From all-round academic master to chief scientist - Chapter 267 The mathematical world is once again stirred up

The Institute for Advanced Study, Princeton, in Pierre Deligne’s office.

At this time, Deligne was leaning on his chair, looking at the recently published mathematics papers.

Suddenly, there was a knock at the office door.

“Please come in.” Deligne said.

Then the door opened and Enrique Pompieri entered.

Seeing this old friend come in, Deligne stood up with a smile and asked: “Enrique, why do you have time to come to my place?”

Seeing Deligne like this, Pompieri smiled and said, “You don’t know?”

Deligne was stunned: “What do you know?”

“It seems you really don’t know, so it’s just a coincidence that I came here.”

Pompieri laughed, and then said: “Do you still remember the interview you gave after the last International Congress of Mathematicians?”

“After the International Congress of Mathematicians? Interview?” Deligne was stunned. This happened three years ago. For an old man like him, it is still difficult to think back. Moreover, he has accepted quite a lot of interviews. A top mathematician like him in the world receives invitations for interviews or lectures basically every day, so he doesn’t remember those interviews very clearly.

Of course, Deligne still had an impression of the interview after the last International Congress of Mathematicians. After all, that interview was about Lin Xiao.

That conference brought together many of the world’s top mathematics masters, and many well-known figures in the mathematics community received invitations from the International Mathematical Union to give reports at the conference. The smartest game in the world was played there.

However, no matter what, among hundreds of reports, only that young man’s report is still fresh in people’s memory. The determination of the distribution of Mersenne’s prime numbers and the proposal of Lin’s conjecture made that report worthy of being listed as an International Congress of Mathematicians. One of the most important reports in history.

After all, not many mathematicians go to the International Congress of Mathematicians to report such mathematical breakthroughs. Most of them are reports on their past research, or discuss future hot topics.

For example, when Deligne’s mentor, Grothendieck, was invited to give a one-hour lecture at the International Congress of Mathematicians, he predicted that he would make new breakthroughs in algebraic geometry, and ultimately relied on his foundation for modern algebraic geometry. work, and then established his reputation as the Emperor of Mathematics.

Of course, I remembered it, but why did Pompierelli mention this?

So Deligne said: “Remember, is there any problem?”

Pompieri smiled: “Do you remember what you said in that interview?”

“Just talking about things related to Lin Xiao, his Lin’s conjecture and so on… Could it be that what you are about to say has something to do with Lin Xiao?” Deligne quickly reacted and asked.

Pompieri laughed and said, “Do you still remember when you talked about Lin’s conjecture, how many years did you say it would take at least a few years for it to be proven?”

“More than twenty years, um… it should be twenty-five years.” Deligne replied, and then he couldn’t help but look at Pompieri and asked with a surprised look on his face: “Don’t tell me, Lin’s conjecture has been proven!!”

Seeing Deligne’s appearance, Pompieri suddenly laughed.

“Bingou! Correct answer!”

Deligne’s eyes widened and he suddenly stood up from his seat, “Are you fucking kidding me?”

“How come Lin’s conjecture was proven so quickly?”

“Impossible, absolutely impossible! Who proved it?”

Seeing Deligne like this, Pompieri laughed even louder. After a while, he stopped because he was almost out of breath.

Deligne looked really depressed and said angrily: “You old guy, I can’t stop laughing at you.”

Pompieri waved his hand, and after he was calm enough, he said: “It was Lin Xiao, Lin Xiao proved it.”

Deligne was stunned for a moment, “Lin Xiao? Really?”

“Of course it’s true, he just posted it on arxiv today.”

“Oh, that’s okay.”

Deligne waved his hand, sat back in front of his seat, and then started operating the computer.

If nothing else, of course it is to log in to arxiv.

“This young man finally published another mathematics paper, and it was Lin’s conjecture. This means he is willing to return to mathematics.”

Pompieri couldn’t help but laugh: “Didn’t he publish a paper before? That submodular form also brought a surprise to us mathematicians.”

“But didn’t he go to work on that semiconductor again later?” Deligne shook his head and sighed: “He should be… 22 years old this year, right? If such a genius can keep studying mathematics, it will be very useful to us. How useful are the developments in mathematics? As for who in the mathematics community now has the best chance of proving the Riemann Hypothesis, I guess it’s Lin Xiao.”

