At the academic lecture of the Steele Prize, Professor Josey Unamuno, a famous mathematician from Germany, was on the stage giving a report.

Professor Unamuno is a retired professor at the Technical University of Munich, but has been awarded the title of lifelong honorary professor. He is the winner of the country's highest scientific research award, the "Leibniz Prize", and the top prize in mathematics, the "Wolf Mathematics Award".

The winner of the "Prize" has a high reputation in the international mathematics community.

Being able to invite such a mathematics master to give an academic report shows the influence of the American Mathematical Society AMS.

The topic of Professor Unamuno's report was very attractive, called "Perspectives on the Possibility of the Unification of Mathematical Theory", and Qin Ke and Ning Qingyun listened with great interest.

The unification of mathematical theory is the ultimate goal of countless mathematicians. There are many sub-subjects in mathematics nowadays, such as number theory, functionals, algebra, geometry, topology, calculus...

In fact, in the final analysis, different sub-subjects study mathematical problems, but their focus is different, and they should be related in essence.

If the grand unification of mathematics can be achieved with a new program and a unified "mathematical language" can be used to describe mathematical problems, then all these mathematics sub-subjects can be merged.

This is like the unification of language. There are dozens of ethnic groups and countless local dialects in the Xia Kingdom, but as long as they can speak Mandarin, they can all communicate. The same characters also allow different cultural customs to circulate throughout the country without any hindrance.

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The goal of the unification of mathematics is similar to that.

This "mathematical language" is a "programme". The three existing programs in the world are: Hilbert's program (which attempts to use finiteism methods to prove the consistency of infinite ideal mathematics), and Erlgen's program (which is based on

Geometry describes mathematical problems) and the Langlands Program, which has become extremely popular recently.

The first two programs have had a profound impact on mathematics for more than a hundred years, while the Langlands program was only proposed in the past fifty years and quickly became the hope for the unification of mathematics.

Simply put, it organically integrates number theory, algebraic geometry and group representation theory through internal connections to form a programmatic guiding ideology.

This is an epoch-making mathematical program. If the conjectures contained in it are fully proven, it will be possible to achieve the almost impossible goal of unifying mathematics.

The Langlands Program also has high hopes in the international mathematics community. Mathematicians who make breakthroughs in this direction are often the most likely to win the Fields Medal, the Abel Prize and the Wolf Prize.

For example, mathematician Wu Baozhu won the Fields Medal awarded by the 26th International Congress of Mathematicians because “by introducing new algebraic geometry methods, he proved the basic lemma in the automorphic form of the Langlands Program

”.

Professor Unamuno focused on his understanding and research results of the Langlands Program, and also expressed a point of view - in the mathematical world, if the Riemann Hypothesis, Goldbach Hypothesis or Hodge Hypothesis can be proved,

The world's top conjectures are indeed very powerful achievements, but the ultimate goal of real mathematicians should be to finally achieve the unification of mathematics through the Langlands Program or to propose a new program.

When he said this, his eyes always fell on Qin Ke in the crowd, intentionally or unintentionally.

Even Ning Qingyun noticed it, and the girl whispered: "Isn't this meant for you?"

Qin Ke rubbed his nose. In fact, he recognized this old gentleman. When he gave a lecture on the derivation of the fourth set of expressions of the Riemann Hypothesis in Germany, Professor Unamuno was sitting in the front row and listened to the whole process.

He had to be very serious and kept writing calculations with a pen to verify his derivation process. Because his white hair was particularly conspicuous, it left a deep impression on Qin Ke.

I just didn't expect that this old man actually wanted him to complete the unification of mathematics? This is even more exaggerated than Mr. Faltings's hope that he could completely prove the Riemann Hypothesis. It is estimated that it is impossible for a master-level mathematical level to solve the system.

Whether the designated highest-level "god of mathematics" can accomplish this grand and far-reaching goal is unknown. After all, powerful figures such as Gauss, Euler, and Riemann have not made any special contributions to the unification of mathematics.

Of course, Riemann's academic achievements in complex variable functions and Riemannian geometry have indeed greatly promoted the development of algebraic geometry, and algebraic geometry is considered the core tool for the unification of mathematics. From this perspective, Riemann

It indeed has a great promotion effect on the unification of mathematics.

In short, Qin Ke shook his head at this. Unless his mathematics level was raised to the "God of Mathematics", he would never consider challenging this huge proposition that was more exaggeratedly difficult than the seven-century conjecture.

