From all-round academic master to chief scientist

Even Viana, who has not studied number theory, has heard of the name of Mersenne primes.

There are too many well-known historical figures who have studied Mersenne prime numbers. Not to mention Euclid and Mersenne, including Fermat, Gauss, Goldbach, etc., they have all conducted research, but they have all failed in this regard. .

Of course, after all, these mathematicians were all figures from a long time ago. The mathematical tools they could use at that time were far from as many as they are now, and their research on mathematics was not as convenient as modern times. They did not have the Internet at that time. Websites like ArXiv allow them to search all papers in the world.

It is precisely because of this that so many great mathematicians were able to appear in the beginning, because they led the take-off and development of mathematics in the world almost relying on their own research, and they were all versatile in their own era. mathematician.

Nowadays, the subject of mathematics is becoming more and more refined, and a lot of new mathematics have emerged. Just say that the algebraic geometry developed by the mathematical emperor Grothendieck is enough for today's mathematicians to study it for a lifetime, not to mention that there are also Those things that Lin Xiao used in his research.

For example, group theory was pioneered by Gavarro more than ten years after Gauss's death. As for modular formal theory, it did not appear until the end of the 19th century and gradually matured after the 20th century.

Therefore, it cannot be said that Lin Xiao solved this problem, which means that he is better than those masters. It is just because he has more mathematical tools. As Newton said, "I stand on the side of giants." on the shoulder".

Although when Newton said this, he was actually trying to mock a mathematician named Hooke...

Marcelo Viana looked at this topic and was surprised at first, but then frowned.

"But, I remember that the paper he was supposed to publish, isn't it related to the Fibonacci sequence? What happened to this? How did it become a Mersenne prime number?"

How could such important results be presented directly to the International Congress of Mathematicians without careful and rigorous review?

Moreover, there is still more than half a month left!

"Oh my god, this is messing with me!"

Marcelo Viana scratched his hair until finally, he gritted his teeth and said, "Forget it, send it to Professor Sarnak first and let him take a look."

"However, that young man from China, you'd better not have too big a problem. If you want to stand out at the International Congress of Mathematicians, you must first ensure that you don't make mistakes. Otherwise, the conference will only prevent you from falling into the trap. It’s a laughing stock.”

After saying this silently, he sent the paper to Peter Sarnak. As a member of the International Mathematical Union, Professor Sarnak was also obliged to undertake this review work.

…………

Princeton University, Fine-Hall.

Professor Peter Sarnak's office.

Peter Sarnak was the winner of the Wolf Prize in Mathematics who originally reviewed Lin Xiao's paper on the prime number problem of the Fibonacci sequence. At this time, he was doing review work. As the editor-in-chief of the "Annals of Mathematics", this It's also his job.

But at this time, he suddenly noticed that he had received a message from the International Congress of Mathematicians.

"Huh? It's from Professor Wiana, the chairman of this conference?"

When he saw the news that it was the chairman of the organizing committee of the conference, he did not hesitate, stopped what he was doing, and then opened the message and read it.

Soon, he learned the purpose of Professor Wiana's visit.

"Lin Xiao has just submitted the report manuscript now?"

After learning the news, Professor Sanak couldn't help but be stunned.

Now there is only more than half a month left before the start of the conference, but that Lin Xiaocai submitted the report?

At the beginning, he took the initiative to ask Lin Xiao to come and give a report. After all, it was rare for a prime number problem to be solved, which was obviously a gratifying thing for workers in the field of number theory, so other professors did not refuse.

Of course, he had the same mentality at the beginning to support young mathematicians and hope to get to know Lin Xiao.

However, a month has passed now. Is Lin Xiao just sorting out the paper now?

This time is a bit slow.

However, he shook his head again. No matter what, just submit it. Even if it's a little late, it doesn't matter.

Then he downloaded the file sent by Chairman Wiana.

However, after opening the file, he couldn't help but be stunned.

"Group transformation method? And the distribution law of Mersenne prime numbers... What is this? In his original paper, did he use modular form? Didn't he use polynomial transformation?"

Professor Sarnak first doubted whether this was Lin Xiao, but after looking at the signature of the paper, he found that it was indeed ‘Lin-Xiao’.

Then he wondered if his memory was confused.

After pinching his head, he took the cup from the side and took a sip of the coffee inside, cheering up a little.

Then, he looked at the summary.

After reading the summary, his eyes widened, and he took another sip of coffee to calm down his shock.

Next he looked at the page numbers. There were seventy-eight pages in total.

He choked on the coffee he just drank.

"Cough cough cough..."

In the room, his graduate students could not help but ask with concern: "Professor, what's wrong with you?"

"It's okay." Sanak patted his chest. After he felt comfortable, he frowned tightly and looked at the paper on the computer.

Until the end he smiled bitterly.

This Lin Xiao really brought him a 'surprise'.

But this 'surprise' was given to him separately. Now he received the 'surprise', and now he hopes that he can successfully receive the second half of the 'joy'.

But that will have to wait until he reads this paper to find out.

"It really posed a problem for me."

Seventy-eight pages, can you finish it in forty-five minutes?

Sighing, he didn't rush to read it directly because the paper was too long and the conclusion was too shocking. He needed to find some mathematician friends to read it together.

And who are his mathematician friends?

"See Pierre Deligne?"

Well, this is a Fields Medal winner, a tenured fellow at the Institute for Advanced Study in Princeton.

"Where's Burgan? But he probably doesn't have time."

This is also a Fields Medal winner.

"How about looking for Langlands? But he is in Turkey now, and I don't know what he is doing all day long."

This is the proposer of the Grand Unified Theory of Mathematics and the Langlands Program.

"Pompieri is still traveling in Europe. He probably won't come until the Mathematicians Conference starts."

"Forget it, just find Deligne. He should have nothing to do recently."

After identifying the person he was looking for, Sarnak contacted Professor Deligne, sent the paper, and then read the paper himself.