100 years ago, any math problem could be explained to an interested ordinary person.

Today, some math problems are difficult to explain to most full-time mathematicians.

One of them is the Hodge conjecture, which was proposed by the British mathematician Sir Hodge in 1950:

"Each (of a certain type) harmonic differential form on a nonsingular projective algebraic cluster is a rational combination of the upper cohomology class of algebraic closure. ”

Whether it's Chinese, English, or any other language, it's hard to read Hodge's conjecture in one go.

Whoever understands even one of the technical terms in this sentence will definitely be able to dominate the class.

"I have been studying mathematics for decades, from a student to the director of the mathematics teaching and research department of the Yan University School of Mathematics, and I have also conceived the role of mathematical analysis methods in the Hodge conjecture, but I have not been able to implement it. Why can't it be implemented, because it is impossible to prove the Hodge conjecture by only knowing the number of points, and it is even difficult to understand the Hodge conjecture. Lu Guozhen said with feeling, and added: "Fortunately, I know a little algebraic geometry, and it is OK for me to understand Hodge's conjecture." ”

Shen Qi said: "Hodge's conjecture looks so profound and unsolvable, tracing back to the source, no matter how difficult it is, it can also find the law through calculus, and the most basic tools can often solve the most profound problems, the key is who uses the tools and how to use them." Mathematical analysis is the basic mathematical tool, differentiation is a jack, integration is a torque wrench, and series is a screwdriver. As long as the tools are used well, the car can be dismantled. ”

Lu Guozhen dipped his fingers in some tea, and sketched an abstract figure on the desktop seemingly aimlessly: "But we use calculus to define an object, and the defined object is not necessarily geometric. ”

Shen Qi wiped off the water mark pattern on the desktop and asked, "Director Lu, what is the nickname that Hodge guesses?"

Lu Guozhen patted his head: "Hodge conjecture, there is no geometry of figures." ”

Shen Qi smiled: "Yes, in another way of thinking, we can formulate the Hodge conjecture from the integrals along the generalized path on the algebraic cluster, if some such integrals are zero, then there is a path in this path class that can be described by a polynomial equation." ”

Lu Guozhen realized that Shen Qi's thinking was more reliable, he patted his chest and asked: "Say, what do you want me to do?" Counting me, there are almost seven or eight backbones of Yan Dashu that I can mobilize. ”

"Three or four more moves, just enough to get a football team. ”

"I'm the director of the teaching and research department, and you are the dean of me?" Shen Qi, what teams are you in this team?"

"The two Ph.D. students I took with me at Princeton are in charge of the algebraic geometry section, the Morningside Math Center is in charge of the topology section, and Director Lu, you and your backbone team are in charge of the mathematical analysis section. ”

"Your net is so big, Chief Designer Shen Qi. Lu Guozhen saw some clues, and he continued: "Shen Qi, one of the two doctoral students you took with you at Puda is a Chinese student, right?"

Shen Qi said: "Yes, my two students, one Chinese and one American. ”

"In your idea, two top universities and a scientific research institute in China and the United States will be divided into three sections to overcome the Hodge conjecture, and finally complete the victory under your integration. There are more than a dozen mathematicians involved in this project of the century, including one American doctoral student, and the rest are all Chinese...... Shen Qi, it seems that your strategic focus is gradually shifting to China, and I absolutely support you. Lu Guozhen analyzed Shen Qi's strategic intentions.

"Transition stage, step by step. Shen Qi has his plan, he wants to give a generous gift to the motherland before returning to China, and Hodge guesses that this project is a good gift.

The main person in charge of the Riemann conjecture project that has been conquered is Shen Qi, and the team at that time included Chinese, Germans, Swedes, and Israelis, who completed a feat in the history of mathematics with the strong support of American academic power, and completely proved the Riemann conjecture.

The most common comment that comes to the Riemann conjecture nowadays is: "A Chinese math genius led an international team to make history in the United States." ”

Although mathematics knows no borders, Shen Qi's ambition is to lead a Chinese team to make history again.

Regarding the new project Hodge's conjecture, Shen Qi and his Princeton team have a total of three people, Lu Guozhen and his Yanda team have seven or eight people, and Director Wu and his team at the Morningside Mathematics Center have five or six people.

For basic mathematics research, the establishment of a special research team of 16 or 7 people for a topic is definitely a luxury lineup of big scenes.

In this luxurious lineup, only Shen Qi's student Ralph is an American doctoral student, and the rest are Chinese mathematicians, which should be regarded as a Chinese team.

Hodge's conjecture is a huge project, and feasibility studies are essential before the project is established.

The two small teams of Lu Guozhen and Director Wu immediately carried out the intensive feasibility study work, and after the feasibility study report was written, they would apply to the relevant departments for the project, which would take several months.

"Hodge guesses that this project has already begun to operate, what about the three problems of the other group?" Shen Qi returned to the hotel, wrote down the N-S equation, the P to NP problem, and the Yang-Mi equation on a piece of paper, and then stared at them in a daze, unable to do anything.

The most difficult of the seven millennial problems is the Hodge conjecture, while Shen Qi thinks that the most difficult is the P-to-NP problem, followed by the N-S equation and the Yang-meter equation.

"The level of physics is still a little lower, two of the four earthquake prediction points are correct, and the other two have not been heard from so far. "Shen Qi has been frantically accumulating physics knowledge this year, and he has reached a bottleneck, and if he wants to seek a breakthrough in physics, it is best to go to the next level.

"One of the conditions for moving from Level 12 to Level 13 in Physics is to work as a physics professor for at least one year, where can I find such a job?"

Shen Qi is currently a professor of mathematics at the University of Hong Kong, a visiting professor of mathematics at Yan University, and a senior mathematics advisor at the Morningside Mathematics Center.

Being able to have three prominent identities in the field of mathematics at the same time is because Shen Qi has made remarkable achievements in mathematics.

Shen Qi has also made some achievements in physics, with one of his papers on condensed matter physics published in PRL and another paper on seismological models published in Science.

"It's been a while since my PhD dissertation in physics "On Complexity" was submitted to PRL, but I don't know what stage it has reached?"

Shen Qi entered PRL's submission system to check the review progress of the paper "On Complexity".

PRL's submission system shows that it has been accepted.

The system brushes out the information, and because the host publishes a paper in a physics journal with an IF value of 7.872, 393,600 points will be awarded.

"Two PRLs, one "Science", I wonder if there is a chance to hang the title of physics professor?" Shen Qi left the hotel and wandered around the campus of Yan University looking for opportunities. ()

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