Professor Unamuno's report finally received warm applause.

In the buffet banquet hall at noon, this old professor with a sharp face, raised eyes, and a particularly serious look that was not easy to mess with sat down beside Qin Ke and Ning Qingyun.

Faltings also came over with red wine, and happened to bump into Professor Unamuno. He raised his eyebrows a little rudely: "You old guy, you are here to fool people again to complete the unification of mathematics."

A great achievement?"

Professor Unamuno was obviously an old acquaintance and old enemy of Faltings. He retorted mercilessly: "It's better than you thinking that proving the Riemann Hypothesis is the end of mathematics!"

Faltings chuckled and said: "At least two-thirds of the Riemann Hypothesis has been solved now, and the end point may not be too far away. And the unification of mathematics you are pursuing, with all due respect, can only be said to be a great goal, but one hundred

There is no possibility of success within the year. Even the Langlands Program that you admire so much is, in the final analysis, just an overall theory that broadens the horizons, or structural integration, and is not a true unification at all.

.Even if you don’t mention the Langlands Programme, you have no idea how many years it took to complete the integration of set theory, group theory, topology, and these composite classification disciplines?”

As he spoke, he turned to Qin Ke and said, "Qin Ke, ignore this old lunatic. He spends all day trying to trick people into studying the Langlands Program. This is a road of no return..."

Professor Unamuno stopped paying attention to Faltings, interrupted him directly, and said to Qin Ke: "Are you Dr. Qin Ke? I listened to your report in March in Germany, it was very exciting. I think it will be

It is necessary for your mathematical talent to withdraw from mathematical conjectures such as the Riemann Hypothesis and the Navier-Stokes equation, which are just special cases, and focus on the greatest end point of human mathematics - the unification of mathematics. For example, Lang

Lantz Programme. I think the great unification of mathematics lies in algebraic geometry and number theory. In both areas, you have shown very outstanding talents. As long as you achieve something in this area, it will be easy to win the Fields Medal. Of course, there are

Dr. Ning Qingyun is the same, he should choose the unification of mathematics as a new research direction..."

Faltings waved his hand and said: "Okay, okay, you go somewhere else to promote your unification of mathematics. I can't see Qin Ke and Ning Qingjun being fooled into this dead end by you. Look at Wu Baozhu, fall

After entering this pit, how long has it been since there was no new achievement? This is simply not a huge undertaking that one or two people can accomplish alone! Without gathering twenty or thirty young Fields Medal winners and investing decades of time,

I'm afraid it won't even make a splash. But do you have the ability to gather so many young and promising mathematicians?"

Professor Unamuno's eyes widened: "Aren't I just looking for a suitable partner? Dr. Qin Ke and Dr. Ning Qingyun are good partners worth attracting. I am afraid that I will only have more than ten or twenty years left in my life.

Years have passed. If we don’t see the dawn of the unification of mathematics before we die, should we inscribe on our tombstone ‘This is a mathematician who regrets not seeing the hope of the unification of mathematics and refuses to go to heaven’?”

The two highly respected mathematics masters were red-faced and attracted a lot of attention from the people around them. After hearing the content of their argument, they all looked at Qin Ke and Ning Qingyun in amazement. They could get Unamu's attention.

Professor Nuo's recognition and invitation is a great thing. You must know that this old man is famous for his eyesight.

Of course, there were actually several outstanding mathematicians present who had received similar invitations from Professor Unamuno, but they all declined. No one wanted to jump into this bottomless pit rashly.

Qin Ke and Ning Qingyun also looked at each other in shock. To be honest, they had never thought about such an ambitious goal of unifying mathematics before coming to Boston. If there was one, it would also be unification of physics. This seems to be more feasible.

some.

Seeing Professor Unamuno's expectant invitation, Qin Ke had no choice but to bite the bullet and said: "Professor Unamuno, we both feel that we still have a lot to learn, both in algebraic geometry and number theory.

, are temporarily not qualified to accomplish such a great goal as the unification of mathematics. Of course, Qingjun and I will use this goal as the motivation to spur ourselves to continue to advance on the road of mathematics."

Professor Unamuno obviously looked disappointed. Fortunately, Qin Ke didn't finish his words. He said regretfully: "Well, if you two are interested in participating in my unification of mathematics project in the future, you can contact me at any time.

, this is my business card with my email address on it." He took out his business card and handed it to Qin Ke and Ning Qingyun, then shook his head and left.

