Chapter 50

"I apologize. I know that since I arrived in Xiangjiang, everyone has been looking forward to me holding a more professional academic lecture here.

I have always been preparing for it. The reason I arranged this academic lecture for today is entirely because I thought that the young people from Xiangjiang in my seminar would also be able to understand the content, find directions they are interested in from the topics I introduce, and produce valuable work."

Inside the lecture hall at the University of Xiangjiang, compared to the sparse single-digit attendance of the previous month, this time it was packed with people.

In addition to local mathematicians from Xiangjiang, there were also mathematicians from all over Asia, with the largest numbers coming from Nihon and India.

Nihon was there because their post-war economy had recovered rapidly, and Kunihiko Kodaira winning the Fields Medal in '54 gave Nihon a strong mathematical atmosphere.

Moreover, Kunihiko Kodaira's research direction was mainly complex algebraic geometry, which had a great deal of overlap with the Langlands program.

This led to a team led by Kunihiko Kodaira, along with a group of mathematicians from the University of Tokyo, Kyoto University, and Osaka University, coming to the University of Xiangjiang, hoping to communicate directly with Lin Ran.

If you won't come to Nihon, then we will come to Xiangjiang.

India was there because of the existence of Ramanujan; mathematical research in India was mainly concentrated in the fields of number theory and statistics, and Fermat's Last Theorem belonged to the crown jewel of number theory.

They also desperately hoped to communicate directly with Lin Ran.

The lecture hall at the University of Xiangjiang was full of people, and Xiangjiang reporters who had heard the news stood at the back taking photos, having already thought of the headline: The Light of the Chinese People Gives His First Lecture in Xiangjiang, Actually Attracting Mathematicians from Asian Countries to Come on a Pilgrimage.

In the eyes of the Xiangjiang media, even if Kunihiko Kodaira had won a Fields Medal, his status was certainly not as high as Lin Ran, who had solved the Fermat conjecture.

"I believe that since you have all come from afar to listen to my lecture, you must have some understanding of the Fermat conjecture and its proof.

I would like to follow the Fermat conjecture to talk about my new conjecture.

I want to start first with Fermat's work on Diophantine problems."

Lin Ran belonged to the type who would grab Fermat and fleece him for all he was worth.

The Diophantine problem was a problem proposed by the ancient Greek mathematician Diophantus: find 4 rational numbers such that the product of any two of them plus 1 is the square of a rational number.

And Fermat found a positive integer solution {1, 3, 8, 120}, and raised the question: could a 5th integer be added to this set such that this new set also satisfies the Diophantine condition?

"I only need one sheet of paper to complete the proof of Fermat's Diophantine conjecture."

The mathematicians present were in an uproar, because although Fermat's Diophantine conjecture was not as famous as Fermat's Last Theorem, it had also plagued the mathematical community and remained unsolved to this day.

As a result, you are now saying that you only need one sheet of paper; this is simply too exaggerated.

"The general process is like this: first establish the Diophantine equation, then convert it into a Pell equation, and then use the theory of linear forms in logarithms to exclude other solutions."

The Indians in the audience could no longer hold back and raised their hands one after another to question: "Professor Lin, what is this theory of linear forms in logarithms here?

How come I have never heard of this theory?"

"I haven't heard of it either."

Discussions broke out in the audience, and Chen Jingrun had already realized what Lin Ran was going to talk about.

"That's right, I am going to continue to talk about the theory of linear forms in logarithms next.

Let us be given algebraic numbers α1, α2..."

"This theory expands the theory of Gelfond and Schneider regarding transcendental numbers, and we have extended the scope of the theory to linear combinations of multiple logarithms.

In addition, we have improved the classical techniques in Diophantine approximation, allowing everyone to use this method to estimate the lower bounds of linear forms."

Enthusiastic applause erupted at the scene; everyone was a mathematician and knew how useful this stuff was.

It can be said that as long as the method Lin Ran constructed has no loopholes, then this so-called theory of linear forms in logarithms will become a powerful tool in modern number theory, capable of helping to solve a whole host of problems in Diophantine analysis and the field of transcendental numbers.

"This method can transform abstract number theory problems into computable calculations; it connects parts of the branches of the Langlands program."

Because the proof of Fermat's Last Theorem used the Taniyama-Shimura conjecture, Goro Shimura, who had leaped to become an associate professor in the Department of Mathematics at the University of Tokyo, also followed the large group from Tokyo University to Xiangjiang.

Sitting in the lecture hall, Goro Shimura felt that Lin Jun was simply a god; the light from the window behind him spilled onto him, as if he were bathed in divine light.

He thought to himself: "Lin Jun is no longer content with making conjectures; he is already making tools. Is he connecting the mathematical map he proposed to completion?

He is worthy of being the man known as the Gauss of our time."

Not only was Goro Shimura impressed to the point of prostration, but there was not a single mathematician present who worked in number theory who was not impressed.

Lin Ran continued: "Then there is the most important content of my day. The theory of linear forms in logarithms mentioned earlier, besides being used to prove Fermat's Diophantine conjecture, has a more important significance in supporting this conjecture of mine.

I have named it the ABC conjecture."

It was that same ABC conjecture that Shinichi Mochizuki claimed to have proven.

After Lin Ran finished introducing the ABC conjecture in detail, there was a round of applause from the audience; the content of this academic lecture was a bit too rich.

First, Fermat's Diophantine conjecture was proven, then Lin Ran proposed a new number theory method, and finally, he pulled out a conjecture that looked incredibly difficult at first glance.

"The reason I thought of the ABC conjecture is that it contains a more concise proof path for Fermat's Last Theorem. I intuitively feel that it is more difficult than Fermat's Last Theorem.

In addition, it connects multiple branches including prime distribution, Diophantine equations, and modular forms; it is the key to understanding the essence of integers."

The lecture, including the Q&A, lasted for a full three days.

None of these Asian mathematicians could escape the fast legs of the Xiangjiang reporters.

"Lin Jun is the most brilliant mathematician in Asia; his achievements in the field of mathematics far exceed mine." — Kunihiko Kodaira's original words.

By the time it reached the Xiangjiang newspapers, it became: "Nihon's Mathematical Emperor Claims He Wanted to Kneel Before Professor Lin."

Kunihiko Kodaira would probably be dumbfounded if he saw it: When did I become Nihon's mathematical emperor, and when did I want to kneel?

The kneeling here was even accompanied by a picture, which greatly increased its credibility.

Because after the lecture ended, the Nihon side strongly requested to treat Lin Ran to a meal, and Kunihiko Kodaira took the lead in bowing at ninety degrees.

The Nihon people's face-saving projects are truly powerful.

It was captured perfectly by a Xiangjiang reporter.

This led to a large number of people on the simplified Chinese internet in the future believing this rumor, and in mathematical wild history, it even turned into: Lin Ran shook his tiger-like body, and Kunihiko Kodaira surrendered at the sight of him.

And Dean Qian, after hearing this, felt a shiver in his heart, thinking that Lin Ran was so calculating that even without returning, he could leave behind a channel for academic exchange between Huaguo and the West in such a way.

During the meal, Lin Ran did not refuse any of the requests for recommendation letters from the local Xiangjiang students present.

It was just that Chen Jingrun wanting to go to Columbia University to follow him for a PhD in mathematics actually surprised him a bit.

"Dehui, you are very talented. I am afraid I won't have much time to teach you starting from the second half of the year. How about this: I will recommend you to study for a PhD under Harvey Cohn. What do you think?"