At the beginning of April, a big event happened in the world of mathematics.

The paper, published in the latest issue of the Annals of Mathematics, announced the solution of the Kakutani conjecture.

The so-called Kakutani conjecture is to write a natural number N arbitrarily, and if it is an odd number, the next step becomes 3N+1. If it's an even number, the next step becomes N/2. After a finite number of cycles, they will inevitably fall to the bottom of [4, 2, 1].

This numbers game was all the rage in North America in the 80s.

Prior to this, some people have tested the natural numbers below 1.1 trillion with the help of supercomputing, and determined that no matter how much the numbers swell during the period, they will not be able to get rid of the curse of "421" in the end.

Because of this miraculous property, this conjecture is also called the "hail conjecture", because the fall of numbers is as swift and unstoppable as hailstone.

And now, the paper of Vera et al. gives a definite proof of this proposition in the language of mathematics -

That is, the Kakutani conjecture is true.

As soon as the paper was published, it received a lot of attention.

What surprised the outside world was not only the proof of Kakutani's conjecture, but also the fact that the main person who completed this paper was Lu Zhou's student.

Conventionally, the proof of such a major mathematical conjecture is often not something that can be done with a single paper. In addition to the recognition of authoritative journals, the prover needs to be recognized by the entire mathematical community.

Normally, Princeton would have arranged a presentation for Vera et al. to present the results of their research and answer questions from scholars in the field.

However, just in time for the quadrennial International Congress of Mathematicians in August, the report will be carried out by the more authoritative International Union of Mathematicians.

Just two weeks after the paper was published, Professor Peter Sanak, a tenured professor at Princeton and editor-in-chief of the Annals of Mathematics, approached Lu Zhou with an invitation letter from the International Union of Mathematicians.

It is rare for someone to receive two invitations at the same International Congress of Mathematicians at the same time.

At least not in Sanak's impression.

“…… The Chairman of the Organizing Committee of the IMU Conference, Professor Viana, has sent me an e-mail asking me to forward this written letter to you. The proof of such a major mathematical conjecture as the Kadoya conjecture should be known by more people. It's a rare opportunity, and it's the International Congress of Mathematicians soon, and they have arranged a 45-minute presentation for you, see if you have time here? ”

Looking at Professor Sanak, Lu Zhou shook his head and said, "I already have a one-hour report meeting, and I've been very busy lately, I'm afraid I don't have time to prepare for the second report meeting. ”

Sanak raised his eyebrows: "About the NS equation?" ”

The "NS" research group has officially applied for the opening of the topic at the Institute for Advanced Study, and the cooperation between Lu Zhou and Professor Feverman is not a secret in Princeton.

However, to Sanak's surprise, this topic was only started at the end of the previous year, and it has not even been a year now.

Obviously, he didn't think Lu Zhou and Feverman would be able to complete the proof of that millennial conundrum in such a short time.

However, Lu Zhou's answer was beyond his expectations.

Lu Zhou nodded: "Yes." ”

Hearing this unexpected answer, Professor Sanak had a surprised look on his face: "Are you so sure that you will be able to solve it before August?" Wouldn't it be too short? ”

Lu Zhou smiled and continued to answer the question in a relaxed tone.

"When a tool is completed, it's only a matter of time before it fulfills its mission. I have a hunch of this, and you should know it. ”

Professor Sanek frowned slightly, then reacted immediately.

"Are you talking about the tool you recently submitted in the Annals of Mathematics paper on the 'L manifold'?"

Lu Zhou smiled and nodded: "Exactly, in my opinion, it is the key to solving the NS equation." ”

Hearing this affirmative answer, Professor Sanek was filled with emotion.

He had heard of that paper before, because it caused quite a bit of controversy in the editorial board of the Annals of Mathematics.

Although the novelty of this particular differential manifold is unquestionable, many academic editors do not see what the significance or usefulness of this thing is.

Sanak doesn't see it either, even if he is not ignorant of the field of partial differential.

But in the end, he accepted Lu Zhou's manuscript and arranged for it to enter the peer review process.

Now it seems that his original decision was really a visionary thing......

……

After saying goodbye to Professor Sanek, Lu Zhou took the invitation to the IMU conference and went to the office of the Institute for Advanced Study to gather three of his doctoral students for an internal meeting.

"I have an invitation letter for a 45-minute presentation at the International Congress of Mathematicians, and although the organizers of the conference have invited me to give a talk, I think you need this opportunity more than me."

After a pause, Lu Zhou's gaze stayed on the faces of the three students for a moment before continuing.

"As is customary, the presentation will be presented by the main paper author, and I will recommend Vera as the speaker to the International Union of Mathematicians, what do you think?"

Qin Yue: "Agreed!" ”

Hardy: "Seconded!" ”

The vote passed by an overwhelming margin.

Looking at the two students who raised their hands, Lu Zhou nodded and said happily, "It seems that we have reached a consensus." ”

Seeing that she was sold by two teammates in an instant, Vera was suddenly a little anxious: "Wait a minute, I'm ......"

Hardy grinned and said, "You don't have to be humble, the main part of the paper is done by you, and this report should naturally be yours." ”

Glancing at Lu Zhou with some embarrassment, Vera's voice became a little stammered because of nervousness: "But I have never made a report at the IMU conference...... I didn't even attend at all. ”

"It's nothing, it's my first time to participate, and even my first time to go to Brazil, I'm afraid I'll have to trouble Hardy to be a guide when the time comes," Lu Zhou smiled and said in an encouraging tone, "Isn't your report at Berkeley going to be very good?" I remember that you also got the certificate of Best Young Speaker. You just have to remember to play normally on stage. ”

Hearing Lu Zhou's encouragement, Vera became a little calmer, but the nervous expression on her face still did not completely ease.

Looking at Vera's nervous look, sometimes Lu Zhou really couldn't help but wonder, is she really a Slav?

Although he did not have an in-depth understanding of what other Slavs were like, based on the impressions he received in various films, he could not match the words timidity and fear of life with the words Maozi.

After a pause, Lu Zhou continued: "In short, don't take it too seriously, just prepare it as an ordinary report." Not to mention that you still have four months to prepare slowly. ”

Fingers pinching the corners of her clothes, Vera whispered, "Can you help me?" ”

Lu Zhou shook his head: "I'm afraid it won't work this time." ”

Looking at the slightly lost expression on Vera's face, Lu Zhou paused for a moment and continued.

"After today, I will continue to start the retreat, and this briefing, you can only rely on yourself."