Faltings looked at his back and sighed: "This old guy is indeed a math addict. He has devoted his whole life to the great unification of mathematics. He did not achieve some results until he was sixty years old. Naturally, he missed it.

He won the Fields Medal, so he only won the Leibniz Prize and the Wolf Prize in Mathematics. To be honest, if he only focused on researching a certain direction, such as algebraic geometry, or number theory, I can guarantee that he could

Winning the Fields Medal before the age of thirty-five means he is such a mathematical genius."

For such a single-minded master of mathematics, Qin Ke could only express his admiration and admiration. Otherwise, he would not be able to devote his whole life to a goal with no clear future at all.

But mathematics is unified...

If you can really rise to the level of "God of Mathematics", then all seven millennium conjectures will be solved. If you have nothing to do, you can try to set this as the ultimate goal of mathematics.

Qin Ke was thinking about it when Faltings turned to look at him and Ning Qingyun: "There are only more than two months left before the International Congress of Mathematicians at IMU. Prepare well. As far as I know, both of you are in this year's International Congress of Mathematicians."

Candidates for the Fields Medal, and they are all ranked in the top 30. Whether you can win such a grand prize depends on your performance at the International Congress of Mathematicians. Some people in history have little chance, but in the end

I succeeded in making a comeback because of my outstanding performance in the report I gave at the conference. I hope to hear good news from you then.”

Qin Ke and Ning Qingyun nodded at the same time and said gratefully: "Thank you, Mr. Sir, for your guidance and concern."

Faltings smiled, turned and left, leaving a sentence before leaving: "If I can see the Riemann Hypothesis completely solved within a few years, this will be the greatest reward for me."

Ning Qingyun looked at the retreating figures of Faltings and Professor Unamuno, and said softly: "Qin Xiaoke, I find that such pure mathematicians are great. There are no nationality differences, no racial restrictions, everything

Just for the mathematics in my heart.”

"Probably because of such purity, they were able to achieve great academic achievements recognized by the world." Qin Ke also felt deeply.

After having more contact with Professor Faltings, Professor Tao, Professor Linden-Strauss, Professor Wiles and other big figures in the Philippine Prize, Qin Ke discovered that the higher you stand, the higher your achievements will be.

The more pure the love of mathematics, the material and fame are nothing to them, let alone the boundaries of nationality, race, age, and gender.

As long as they also like mathematics and can communicate effectively with them on mathematics, they will regard them as confidants, release their goodwill without reservation, and provide them with the help they can.

"It seems that I really need to work harder..." Qin Ke said in a low voice.

"Huh? What did you say?" Ning Qingyun didn't hear clearly and blinked curiously.

Qin Ke put down his spoon and said with a smile: "I said, starting from tonight, I want to run on the MIT campus. Our report will be in four days. I hope I can run enough in these two days."

inspiration."

"You mean..." Excited joy flashed in Ning Qingyun's eyes.

"Yes, just a little bit closer, the derivation of the last set of expressions of the Riemann Hypothesis."

Since absorbing the master-level knowledge of number theory, Qin Ke's rich knowledge reserve in number theory has surpassed any Philippine Prize boss in the world. After all, even the Philippine Prize bosses mostly only specialize in a certain area.

Direction, for example, Professor Wiles specializes in number theory knowledge related to Fermat's Last Theorem.

And Qin Ke is proficient in all sub-subjects of number theory, whether it is elementary number theory, analytic number theory, algebraic number theory, geometric number theory, stacked number theory, Diophantine equations, class field theory, automorphic forms, zeta functions, Shimura varieties,

Algebraic groups...he is proficient in all of them. He can be said to have combined the knowledge of number theory masters from ancient and modern times, both at home and abroad.

Coupled with keen mathematical intuition, strong mathematical thinking ability, and the correct direction he has found, Qin Ke wants to deduce the last set of expressions of the Riemann Hypothesis. He only lacks the last bit of inspiration to complete the puzzle.

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If you want to find inspiration, the best and most familiar way is long-distance running. During long-distance running, you can relax your body and mind, focus on thinking, and finally stimulate the "inspiration amplification" state, enter the wonderful world of inspiration, and solve this great Riemann Hypothesis in one fell swoop.

Completely conquered!

So that night, Qin Ke, accompanied by Chen Ming and Zheng Haiqiao, and under the gaze of Ning Qingyun who was looking forward to but also worried about his recklessness, stepped on the bright moonlight and began his most glorious journey in the past twenty years.
Chapter completed!