“What a pity, what a pity.”

Sighing, he also opened arxiv at this time and found Lin Xiao’s paper.

Looking at this title and Lin Xiao’s name, it is not difficult to give people a sense of trust in this mathematics paper with a very impressive title just because of Lin Xiao’s reputation in the mathematics community.

This is the influence of a top mathematician. Because of various deeds in the past, even when he announces that he has solved a problem, others will believe it even if they don’t read it.

Deligne couldn’t help but sigh: “It’s really amazing.”

Pompieri also walked to the side, looked at the page that Deligne opened after downloading the paper, and said: “It is indeed amazing.”

Then he sighed again: “But I am worried that if he solved Lin’s conjecture, he was actually trying to solve some problem in semiconductors. Do you know where Lin’s conjecture is needed to build a lithography machine?”

“How do I know? I don’t study this stuff.” Deligne replied without paying much attention and continued to read the paper.

When Pompieri saw him like this, he shook his head, said no more, and read the paper beside him. Although he had already read it once, reading it again would help him deepen his understanding.

Although he is quite old, after all, there is no end to learning. When he is old, when he dies, he hopes to leave this world with the most knowledge in his head.

Of course, it takes a lot of time to read this paper. After all, the whole article only lasts for more than thirty pages. This is because the content is very concise.

When Lin Xiao was organizing the paper, in order to rush for time, he no longer wrote every step in detail as before. Instead, he omitted a lot of content with words such as “obvious” and “well-known”. .

So this is also a challenge for people who read the paper. If you don’t have enough knowledge, you may not be able to understand it.

This can also be regarded as a kind of “bullying” in terms of IQ. After all, if you want to understand a math paper written by a certain boss, you must first be prepared to ask the teacher about all the “obvious” content in it. Maybe even your own teacher doesn’t understand.

Of course, there are also many cold jokes about the “obviousness” in mathematics. For example: when Andrew Wiles said it was obvious, it would be obvious about two years later – because when he announced that he had proved When it came to Fermat’s last theorem, it actually had to wait two years before he could actually prove it.

Of course, it is easy for Deligne to understand. After all, he is the proud disciple of the founder of modern algebraic geometry. As an important conjecture in algebraic geometry, Lin’s conjecture has certainly been studied in depth a lot.

So, as he turned through the pages, until the end, Deligne sighed, “His mathematical ideas and the ability to realize his ideas are still the same as before.”

“It’s really a wonderful step to be able to connect the form of layers to elliptic curves!”

Pompieri, who read it again, became more aware of the power of Lin Xiao’s paper.

He also praised: “Yes! If it were me, I probably wouldn’t be able to do this.”

“It’s topology, algebraic geometry, and it involves cohomology… Oh, it’s so amazing. If that old guy Langlands were here, he would definitely jump up with excitement to realize the Langlands program. One day is approaching again!”

“Yes.”

Deligne nodded, unifying the mathematical world!

What an exciting thing for mathematicians like them.

Lin Xiao took a more important step towards this end.

Weil’s Rosetta Stone also made it a little clearer again.

Deligne said with emotion: “Before the 20th century, mathematics was still very ‘simple’, and there were many mathematical geniuses, like Gauss, who could be called omnipotent geniuses in their time.”

“However, since the twentieth century, our mathematics has developed better and better, and has become stronger and stronger. Group theory, algebraic geometry, fiber bundles, cohomology theory, modular forms and layers…”

“So many new mathematical theories have made our field of mathematics so complex, and the division of labor has become more and more detailed. Just studying one thing is enough for people to be completely immersed in it. Even what I am studying now is only limited to Algebraic geometry, while there is little research on other theories.”

“So I have always believed that many geniuses will emerge in our mathematics community, but there will never be an all-rounder like in the past era.”

Geniuses could appear in the past era, and of course geniuses can appear in this era as well. Moreover, you must know that human beings are getting smarter and smarter. In addition, human beings today no longer lack food. They have sufficient nutrition since childhood, so their brains develop when they grow up. Therefore, the average intelligence of human beings in this era must be higher than that of people more than two hundred years ago. Even if there is not much difference among the most intelligent people, the total population in the twenty-first century is higher than that of people ten years ago. The population in the ninth century was several times higher.

Therefore, the geniuses of this era, whether in terms of statistics or evolution, actually need more.

