Conception

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

Today, some mathematical problems are even difficult to explain to most professional mathematicians.

The Hodge conjecture is one such example; it was proposed by the British mathematician Sir Hodge in 1950.

"Every harmonic differential form (of a certain type) on a nonsingular Projective algebraic variety is a rational combination of the cohomology classes of the algebraic closed chain."

Whether it's Chinese, English, or any other language, reciting the Hodge conjecture in its entirety in one breath is a strenuous task.

Anyone who can understand even one technical term in this sentence will definitely be the king of the class.

"I've studied mathematical analysis for decades, rising from a student to the head of the Mathematical Analysis Department at Yenching Big Mathematics Department's School of Mathematical Sciences. I've also considered the role of Mathematical Analysis methods in the Hodge conjecture, but I've never been able to implement it. Why? Because simply understanding mathematical analysis isn't enough to prove the Hodge conjecture; even understanding it is difficult," Lu Guozhen said with considerable feeling, adding, "Fortunately, I know an Algebraic Geometry, so understanding the Hodge conjecture is OK for me."

Shen Qi said, "The Hodge conjecture seems very profound and unsolvable, but if you trace it back to its origins, no matter how difficult it is, you can find the pattern through calculus. The most basic tools can often solve the most profound problems; the key is the person using the tool and how they use it. Mathematical Analysis is a basic mathematical tool. Differentiation is the jack, integration is the torque wrench, and series is the screwdriver. As long as you use the tools well, you can disassemble even the most sturdy car."

Lu Guozhen dipped her finger in tea and seemingly aimlessly sketched an abstract shape on the table. "But when we use calculus to define an object, the defined object is not necessarily geometric."

Shen Qi wiped away the watermark pattern on the table and asked, "Director Lu, what is the alternative name that Hodge conjecture?"

Lu Guozhen slapped his forehead. "Hodge conjecture, geometry without figures."

Shen Qi smiled and said, "Yes, to put it another way, we can propose the Hodge conjecture from the integrals along generalized paths on Algebraic variety. If some such integrals are zero, then there exists a path in this path class that can be described by a polynomial equation."

Lu Guozhen realized that Shen Qi's idea was more reliable, so he patted his chest and volunteered. "Tell me, what do you want me to do? Including me, I can mobilize about seven or eight key members of the Yenching University's mathematical analysis team."

"If we transfer three or four more, we'll have a complete football team."

"I'm just a head of a teaching and research office, do you think I'm the dean? Shen Qi, what teams are included in this team you've assembled?"

"My two doctoral students at Princeton are in charge of the Algebraic Geometry section, the Morning Star Mathematics Center is in charge of the topology section, and Director Lu, you and your core team are in charge of the Mathematical Analysis section."

"You've cast a wide net, Chief Designer Shen Qi." Lu Guozhen noticed something amiss and continued, "Shen Qi, one of your two doctoral students at Princeton University is a Chinese exchange student, right?"

Shen Qi said, "That's right, my two students, one Chinese and one American."

"In your vision, two top universities in China and the United States, along with a research institution, will work in three separate groups to tackle the Hodge conjecture, ultimately converging under your integration. More than a dozen mathematicians will participate in this monumental project, including one American doctoral student, and the rest are all Chinese... Shen Qi, it seems your strategic focus is gradually shifting towards China. I absolutely support you." Lu Guozhen analyzed Shen Qi's strategic intentions.

"Let's take it one step at a time during the transition phase." Shen Qi had his own plans. Before returning to China, he wanted to present a generous gift to his motherland, Hodge conjecture this project would be a good gift.

The main person in charge of the project that solved the Riemann Hypothesis was Shen Qi. At that time, the team included Chinese, Germans, Swedes, and Israelis. With the Strong Force support of American academic forces, they accomplished a feat in the History of Mathematics, completely proving the Riemann Hypothesis.

When people mention the Riemann Hypothesis now, the most common comment is. "A Chinese mathematical genius led an international team and made history in the United States."

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

Regarding the new project Hodge conjecture, Shen Qi and his Princeton team consist of three people, Lu Guozhen and his Yenching University team have seven or eight people, Director Wu and his Morning Star Mathematics Center team have five or six people.

For basic Mathematical Research, forming a dedicated research team of sixteen or seventeen people for a single topic is undoubtedly a grand and impressive undertaking.

In this impressive lineup, only one American doctoral student, Ralph, a student of Shen Qi, is present; the rest are Chinese Mathematician, making this a Chinese team.

The Hodge conjecture is a massive undertaking, and a feasibility study is essential before it is approved.

Lu Guozhen and Director Wu's two small teams immediately began intensive feasibility studies. After completing the feasibility study report, they will apply to the relevant departments for project approval, which will take several months.

"The Hodge conjecture project has already started, but what about the other three problems?" Shen Qi returned to the hotel, wrote down the Navier-Stokes equations, the P versus NP problem, and the Yang-Mi equations on a piece of paper, then stared at them blankly, at a loss for what to do.

The Hodge conjecture is considered the most difficult of the seven Millennium Prize Problem, while Shen Qi believes that the P versus NP problem is the most difficult, followed by the Navier-Stokes equations and the Yang-Mille equations.

"My physics level is still a bit low. I got two of the four earthquake prediction points right, but there's still no news about the other two." Shen Qi has been frantically accumulating physics knowledge this year, and he's reached a bottleneck. He needs to seek a breakthrough in physics, and it would be best if he could advance another level.

"One of the requirements for advancing from Physics Level 12 to Level 13 is to work as a Physics professor for at least one year. Where can you find such a job?"

Shen Qi's current main position is a mathematics professor at Princeton University, a visiting mathematics professor at Yenching University, and a senior mathematics advisor at the Morning Star Mathematics Center.

Shen Qi is able to hold three prominent positions in the field of mathematics because of his world-renowned achievements in mathematics.

Shen Qi has also made some achievements in physics. One of his papers on Condensed Matter Physics was published in PRL, and another paper on seismological models was published in Science.

I submitted my physics Doctoral Thesis, "On Complexity," to PRL some time ago, but I'm wondering what stage it's at?

Shen Qi accessed the PRL submission system to check the review progress of his paper, "On Complexity".

PRL's submission system shows: Accepted.

The system displayed a message: "The host has published a paper in a physics journal with an impact factor of 7.872, and is awarded 393,600 academic points."

"Two PRL papers and one Science paper—I wonder if there's any chance I could get a professorship in physics?" Shen Qi left the hotel and wandered around the Yenching University campus, searching for an opportunity.