Chapter 22: Birds and Frogs

"I think mathematics should be beautiful. It certainly won't be boring; it contains a unique aesthetic."

"I don't really like the media calling me a hermit-like character. I just happened to do the first big paper on Fermat's Last Theorem, which doesn't mean I only do big problems. Not everyone can be as lucky as I am, being able to produce results on big topics.

I think young scholars still need to consider survival. They must first do some easy topics to prove their value, so that it is easy to find a good teaching position, and then try to do some difficult problems and some big topics after stabilizing, which can better balance life and academic ideals."

"I like my professor's metaphor about mathematicians very much. He compares mathematicians to two types: one is a frog, and one is a bird.

Birds soar in the high sky, overlooking the vast mathematical landscape extending to the distant horizon. They like concepts that unify our thinking and integrate many problems in different fields. Frogs live in the mud under the sky, only seeing the flowers growing around them. They are happy to explore the details of specific problems, solving one problem at a time."

"No, there is no distinction between birds and frogs. Mathematics needs both birds and frogs.

Mathematics is rich and beautiful because birds give it a vast and spectacular landscape, and frogs clarify its intricate details. Birds see further and frogs see deeper.

The world of mathematics is both vast and profound. We need birds and frogs to work together to explore."

Most of Lin Ran's interviews revolved around mathematics itself. The definition of birds and frogs in the interview was widely circulated among mathematicians after being translated into English because of its profound meaning.

After the news reached Europe, Horkheimer, Lin Ran's nominal mentor, had to face the questioning of his colleagues, asking him whether he was a bird or a frog, and why he didn't tell them if he had such a profound understanding before.

And young mathematicians were all thinking about whether they were frogs or birds, and whether they had the talent to be birds.

On the way back to Tsung-Dao Lee's residence, Yang Chen-ning sighed: "It's really well said. Physicists can also be divided into birds and frogs. People like Einstein point out the direction for us, divide the scope, and tell everyone what can be studied, while physicists who do specific problems are like frogs, deeply buried in a field and constantly digging into its potential."

Tsung-Dao Lee nodded and said: "Randolph doesn't look like a young man in his early twenties at all. He gives me the feeling that he is very clear about what he is doing and what he wants to do. I have always been pushed by problems until now, pushed by the surprises that the physical world constantly brings me.

And he already had a complete mathematical map at this age, clearly depicting his understanding of the mathematical world, which is really rare."

Two big shots who won the Nobel Prize in Physics in their thirties actually had the illusion of being shot on the beach in front of the young back waves.

"Taniyama-kun, do you see it? Our conjecture back then was indeed correct. All elliptic curves over Q are modular. This conjecture really plays a vital role in the field of mathematics as we expected back then.

It's a pity that you can't see it anymore.

I really can't understand why you passed away suddenly. If Lin-kun could have proven the Taniyama conjecture two years in advance, could you still be talking about mathematical problems with me in the seminar room of the University of Tokyo now?

Lin-kun is truly an amazing figure. The Randolph Program he proposed brought a shock to the entire mathematics community. Many problems in many fields can be connected with the program itself, and the significance contained behind the completion of the program makes all mathematicians feel excited.

I really hope you can see this scene too."

In a temple five kilometers southwest of Kita-Saitama-gun, Saitama Prefecture, Neon, a young man in a suit and leather shoes held a copy of the latest "New Progress in Mathematics" magazine and whispered in front of the cemetery.

Standing in front of the cemetery was Goro Shimura in the Taniyama-Shimura conjecture, and lying in the cemetery was his close friend, Yutaka Taniyama, who was also in the Taniyama-Shimura conjecture.

Before Taniyama's death, both were teachers at the University of Tokyo, the former as an associate professor and the latter as a lecturer. The two completed the Taniyama-Shimura conjecture together on the basis of Taniyama's conjecture.

Because this conjecture was proposed by Neon mathematicians, Neon mathematicians belonged to the unknown in the 50s and had no status in the international mathematics community, so the Taniyama-Shimura conjecture was also buried in the pile of old papers.

Except for Taniyama and Shimura, no one felt that this conjecture was anything great. It was originally waiting for the great god André Weil to dig it out in the 70s and feel that it was very important, and then it was promoted. It was not until the 80s that German mathematician Gerhard Frey proposed that the Taniyama-Shimura conjecture should be equal to the Fermat Conjecture to some extent.

Finally, Andrew Wiles completed the Taniyama-Shimura conjecture in a special form on the basis of his predecessors, and then completed the Fermat Conjecture, making the Taniyama-Shimura conjecture famous with Fermat's Last Theorem.

Among them, Taniyama committed suicide in 1958. Judging from the content of Taniyama's suicide note, he committed suicide because of fatigue and loss of confidence in the future. In the environment of post-war Neon, Taniyama's ideas were criticized as baseless and sometimes even criticized as eccentric, which meant not being gregarious in Neon.

To add a word, Taniyama's fiancée also committed suicide after Taniyama's suicide. Her suicide note wrote: "We agreed that no matter where we are, we must be together and never separate. Since he is dead, I will follow him."

Originally, Wiles's proof of Fermat's Last Theorem was traceable, and it was the result of generations of mathematicians continuing, and finally completed by him. And now it is proven in Lin Ran's hands, which is quite a bolt from the blue.

For everyone who knows and has studied the Fermat Conjecture—no, it should be called Fermat's Last Theorem now—it is an incredible thing.

Because the method he used had never been thought of by mathematicians before. Taniyama-Shimura conjecture? These two mathematicians had never even heard of it.

And in Shimura's view, it was quite a feeling of meeting a bosom friend in high mountains and flowing water. The conjecture he made was actually used in the proof of Fermat's Last Theorem, which not only meant fame but also meant the improvement of real treatment. Originally, he couldn't get a teaching position at the University of Tokyo and was forced to move to Osaka University, and later he was dissatisfied with Osaka University and ran to Princeton.

Now because the Taniyama-Shimura conjecture is the core of Fermat's Theorem, the University of Tokyo contacted him overnight, asking him to come to work immediately and give him a full professor position.

Besides being happy, Taniyama was sentimental. Just two years late, his close friend could not see this scene.

"The University of Tokyo mathematics department has sent an invitation letter for a visiting professor to Lin-kun, hoping that he can accept his teaching at the University of Tokyo this summer." ===== CHAPTER 23 =====