In the morning, mathematicians from various halls of mathematics took the stage to explain their views on the future of mathematics, Edward Witten showed the latest achievements of using mathematics to promote the development of high-energy physics, and Tao Zhexuan reported on the problems he encountered in his work to solve the Eldsch difference problem.

Of course, the biggest sensation in the room came from the two neon people, Shinichi Mochizuki took the lead, claiming that he saw hope in cracking the "ABC conjecture" by establishing a new world he called the "intercosmic Teichmüller theory", and he defined all kinds of mysterious terms that had never been seen before, such as "Hodge Cinema" and "Extraterrestrial Arithmetic Pure Structure" And so on, and I want you to admit that you have created a whole new system of mathematics in the same way that you admit to Lobachevsky's non-Euclidean geometry, but all this is useless, and you don't understand what he is talking about.

Another guy named Satoshi Nakamoto claimed to have used his knowledge of cryptography to create a new digital currency, which does not have a centralized issuer, but is generated by the calculation of network nodes, which can be made by anyone, and can be circulated all over the world, can be bought and sold on any computer connected to the Internet, no matter where they are, anyone can mine, buy, Selling or receiving this currency is not recognizable to outsiders during the transaction and is not controlled by any central bank or financial institution.

He regarded this currency as the universal currency of the future Internet age, 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 money! But like his compatriots, it did not win the approval of many mathematicians.

Of course, the morning exchange was not without results, such as the Langlands Program, which most mathematicians considered to be the next major breakthrough in mathematics.

Robert Langlands, a Canadian, came to the United States to earn his Ph.D. at Yale University, then to the Institute for Advanced Study in Princeton, where he received the Wolf Prize in 1996.

In 1967. In the year in which he became a professor, he wrote a letter to André Weiy, one of the early members of the Bourbaki School and an authority on number theory and algebraic geometry, in which he proposed a set of far-reaching conjectures that accurately predicted the possible connections in mathematics between the interdisciplinary fields of noncommutative harmonic analysis and analysis, self-defying formal theory, and number theory, and attempted to unify them.

This conjecture was increasingly confirmed by his efforts and that of other mathematicians, who, in Freeman Dyson's words, were working with birds.

This session greatly stimulated the enthusiasm of mathematicians, because although the solution of Poincaré's conjecture is great, it does not necessarily directly affect their own research field, and the spark of inspiration generated by the fierce collision of various ideas at the conference may directly benefit them!

All the way up to the time of the lunch break. They also divided into several groups to have a heated debate as they went, all trying to convince the object of the debate that their views were correct and that modern mathematics should be the way forward.

"The advent of irrational numbers allowed mankind to study precisely the properties of the static world, and the emergence of calculus allowed mankind to study the properties of the dynamic world, fluids, heat, and electromagnetism. The theory of relativity and so on. Breakthroughs in mathematics should not be a solo dance in front of a mirror in an empty room, but should provide strong support for the development of physics and other real-world disciplines, 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!"

"And then the mathematicians let you down, that's why you started studying math on your own?" someone joked. However, Witten's identity is indeed interesting, obviously an authority on physics, but he has won the Fields Medal, and Nobel has always refused to be attached to him.

"I was just looking forward to a breakthrough in quantum algorithms. Lu painted a wonderful picture for us last night, and I hope he can make a difference in this field as soon as possible!" said another.

"I don't think it's likely, he's already decided to graduate," Witten shook his head. He had written a letter of recommendation for Lu Qiujian, but after thinking about it, it seemed a little bad that Lu Qiujian did not announce that he was exposed, so he quickly changed the topic, "By the way, might as well guess who will come to make the closing speech?"

"Now that Alexander is here, who else but him will be qualified?" compared to the status of the rivers and lakes, there was indeed no figure present who could stand side by side with Grothendieck.

"I think it's Alexander, too!" someone immediately chimed in, "I was stunned when I saw him at the time, he hasn't appeared in the mathematical world for more than ten years!

"Poincaré's conjecture alone is not enough to attract him, and it seems that he does admire Luqiujian!" the man turned his head to Witten, "What did Monsieur de Ligne say to Mr. Grothendieck? You and Mr. Deligne are colleagues, so you should know something, right?"

"I don't know, actually, but I also think that Mr. Grothendieck is the best person to give the closing speech!" "If Grothendieck hadn't come, he might have been qualified, but even he wouldn't have had the same influence on the mathematical community as Grothendieck.

"But the theme of this meeting is the Poincaré conjecture, and Mr. Grothendieck is good at algebraic geometry!"

"At the turn of the century, would it not be more appropriate for Mr. Grothendieck to envision the future of mathematics, as Hilbert did?"

"It's been too long since Mr. Grothendieck left the mainstream of mathematics!"

There was a heated debate, but most people agreed that Grothendieck was the one who was best qualified to make a concluding remarks.

After dinner and rest, it was time for the final session of the meeting, and at three o'clock in the afternoon, the mathematicians returned to the lecture hall and waited quietly for the start of their concluding remarks.

To their surprise, Grothendieck sat in the front seat, talking and laughing with the people next to him, not ready to give a speech.

Just as they continued to speculate, the last process of the meeting began, and Lu Qiujian's three words slowly spit out from the host's mouth, and they all grew their mouths in surprise! )

PS: The seventh watch, the results are good, and the tenth watch will be released at nine o'clock in the evening;