“I didn’t expect that such a mathematical all-rounder would appear in this century.”

Deligne sighed: “If my teacher is still here, he will definitely be very happy.”

Pompieri smiled and said, “You probably overlooked one more thing.”

“Oh? What happened?”

“Lin Xiao is not just an all-rounder in mathematics.”

Deligne was stunned for a moment, and then realized what Pompieri meant.

After all, Lin Xiao is not just good at mathematics.

Instead, it also includes physics, even a little bit of material chemistry, and an important breakthrough has been made in mechanical structure.

Now he has transformed into the chief designer of lithography machines for a potential superpower.

Thinking of this, Deligne sighed deeply again.

“What are you sighing for?” Pompieri couldn’t help but ask.

“It’s a pity that he didn’t come to Princeton to study for graduate school. Otherwise, I would have had to accept this student.”

Pompieri couldn’t help laughing: “Then I became Professor Serge’s student, and I am your equal.”

Deligne said angrily: “I want you to take care of it?”

“Hahaha!”

Pompieri laughed again.

The laughter spread and was heard by people outside, but after hearing the voice of Pompieri, they were curious, what made Professor Pompieri laugh so happily?

Of course, being doubtful, these people turned around and studied the paper that proved Lin’s conjecture – it is normal for mathematicians at the Institute for Advanced Study in Princeton to pay attention to such a major event in the world of mathematics.

And it’s not just math, it’s also physicists.

In physics, algebraic geometry and topology can be used in many places, not to mention those very basic functions. The significance of Lin’s conjecture to their research is also very great.

In addition, those scholars who previously assumed that Lin’s conjecture was true and came up with dozens of propositions, now, as long as Lin’s conjecture is recognized as true, these dozens of propositions will become theorems, and these scholars They will also enjoy the honor, so these scholars are even more excited.

On the Internet, there are even more people discussing it.

On the international mathematics forum mathoverflow, there have been dozens of posts discussing the proof of Lin’s conjecture, and the post with the most discussions was initiated by Terence Tao.

Tao Zhexuan: “I have read Lin’s paper, and now I just want to say: Lin is the real Mozart of mathematics!” 』

The people who commented below are basically mathematics professors from famous universities in the world.

For example, Professor Yau Shing-tung of Harvard University commented: “Lin’s work can only be called great.”

For example, Professor Laurent Laforgue from the Ecole Normale Supérieure in Paris also said: “I really can’t imagine that such an important conjecture would be solved three years after it was proposed, let alone the solution provided by the proposer.”

Under Professor Laforgue’s comment, someone laughed and said: “At the International Congress of Mathematicians, I still remember Lin jokingly saying that even if he had a perfect way to prove Lin’s conjecture, the blackboard would be too small to write on it. . Looking back now, maybe what Lin said at the beginning was true? 』

In addition, a mathematics professor from ETH Zurich began to express his depression: “Oh! Farke! I was originally invited to give a 45-minute speech at this year’s International Congress of Mathematicians to share my research on Lin’s conjecture. But now it’s better. The conjecture has turned into a theorem, and what I want to share has become meaningless. 』

Upon seeing this professor’s unfortunate incident, many people commented with sympathy and gloating: “Hahahahahaha, it’s okay, the deadline is nearly four months away, don’t rush!” 』

“Now you can share Lin’s theorem instead!” it’s the same! Hahahahaha”

…

Of course, in addition to these big names in mathematics, the commenters on this post are mostly students.

“Thank you Lin!” My graduation thesis is on track! I couldn’t get through one step of my thesis before, but after using Lin’s conjecture and theorem, I can easily prove it. Now I only hope that Professor Lin’s thesis can be passed as soon as possible! 』

“Professor Lin is my idol!” 』

“A doctoral student in physics came here to leave a message: My supervisor studies quantum topology, and he almost hugged Professor Lin’s photo and kissed him!” Because Lin’s theorem is very helpful for his topic.』

“…”

…

The originally calm world of mathematics once again seemed to be stirred up into a craze.

[PS: I will be returning home from college in the next few days. Due to special circumstances, it may take a few days to get home. Updates cannot be guaranteed. After returning home, make sure to devote yourself to coding without any distractions]

[PPS: Except if you are traveling next month o(*￣3￣)o】