Mathematics is different from other disciplines because the categories and knowledge involved are too large, and it requires a continuous accumulation and learning process to reach a peak.

Ordinary young people in their twenties, even if they are genius enough, are unlikely to achieve much because the study time is too short and the amount of knowledge they absorb is not enough.

As far as the mathematical community is concerned, it is internationally recognized that mathematicians who are less than 40 years old are called young mathematicians, and they are all called young.

Of course, this only applies to most mathematicians.

To be able to become a mathematician, most of them are scholars, but there is obviously the existence of the god of learning above the top student, in this world of the big bang of life, Sheldon's IQ is the top, it is the god of learning.

And Peggy, who can be compared to him in the setting, is obviously also a god of learning, and what ordinary scholars can understand after studying for several months, she may be able to figure it out in a few days.

So her knowledge is no worse than that of many forty-year-old mathematicians, the only thing that is inferior is experience and experience.

Now that she got the right ideas and methods from Link, with her computing power and knowledge, she soon began to have some ideas.

Link was here watching Peggy's calculations, and at first he was able to follow what she had written, but gradually he found that he couldn't keep up with Peggy's calculations and ideas.

Knowing that this is a gap in IQ, even if he has just raised his intelligence to 18 points, he still has a lot of distance from Peggy, which makes him much worse than Peggy in mental arithmetic.

What's more, the improvement of intelligence does not mean the improvement of knowledge reserves, Link's intelligence has improved, and there is also a big gap between the relevant knowledge reserves and Peggy's, and some of the methods and theorems cited by Peggy have only been slightly involved in Link before, and he is not proficient.

Of course, Fermat's conjecture is not so simple to prove, the last life Link has seen many brief proof methods circulating on the Internet, and even some proofs can be proved with only the knowledge of the second year of junior high school, that is, the Pythagorean theorem.

But when he actually started to study math, Link knew that the methods of proof seemed rigorous, but in fact they were full of loopholes.

Otherwise, for more than three hundred years, wouldn't anyone have thought of a similar method? Are these people the only ones in the world who are smart? All the mathematicians before were stupid?

And even now, with the right ideas and methods, it is not easy to complete this proof, just when Peggy was forced by Linda to go to the restaurant to finish eating, she also said to Link while eating:

"The method you came up with is really great, if everything goes well, maybe six or seven months, we can complete the relevant proof, and if we can prove that it is completed, then we may even win the Fields Medal!"

Link nodded and said, "I'm also looking forward to that day, when I think of the awards, those old men in the audience will definitely want to kill themselves in shame when they look at a teenage girl receiving the award on stage!" ”

"Hee-hee-hee, indeed, it's interesting to think about." Peggy laughed and said, "Maybe I'll be the youngest Fields Medal winner in history." ”

The Fields Medal is an international mathematics award established at the request of Canadian mathematician John Charles Fields, and was first awarded in 1936. Since the Nobel Prize does not have a prize in mathematics, the Fields Medal is often regarded as the Nobel Prize in mathematics.

It is awarded every four years, to two or four people at a time, and this year it is the fourteenth time.

The professor who solved the Fermat conjecture in the previous life won the Fields Medal for it, and Link believes that if the Fermat conjecture is solved by himself and Peggy in this world, the only thing that may prevent him and Peggy from winning the award may be age and education.

For the following summer vacation, in addition to exercising according to the plan, Link spent the rest of his time working with Peggy to solve the Fermat conjecture.

Of course, while Link wants to say that he played a huge role in the next proof, in reality he may not even be half as much as Peggy's.

In the process of unraveling, the two people will inevitably encounter various problems, so they need to check the information.

In the end, the two even enlisted the help of Dr. Sturgis, who helped them get a library card at the nearest library at the University of Texas at Austin, and waited until Caltech reopened before the two hurriedly packed up their materials and boarded the plane.

It lasted until December, at the end of the first quarter of the new year, when Link and Peggy wrote the completed proofs into rigorous papers and handed them over to their supervisors in charge of their dissertations.

Their mentor is Professor Diane Adler, who is also a gifted mathematician and a relatively rare female mathematician, only twenty-three years old this year, but already quite accomplished in the field of mathematics, and has been awarded the position of assistant professor.

After spending several days poring through the 130-page proof of the two Links, she called them into her office and looked at them with very strange eyes before she spoke:

"Although I have only roughly calculated the process of proof, many of the details have not been carefully verified, and even the correctness of your paper needs to be rigorously demonstrated, what I want to say is,

If you turn out to be right, this may be the greatest mathematical discovery of the twentieth century. With this one thesis, there is no problem in obtaining a bachelor's degree, even a doctorate, and even any university will be willing to offer you a professorship. ”

According to the academic system of the United States, bachelor's, master's, doctoral, and doctoral degrees are already the highest degrees, and professors are teaching positions.

The number of PhDs has been growing, while the position of assistant professor has remained basically constant, so it is considered a promotion and salary increase, and a probationary period of 3 to 7 years is generally required.

If the assistant professors perform well during the probation period, they will be hired as tenured professors and then promoted to associate professors.

And only after achieving academic excellence will an associate professor be promoted to full professor!

Although the professor was exaggerating, Link was not arrogant, and he smiled: "Thank you for the compliment, Peggy and I have mailed this paper to several well-known academic journals now, and I believe it will be published soon."

Whether this method is really perfect proves Fermat's conjecture will have to wait until the process of proof is tested. Now all we want is that this thesis will allow us to get a bachelor's degree in the first place. ”

The remarkable achievement of solving Fermat's conjecture is indeed enough for a Ph.D. to become a full professor, but they are still only students.

Even in the United States, where seniority is far less than on the other side of the Pacific, many things still need to be done step by step, especially in the academic world.

Link estimates that at most, he and Peggy will have a direct Ph.D. path, and at the same time, it will be easier for the next two people to get a formal Ph.D., and all aspects will be given the green light to get a Ph.D. in a few years.

Both Link and Peggy are confident that their knowledge of mathematics is now enough to earn a Ph.D.

This is actually the benefit of super high IQ, the knowledge that ordinary people need more than ten years to learn, but now it only takes one or two years to master, after the continuous improvement of intelligence, Link can understand the gap more clearly through comparison.

When the time comes, because of the academic status and knowledge gap between the two sides, it is very likely that it will not be clear, so it is safe to take it out in advance.

At the same time, shortly after Link finished his thesis, a new space-time mission appeared, and Link had to start preparing for the mission.