In the morning, mathematicians from various mathematics palaces took to the stage to explain their views on the future of mathematics. Edward Witten showed everyone his latest achievements in using mathematics to promote the development of high-energy physics; Tao Zhexuan reported on his efforts to decipher the Erdos difference.

Problems encountered at work.

Of course, the biggest sensation at the venue came from the two neon people. Mochizuki Shinichi was the first to appear, claiming that he had established a new world he called the "teichmuller theory of the universe" and saw the hope of cracking the "abc conjecture".

defines various unprecedented

Mysterious terms, such as "Hodge Cinema", "Alien Arithmetic Holomorphic Structure", etc.; I hope everyone will admit that they have created a new mathematical system just like Lobachevsky's non-Euclidean geometric system. However, all this does not

It was of no use, and no one could understand what he was talking about.

Another guy named Satoshi Nakamoto claimed that he used the knowledge of cryptography to create a brand new digital currency. This currency does not have a centralized issuer, but is generated by the calculation of network nodes, and anyone can participate in its creation.

, and can be circulated all over the world, and can be bought and sold on any computer connected to the Internet. No matter where you are, anyone can mine, buy, sell or collect this currency, and outsiders cannot identify the user during the transaction process.

Information is not controlled by any central bank or financial institution.

He regarded this currency as the universal currency in the future Internet era, and tried his best to describe the bright future of this currency, calling it another great revolution in economic history since paper money replaced financial currency! But just like his compatriots

Likewise, it is not recognized by many mathematicians.

Of course, the morning exchange did not achieve any results. For example, the Langlands Program was recognized by most mathematicians as the next major breakthrough in mathematics.

Robert Langlands is a Canadian. He later came to the United States to obtain a doctorate at Yale University, and then came to the Institute for Advanced Study in Princeton to conduct research, and won the Wolf Prize in 1996.

In 1967, the year he was promoted to professor, he wrote a letter to Andre Weil, one of the early members of the Bourbaki school and an authority on number theory and algebraic geometry, in which he proposed a

A group of far-reaching conjectures, which accurately predict the possible connections between the interdisciplinary fields of non-commutative harmonic analysis, automorphic formal theory and number theory in mathematics, and attempt to unify them.

This conjecture was increasingly confirmed through the efforts of him and other mathematicians; in the words of Freeman Dyson, Langlands was doing the work of a bird.

This link has greatly stimulated the passion of mathematicians, because the cracking of the Poincaré conjecture is great, but it will not necessarily directly affect their own research fields, and now the fierce collision between various viewpoints at the conference has caused

The spark of inspiration generated may directly benefit yourself!

Until the lunch break, they divided into several groups to engage in heated debates while walking, trying to convince the people they were debating that their views were correct and the direction modern mathematics should develop.

They refused to stop when they entered the restaurant, and gathered together with plates in hand, talking and eating.

"The emergence of irrational numbers allows humans to accurately study the properties of the static world, and the emergence of calculus allows humans to study the properties of the dynamic world, fluids, heat, electromagnetism, relativity, etc. Breakthroughs in mathematics should not become a mirror in an empty room

It should provide strong support for the development of real disciplines such as physics, so I hope that the next breakthrough will provide the entire modern physics with a solid mathematical foundation like the original calculus and differential equations!" Witten

He described his expectations with excitement.

"Then those mathematicians disappointed you, so you started to study mathematics on your own?" Someone made a joke. But Witten's identity is indeed interesting. He is obviously an authority in physics, but he has won the Fields Medal, and

Nobel has always refused to be attached to him.

"I just look forward to a breakthrough in quantum algorithms. Lu painted a wonderful picture for us last night. I hope he can make achievements in this field as soon as possible!" said another person.

"I don't think it's possible. He has decided that after graduation..." Witten shook his head. He had written a recommendation letter for Lu Qiujian, but then he thought about it. Lu Qiujian did not announce his exposure.

It seemed a little bad to come out, so I quickly changed the subject, "By the way, guess who will give the closing speech?"

"Now that Alexander is here, who else would be qualified besides him?" Compared with his status in the world, there was indeed no one present who could stand shoulder to shoulder with Grothendieck.

"I think it's Alexander too!" Someone immediately echoed, "I was shocked when I saw him. He hasn't appeared in the mathematics world for more than ten years! I didn't expect that he would come to China!"

"The Poincaré conjecture alone is not enough to attract him. It seems that he really admires Lucius!" The man turned his head to Witten, "What did Mr. Deligne say to Mr. Grothendieck? You and Deligne

Sir, he is a colleague, so he should know something about it, right?"

"Actually, I don't know! But I also think Mr. Grothendieck is the best candidate for the closing speech!" If Grothendieck had not come, then he might be qualified, but even he, from the current point of view, is not qualified for mathematics.

The influence in the world still cannot be compared with Grothendieck.

"But the theme of this meeting is Poincaré's conjecture, and Mr. Grothendieck is good at algebraic geometry!" Of course there will always be people who have different opinions, "I think Professor Thurston or Hamilton are more suitable!"

"At the beginning of the century, wouldn't it be more appropriate for Mr. Grothendieck to look forward to the future development of mathematics just like Hilbert did?"

"Mr. Grothendieck has been out of mainstream mathematics for too long!"

Everyone fell into a heated debate, but most people believed that Grothendieck was the person most qualified to make a concluding speech.

After dinner and rest, it was time for the last part of the meeting; at three o'clock in the afternoon, these mathematicians returned to the lecture hall, quietly waiting for the beginning of the concluding remarks.

What surprised them was that Grothendieck was sitting in the front seat, talking and laughing with the people next to him, without any preparation for a speech.

Just as they continued to guess, the last process of the meeting began; the three words Lu Qiujian came out slowly from the host's mouth, and they all opened their mouths in surprise! (To be continued.)
Chapter completed!