The Summit
Two days later, Shen Qi ran into Mary at work and learned that Schultz had a very strong desire to remarry Mary.
Mary resolutely stated that she would rather starve to death or jump off the mathematics building than remarry Schultz.
"Then find an even better man," Shen Qi advised, before starting his work.
Shen Qi is very interested in the news about this year's Chinese Mathematical Olympiad. The CMO national finals have just ended, and only one contestant got a perfect score.
The last optional question was set by Shen Qi, and only one contestant successfully proved that there are 3n planes—that was the contestant who got a perfect score.
"Sigh, each graduating class is worse than the last. I'll treat you to a big meal when I get back to China," Shen Qi texted Vice President Tan of the Chinese Mathematical Society, acknowledging his defeat in the bet.
In early July, Lu Guozhen and Director Wu went to the United States and successfully met up with Shen Qi.
The three held secret talks for several days, discussing important matters.
In Shen Qi's office.
Shen Qi wrote some mathematical formulas on the blackboard and said, "My understanding of the simplified version of the Hodge conjecture is: Let X be a Projective Algebraic Manifold, and p be a positive integer. Let H^2p(X, Q)algH^2p(X, Q) be an algebraically closed subspace, that is, the Q -Vector Space produced by the basic classes of Algebraic Subvariety p in X. I have proven that H^2p(X, Q)alg=H^p, p(X)∩H^2p(X, Q), which proves the Hodge conjecture."
"Proving the conclusions described in this passage is extremely difficult. We in China also pay close attention to the developments in the international Mathematics Community. Schultz's team is working on such a highly challenging task, and we have reason to believe that Schultz's team has made significant progress." Lu Guozhen did her homework before going to the United States.
"Schultz's team must be doing well. Who knows, they might release all their research results someday." Shen Qi felt that Schultz had something substantial to offer, otherwise Schultz wouldn't have dared to be so arrogant, single-handedly storming into Princeton and forcefully demanding that his ex-wife remarry him.
"Professor Shen, your overall plan comprises three sub-plans, namely the Algebraic Geometry section, the Mathematical Analysis section, and the topology section, which are each handled by the three of us. Now that all three sub-plans are here, what is the specific concept behind your overall plan?" Director Wu asked.
"My grand plan is to use Algebraic Geometry as the skeleton, topology as the muscles and internal organs, and Mathematical Analysis as the blood and body fluids to create a new system, and the Hodge conjecture is a part of that system. It's a bit complicated, so let me explain the core logic." Shen Qi erased the contents of the blackboard and drew three boxes side by side.
Above each box are two English letters: AG for Algebraic Geometry, TP for Topology, and AN for Mathematical Analysis.
Shen Qi first filled in the content in the AG box:
Σσv=m*n
η0:η1:...ηn=ψ0(ε):ψ1(ε):...ψn(ε)
f(z1z2, z2z0, z0z1)=z0^rz1^sz2^tg(z0, z1, z2)
Although Lu Guozhen and Director Wu's main areas of expertise are not Algebraic Geometry, these two senior Mathematics Community who have spent their entire lives studying Algebraic Geometry and recognize most of the classic expressions in the AG box and their meanings.
"Bezuo's theorem, Kassler's correspondence principle, Cremona transformation... Hey, Shen Qi, what's the last expression in the AG part?" Lu Guozhen asked.
The last formula is ζ'd+1=ζd+1+αd+2ζd+2+...αndn. Shen Qi said, "The application and generalization of the classical Algebraic Geometry theory in the AG part was completed by my two doctoral students. Oh, they have now graduated with their doctorates. One went to Shuimu University, and the other stayed at Princeton."
"I derived the last formula myself, which is the special characteristic of d-dimensional irreducible algebraic manifolds. I'll call it the 'S-type characteristic' for now, which is a small innovation. I won't go into the specific derivation process of the 'S-type characteristic'; you two just need to know the conclusion," Shen Qi explained his thought process.
"Therefore, the core of the AG part is to combine classic elements with innovation and build a system framework." Lu Guozhen and Director Wu roughly understood the core logic of the AG part that Shen Qi personally took charge of.
"Yes, my two doctoral students and I have done a pretty good job." Shen Qi then filled in the content in the second box, which was TP, the topology section.
Shen Qi has reviewed the topology materials brought by Director Wu in full. He wrote eight expressions in the TP box, "I am very grateful for the hard work of Director Wu's team over the past year. You have done a great job. The derivation of the eight Standard Model of the Geometric conjecture has been successfully completed. These are the muscles and internal organs, providing the system with the necessary power and energy."
"Professor Shen's insights were the main source of our help," Director Wu said modestly.
"Inspiration is directional, but the specific work requires a lot of manpower to push forward and complete. The fact that we were able to start the compilation work on the Hodge conjecture project within a year is thanks to the hard work of every member of our large team of twenty people. You should know that Schultz's team worked on it for three years, and the Mathematics Department at the University of Bonn mobilized almost all its resources to help him. This project cannot be accomplished with just a few people, at least not within a year." Shen Qi expressed his gratitude to Director Wu and Lu Guozhen's team, and filled in the content in the third box.
The third box is AN. Lu Guozhen's Mathematical Analysis section has been going smoothly, and Shen Qi has hardly had to worry about it in the past year.
The research data from Lu Guozhen's team has been handed over to Shen Qi; the premises, derivation process, and final conclusions are very clear.
Shen Qi extracted the core elements and filled them into the AN box. "Director Lu's research results can be summarized in one sentence: a novel Mathematical Analysis and treatment of ordinary singularities of plane curves and ordinary singularities of deflections in space. AN is the blood, continuously supplying oxygen to our system."
Shen Qi continued writing two plus signs, one equal sign, and one question mark on the blackboard: AG + TP + AN =?
"Gentlemen, how should this system be named? Following international convention, shall we tentatively name it the SLW system? Or WLS, LSW?" Shen Qi asked.
S stands for Shen, L for Lu, and W for Wu.
A total of 20 people from three research institutions in China and the United States participated in the Hodge conjecture Project. The three academic leaders were Shen Qi, Lu Guozhen, and Director Wu.
The new theoretical system certainly can't be named SLWYTP... Putting all twenty people's surnames on it is something no one has ever done before.
International practice is to include the surname of the person who has made the greatest contribution to the project in the name; these people are often academic leaders.
Therefore, everyone wants to be an academic leader, firstly because it brings high academic and social status, and secondly because it offers the opportunity to be remembered in history.
Lu Guozhen and Director Wu said in unison, "Of course, 'S' should be placed at the very beginning."
Shen Qi cupped his hands in a respectful gesture and smiled, "You flatter me."
After finishing, Lu Guozhen and Director Wu discussed it for a while and decided that whoever went to university earlier should have their surname listed second, which was fair and reasonable.
After exchanging information, the two discovered that Lu Guozhen had entered university a year earlier than Director Wu. Therefore, the new theoretical system was temporarily named the "Shen-Lu-Wu System", or SLW system for short.
Shen Qi erased the question mark on the blackboard, making AG + TP + AN = SLW.
And HC∈SLW.
HC is an abbreviation for the Hodge conjecture.
Shen Qi said, "Next, what we need to do is to sort out the details of SLW and then prove that HC belongs to SLW."