi suddenly remembered this sentence.

"That's right. Faltins said.

Shen Qi: "The Annals of Mathematics is run by Princeton, as well as the Institute for Advanced Study in Princeton. ”

Faltins: "The IMU admits that your new theorem doesn't count, and the Princeton and Princeton Institute for Advanced Study does." ”

Princeton and Princeton Advanced Studies overturned, and Shen Qi laughed, not in a happy mood.

Because of the process that had to be followed, a month later, the problem of concave points and strongly smooth spaces in Barnach spaces was published in the latest issue of the Annals of Mathematics.

At the same time, the IMU recognized a new theorem about the Banach space, the Müller-Shen theorem, which can be found in the IMU's database and its description.

The official description of the IMU is:

Alan Mill and Shen Qi proved the following theorem:

Let X be the Banach space, then the following argument is equivalent as:

(1) If x*S(X*) reaches its norm on S(X), then x* is the *concave point of the unit ball B(X*);

(2) X is a strong smooth space.

From now on, this theorem is named the 'Muller-Shen theorem'.

Related Literature, Annals of Mathematics, 20XX, 273:20-44. ”

"Finally, finally" Shen Qi collected the latest issue of the Mathematics Yearbook, and the four major journals have collected two copies.

The IF value of the Annals of Mathematics is the highest of all mathematics journals at 4.642.

System: "New Achievement!Congratulations to the host for publishing a paper in the Annals of Mathematics, which will reward 50,000 points of Xueba, multiplied by the IF value of 4.642, and then multiplied by the main talent of mathematics 2.0, and the final reward will be 464,200 points of Xueba. ”

Congratulations to the host for completing a new theorem named after his surname, which will reward 200,000 points for the main talent of mathematics, multiplied by 2.0 for the main talent of mathematics, and the final reward will be 400,000 points. The balance is 1688300 Xueba points, please confirm with the host. ”

"Confirmed. Shen Qi said to himself, he was in a good mood, the mathematics level was still a little more than 300,000 points away from level 12, and one or two papers could be done.

“Cheers！”

In the Observatory Restaurant, Shen Qi and Muller clinked glasses and drank some champagne.

The Observatory dining hall is Princeton's faculty dining room, and professors can bring a small number of relatives or friends in for a meal.

"Strange, how does it feel to have a theorem named after your own surname?" asked Professor Müller, who was actually the first theorem to bear his own name.

Shen Qi said: "It always feels weird, in my taro, once it is named, it is not far from retirement." ”

"That's right. Professor Müller said he was at the end of his career.

There are exceptions, however, that both authors were under the age of 40 when the Green-Tao theorem was proved. Professor Müller added.

"Green's-Tao theorem" is a theorem about prime array AP, whose name Green is Ben-Green, and Tao is Tao Zhexuan.

"But you're younger than Tao. Professor Müller did not hide his admiration for Shen Qi, and said: "Maybe in the near future, Qi, you will achieve greater achievements, come, raise a glass, toast to an outstanding young mathematician!"