Named

Faltings returned to the editorial office upstairs in the café and searched for the paper "Problems of Concave Points in Banach space and Strongly Smooth Spaces" in the Annals of Mathematics' submission system.

This paper is currently in the initial editing review stage, so it hasn't reached the editor-in-chief yet.

Faltings changed the status directly to "under review by peer reviewers" and then sent Muller and Shen Qi's paper to the Mathematics Division of the Princeton Institute for Advanced Study.

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

The Princeton Institute for Advanced Study is an independent private research institution. Although closely related, the Institute for Advanced Study and Princeton University are not affiliated.

Faltings thought that Muller and Shen Qi's paper was well-written, insightful, and had broad applicability.

Faltings found two reviewers for Muller and Shen Qi's paper, "Problems with concave points in Banach space and strongly smooth spaces," both of whom were senior researchers at the Princeton Institute for Advanced Study.

This remarkable article is worth appreciating. The two reviewers were Fields Medal winner Deligne and Wolf Prize winner Saunders.

The jury, comprised of two Fields Medal winners and one Wolf Prize winner, was quite impressive, including editor-in-chief Faltings, who had the final say.

After submitting his paper, "Problems with Concave Points in Banach space and Strongly Smooth Spaces," Shen Qi was still quite concerned about it.

Within a week, Shen Qi encountered Faltings three times in the Mathematics Department building.

"Hey, Professor Faltings, hello."

"Qi, hello."

"My paper with Professor Muller is still under review."

"Wait for news, young man, there's no need to rush."

"Okay, Professor Faltings, goodbye."

The conversation between the two went something like this, and Shen Qi wasn't sure who the reviewer was or what the review process was like.

"But thinking about it, it makes sense. The approval of a new theorem would take at least ten days to half a month, or even several months. I wouldn't believe it if it were approved in a week."

Today is the eighth day that the paper is "under review". Shen Qi habitually logs into the <Annals of Mathematics> submission system and checks it as usual.

This change startled Shen Qi; he had changed "Under Review" to "Review Passed".

Shen Qi quickly checked his email, but did not receive a new email from the editor of the <Annals of Mathematics>.

What does this tell us?

"Does this mean that my paper with Professor Muller passed the reviewers' assessment within 8 days, without needing any revisions?"

"This is the 'Muller -Shen Theorem,' which reviewer would be so perfunctory?"

Shen Qi ran to the editorial office of the * Annals of Mathematics Department * on the fourth floor of the mathematics building, found Faltings, and asked, "Professor Faltings, has my paper with Professor Muller been approved?"

"It's done. The status can be changed to 'Included' immediately," Faltings said definitively, extending his hand. "Congratulations on joining the 'Naming Club,' Qi!"

Shen Qi hesitated for a moment, not immediately shaking hands with Faltings, and asked, "Now that it's approved, can I know who the reviewers are?"

Faltings: "Andrew Saunders."

"It's Mr. Saunders!" Shen Qi was very excited. Saunders was last year's Wolf Prize winner and a big name in the industry.

"Then I'm relieved." Shen Qi warmly shook hands with Faltings. I knew it! Which genius could complete the verification of the "Muller -Shen Theorem" in 8 days? Turns out it's a Wolf Prize winner!

Faltings added, "Saunders is one of the reviewers; the other is Pierre- Deligne."

"Mr. Deligne!" Shen Qi was completely relieved. Deligne was a grand slam winner of the F+W+A and Crawford Awards, a super big shot.

So, both reviewers of this paper are top experts from Institute for Advanced Study. What else could Shen Qi possibly worry about?

"It doesn't matter if the journal approves it, only if Princeton approves it." Shen Qi suddenly remembered this sentence.

"That's right," Faltings said.

Shen Qi: "The * Annals of Mathematics * is published by Princeton University, as is the Princeton Institute for Advanced Study."

Faltings: "IMU admits your new theorem doesn't count; it only counts if Princeton and the Princeton Institute for Advanced Study acknowledge it."

Princeton and Princeton Advanced Institute of Technology are absolutely amazing! Shen Qi laughed heartily, in a very pleasant mood.

Because of the necessary procedures, a month later, the problem of "Concave Points in Banach space and Strongly Smooth Spaces" was published in the latest issue of the "Annals of Mathematics".

At the same time, IMU has recognized a new theorem concerning Banach space, the "Muller -Shöhn theorem," which can be found in IMU's database along with its description.

The official description from IMU is:

"Allen Muller and Shen Qi proved the following theorem:"

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

(1) If x*∈S(X*) attains its norm on S(X), then x* is an ω* concave point of the unit sphere B(X*);

(2) X is a strongly smooth space.

From this day forward, this theorem will be named the 'Muller -Shen Theorem'.

Relevant literature, <Annals of Mathematics>, 20XX, 273:20-44."

"Finally, finally..." Shen Qi carefully put away the latest issue of the <Annals of Mathematics>, now he had collected two of the Top Four Journals.

The Impact Factor (IF) of the Annals of Mathematics is the highest among all mathematics journals, at 4.642.

System: "New achievement! Congratulations to the host for publishing a paper in the <Annals of Mathematics>. The basic reward is 50,000 Academic Excellence Points, multiplied by the IF value of 4.642, and then multiplied by the main mathematical talent of 2.0, for a final reward of 464,200 Academic Excellence Points."

"New achievement! Congratulations, host, for completing a new theorem named after your own surname. The base reward is 200,000 Academic Points, multiplied by the Mathematics Main Talent 2.0, resulting in a final reward of 400,000 Academic Points. Remaining Academic Points: 1,688,300. Please confirm."

"Confirmed." Shen Qi muttered to himself, in a good mood. He still had a little over 300,000 academic points to go before reaching level 12 in mathematics, which he could manage with one or two papers.

"Cheers!"

At the Outlook Building restaurant, Shen Qi and Muller clinked glasses and drank some champagne.

The Observation Hall restaurant is Princeton's faculty and staff dining hall, where professors can bring a small number of family members or friends to dine.

"How does it feel to have a theorem named after yourself?" Professor Muller asked. In fact, this was his first theorem named after himself.

Shen Qi said, "It feels a bit strange. In my impression, once someone gets a name, retirement isn't far off."

"That's true," Professor Muller said, as he was entering the later stages of his career.

"However, there are exceptions. When the Green -Tao theorem was proven, both authors were under 40 years old," Professor Muller added.

The "Green -Tao theorem" is a theorem about prime arrays AP, where Green refers to Ben- Green and Tao refers to Terence Tao.

"But you are younger than Tao." Professor Muller did not hide his admiration for Shen Qi, saying, "Perhaps in the near future, Qi, you will achieve even greater things. Come, raise a glass to a distinguished young mathematician!"