Technology invades the modern world

Chapter 49 Outrageous News (Please read more!)
"I'm sorry, I know that ever since I came to Hong Kong, everyone has been looking forward to me holding a more professional academic lecture in Hong Kong.

I have been well prepared. I scheduled this academic lecture today because I thought the young people from Hong Kong in my seminar would also understand the content, find areas of interest in the topics I introduced, and produce valuable content. "

The lecture hall at Hong Kong University was now full of people, compared to the sparse single-digit number of people in the previous month.

In addition to mathematicians from Hong Kong, there are also mathematicians from all over Asia, with the largest number coming from Japan and India.

Japan's economy recovered rapidly after the war, and Kunihiko Kodaira won the Fields Medal in 54, which created a strong mathematical atmosphere in Japan.

Kunihiko Kodaira's research direction is mainly complex algebraic geometry, which has a lot of overlap with the Randolph Program.

As a result, a group of mathematicians from the University of Tokyo, Kyoto University and Osaka University, led by Kunihiko Kodaira, came to Hong Kong University, hoping to communicate directly with Lin Ran.

If you don’t come to Neon, then we’ll come to Hong Kong.

Because of Ramanujan, India's mathematical research is mainly concentrated in the fields of number theory and statistics, and Fermat's Last Theorem is the jewel in the crown of number theory.

They also eagerly wanted to communicate directly with Lin Ran.

The lecture hall at Hong Kong University was packed with people. Hong Kong reporters who had heard the news stood at the back to take pictures, and had already thought of a title: "The Pride of the Chinese's First Lecture in Hong Kong" attracted mathematicians from all over Asia to come and pay their respects.

In the view of Hong Kong media, even if Kunihiko Kodaira won the Fields Medal, his status would definitely not be as high as that of Lin Ran, who proposed the Fermat conjecture.

“I believe that you have come from afar to listen to my lecture, and you must have some understanding of Fermat’s conjecture and its proof.

I would like to talk about my new conjecture based on Fermat's conjecture.

I would like to start with Fermat's Diophantine problem."

Lin Ran was the type who tried his best to get the most out of Fermat.

Diophantine problem is a problem posed 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.

Fermat found a positive integer solution {1, 3, 8, 120} and raised the question: Can a fifth integer be added to this number set so that this new number set also satisfies the Diophantine condition?

"I only need one piece of paper to prove Fermat's Diophantine conjecture."

The mathematicians present were shocked, because although Fermat's Diophantine Conjecture was not as famous as Fermat's Last Theorem, it also puzzled the mathematical community and has not been solved to this day.

Now you say you only need a piece of paper, which is a bit exaggerated.

"The general process is this: first establish the Diophantine equation, then convert it to the Pell equation, and then use linear form logarithm theory to eliminate other solutions."

The Indians in the audience could no longer hold back their excitement and raised their hands to question, "Professor Lin, what is the linear form logarithmic theory here?
How come I’ve never heard of this theory?”

"I haven't heard of it either."

There was a lot of discussion in the audience, and Chen Jingrun had already realized what Lin Ran was going to say.

"Yes, I will continue to talk about the theory of linear form logarithms.

We are given algebraic numbers α1, α2"

"This theory extends the theory of transcendental numbers by Gelfond and Schneider, and we extend the scope of the theory to linear combinations of multiple logarithms.

In addition, we have improved the classic technique of Diophantine approximation, so that we can use this method to estimate the lower bound of linear forms."

There was warm applause from the audience. We were all mathematicians and knew how useful this thing was.

It's safe to say that as long as Lin Ran's method is flawless, this so-called linear form logarithm theory will become a powerful tool in modern number theory, helping to solve a host of problems in Diophantine analysis and transcendental numbers. "This method can transform abstract number theory problems into actionable calculations, connecting some branches of the Randolph Program."

Because the proof of Fermat's Last Theorem used the Taniyama-Shimura conjecture, Goro Shimura, who became an associate professor in the Department of Mathematics at the University of Tokyo, also came to Hong Kong with the large group of people from the University of Tokyo.

Sitting in the lecture hall, Goro Shimura felt that Lin Jun was simply a god. The light from the window behind him shone on him, just like bathing in divine light.

He thought to himself: "Lin Jun is no longer content with making conjectures. He is already making tools and connecting the mathematical map he proposed to complete it.

As expected of a man called Gauss."

Not only was Goro Shimura full of admiration, but all the mathematicians working on number theory present were also full of admiration.

Lin Ran continued, "Then comes my most important topic today. The linear logarithm theory mentioned above is not only used to prove Fermat's Diophantine conjecture, but more importantly, it supports my conjecture.

I named it the ABC conjecture."

This is the ABC conjecture that Shinichi Mochizuki claimed to have proved.

After Lin Ran gave a detailed introduction to the ABC conjecture, the audience burst into applause. The content of this academic lecture was a bit too rich.

First, Fermat's Diophantine conjecture was proved, then Lin Ran proposed a new number theory method, and finally he came up with a conjecture that looked extremely difficult at first glance.

“The reason I thought of the ABC conjecture is that it contains a simpler proof path for Fermat’s Last Theorem, and I intuitively feel that it is more difficult than Fermat’s Last Theorem.

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

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

None of these Asian mathematicians can escape the swiftness of Hong Kong reporters.

"Mr. Lin is the most powerful mathematician in Asia. His achievements in mathematics far exceed mine." These are the original words of Kunihiko Kodaira.

When it was published in Hong Kong newspapers, it became: "The Japanese Mathematics Emperor claimed that he wanted to kneel down when he saw Professor Lin."

Kunihiko Kodaira would probably be dumbfounded if he saw this. When did I become the emperor of Japanese mathematics? When did I want to kneel down?

The kneeling here is accompanied by a picture, which greatly increases its credibility.

After the lecture, the Japanese side strongly wanted to invite Lin Ran to dinner, and Kunihiko Kodaira took the lead in bowing 90 degrees.

The Japanese are really good at face-saving projects.

It was captured by a Hong Kong reporter.

As a result, a lot of people believed this rumor on the Internet in the future, and it even became a rumor in the unofficial history of mathematics. Lin Ran was shocked and Kodaira Kunihiko surrendered.

Lin Ran had prepared an excuse in advance, saying that he wanted to treat his students to a meal, and rejected the Japanese side on the grounds that it was inconvenient.

During the dinner, Lin Ran accepted all requests for recommendation letters from local Hong Kong students present.

However, he was a little surprised that Chen Jingrun wanted to go to Columbia University to study for a doctorate in mathematics with him.

"Dehui, you're very talented. Starting from the second half of the year, I'm afraid I won't have much time to teach you. So, I recommend that you study for a doctorate with Harvey Cohen. What do you think?"

　I'll add more chapters and ask for more reading, and I'll ask for monthly tickets. Anyway, I'll give you whatever I can! Finally, don't talk about Yashui! Even if you talk about Yashui, Ya won't admit it!

　　
　
(End of this chapter)