Scholar’s Advanced Technological System

Translator: Henyee Translations Editor: Henyee Translations

At the beginning of April, a major event took place in the mathematics community.

In the latest issue of Annual Mathematics, the proof to the Collatz conjecture was published.

The Collatz conjecture was as followed: Start with any natural number N. If it was odd, then the next number was 3N+1. If it was even, then it became N/2. After some limited number of iterations, the sequence would inevitably fall into [4,2,1].

This conjecture was popular during the 1980s.

Prior to this, some people had used supercomputers to test numbers below 1.1 trillion. They determined that no matter what number they chose, they would end up in the “421” curse.

Due to this miraculous property, this conjecture was also known as the “Hail conjecture” because it was like a hail—fast and unstoppable.

But now, Vera’s thesis provided proof for this age-old conjecture.

That the Collatz conjecture was true.

The thesis received worldwide attention.

What astonished the world wasn’t just because the thesis was the proof of the Collatz conjecture, but this conjecture was proved by Lu Zhou’s students.

By convention, a proof for a major mathematics conjecture often required more than a thesis publication. Other than the journal review process, the proof had to be recognized by the entire mathematics community.

Normally, Princeton would have arranged a report meeting for Vera and others to report on the relevant research results and to answer questions from other scholars.

But coincidentally, the quadrennial International Congress of Mathematicians was going to happen in August. Therefore, Vera’s report would be taken care of by the International Mathematical Union.

Two weeks after the thesis was published, Peter Sarnak, Princeton professor and editor-in-chief of Annual Mathematics, found Lu Zhou and brought him an invitation from the International Mathematical Union.

Very few people received two invitations from the International Congress of Mathematicians.

Sarnak had never heard of this happening before.

“… Professor Viana, the chairman of the International Congress of Mathematicians, sent me an email asking me to forward this letter to you. A major conjecture like the Collatz conjecture should be known by more people. This is a rare opportunity, and they’ve arranged a 45-minute report for you. Are you available?”

Lu Zhou looked at Professor Sarnak and shook his head. He then said, “I already have a one-hour report to do, so I’m pretty busy. I’m afraid I don’t have time to prepare for a second report.”

Sarnak raised his eyebrows. “Is it about the Navier–Stokes equation?”

The Navier Stokes equation research group applied for an official research project at the Institute for Advanced Study. Therefore, Lu Zhou and Professor Fefferman’s collaboration was not a secret.

However, what surprised Sarnak was that this research project had only begun at the end of last year; it had been less than a year.

He didn’t think Lu Zhou and Fefferman could solve the Millennium Prize Problem in such a short amount of time.

However, he didn’t expect Lu Zhou’s answer.

Lu Zhou nodded. “Yes.”

When Professor Sarnak heard his answer, he had a surprised look on his face.

He then said, “Are you confident that you can solve it before August? You don’t have much time left.”

Lu Zhou smiled and answered the question with ease.

“Once a tool is crafted, applying it is only a matter of time. That’s how I feel right now. You must know this feeling as well.”

Professor Saneck frowned and immediately reacted.

“Is the tool you’re talking about the L Manifold thesis that you recently submitted to Annual Mathematics?”

Lu Zhou smiled and nodded his head. “Exactly! I think it’s the key to solving the Navier–Stokes equation.”

When Professor Saneck heard this confident answer, he began to think.

He had heard of Lu Zhou’s recent Annual Mathematics thesis before, and it caused a lot of controversy in the editorial department at Annual Mathematics.

Although this particular differential manifold was novel, most academic editors couldn’t see the meaning or use behind it.

Sarnak also couldn’t see the use behind it despite knowing a little about partial differentials.

In the end, he accepted Lu Zhou’s thesis and allowed it to enter the peer review stage.

Now, it seemed his decision was quite intelligent…

…

After Lu Zhou bade farewell to Professor Sarnak, he brought the IMU invitation back to his office at the Institute for Advanced Study. He then held an internal meeting for his three PhD students.

“In my hand is an invitation letter by the International Congress of Mathematicians to do a 45-minute report. Although the organizers invited me to do the report, I know that you guys need this opportunity more than me.”

Lu Zhou paused for a second as he looked at his three students.

He then continued, “Normally, the report will be completed by the main contributor to the thesis. I will give my recommendation to the International Mathematical Union for Vera to be the presenter. What do you guys think?”

Qin Yue: “Agreed!”

Hardy: “Me too!”

The students reached a consensus.

Lu Zhou looked at his two students and nodded.

He then said, “It seems like we’ve reached an agreement.”

Vera was a little anxious. “Wait a second, I…”

Hardy grinned and said, “You don’t have to be modest. Since most of the thesis was completed by you, you should be the one to do the report.”

Vera looked embarrassed, and she started to get nervous. She began to stutter as she said, “But I’ve never reported at an IMU conference before… I’ve never even been to one.”

“That’s fine, this is my first time going as well. As a matter of fact, it’s actually my first time going to Brazil, so I’ll have to ask Hardy to act as a tour guide.” Lu Zhou smiled as he said in an encouraging tone, “Your report at Berkeley went pretty well, right? I remember you even received the Best Young Speaker Award. Just remember to do your thing.”

Vera calmed down a bit after hearing Lu Zhou’s words of encouragement. However, she still looked a little nervous.

Lu Zhou looked at Vera being shy and couldn’t help but wonder.

Is she really a Slav?

Although he didn’t know much about Slavs, from what he saw in movies, he would never imagine Slavs as being timid and fearful.

Lu Zhou said, “In short, don’t take it too seriously. Just pretend as if it’s a normal report. Also, you have 4 months to prepare.”

Vera twiddled her fingers as she asked in a hushed tone, “Can you help me?”

Lu Zhou shook his head and said, “I’m afraid I can’t.”

Seeing that Vera looked disappointed, Lu Zhou paused for a second before he continued, “I will be going on a retreat, so you will have to do this report by yourself.”