A Milestone Achievement
"Professor Shen, the Grand Unification we understand is the kind of programmatic Grand Unification that can use one system to explain all mathematical problems!" someone shouted from the audience.
"Perhaps I used the wrong words. 'Partial' and 'Grand Unification' are contradictory. The significance of the SLW system should be 'phased Grand Unification.' I will revise the relevant wording in the report later. So let's not dwell on these minor details of wording for now and just look at the content." After stabilizing the situation, Shen Qi moved on to the main text of <Systematization and Hodge Conjecture>.
"Ninety percent of my report is about systems, and the last part proves that the Hodge conjecture belongs to the SLW system, or that the SLW system can completely explain the Hodge conjecture."
"Part One, Algebraic Geometry, is titled 'AG Framework Principles' in the report."
"This section focuses on adding 'properties of S-type characteristic surface's to the existing classical Algebraic Geometry theories such as Bezout's theorem, Kassler's correspondence principle, and Cremona transform."
"What I want to say is that no system can be completely new; it cannot be created out of thin air. They must innovate upon the foundations laid by their predecessors and on the basis of classical theories..."
Shen Qi first explained the most complex and innovative section, AG.
Ralph sat there, staring at Shen Qi as if he were a god, tears welling up in his eyes without him even realizing it.
Yu Lei returned to Princeton not long after leaving, his expression similar to Ralph's; Shen Qi was a god in his eyes.
According to Shen Qi's instructions, Yu Lei and Ralph, under pressure, managed to produce an initial version of the "AG Framework Principles".
After working on the first version, Yu Lei and Ralph graduated with their doctorates.
After being further developed by Shen Qi, the "AG framework principle" was presented to mathematicians worldwide.
Clap clap clap!
Applause rang out from time to time, and Shen Qi's report was interrupted by the enthusiastic applause of the guests more than once.
"Part Two, Topology Section, is titled 'TP Remodeling Principle' in the report."
"This section focuses on reshaping space theory based on the eight Standard Model of the Thurston's Geometrization Conjecture, resulting in a more fault-tolerant algebraically closed chain space."
"If anyone is interested, they can use the 'TP reshaping principle' in the SLW system to verify the Poincaré conjecture. I can guarantee that this is different from Mr. Perelman's work."
Director Wu's hands were trembling in the audience. He deeply understood that the same weapon could have completely different power in the hands of different people.
In the process of tackling the field of topology, Director Wu and his researchers did not think that far ahead. They followed Shen Qi's instructions and ended up accidentally achieving a "progressive Grand Unification".
In the morning session, Shen Qi presented the "AG Framework Principles" and the "TP Restructuring Principles," captivating the audience and leaving them thoroughly entertained.
The afternoon report continued, Shen Qi discussed the third principle. "The third part, the Mathematical Analysis section, is titled 'AN Standardization Principle' in the report."
"The focus of this section is on novel Mathematical Analysis and processing of ordinary singularities of plane curves and ordinary singularities of deflections in space, using special cases to extrapolate the whole picture, and establishing a forward standardization principle through inverse Mathematical Analysis."
Lu Guozhen clapped his hands. He was not a shill; he was genuinely applauding Shen Qi.
The report materials were created collaboratively by everyone, but only Shen Qi had the ability to integrate, sort out, and synthesize them into a systematic theory.
Moreover, Shen Qi's stage presence was natural and effortless; if Lu Guozhen or Director Wu were to give a speech on stage, they probably wouldn't be able to handle it.
"Algebraic Geometry, topology, and Mathematical Analysis —these three principles ultimately merge to form the SLW system. Please look at the big screen." Shen Qi turned halfway to look at the screen, and all the guests stood up, their eyes glued to the screen.
This slide is presented in animated form, with Shen Qi explaining simultaneously, "Static graphics are difficult to describe high-dimensional situations, and of course, dynamic models cannot describe them either. However, dynamic models are more vivid. What's on the screen is just an illustration. Combined with my explanation, you can fully unleash your imagination."
The curved surface on the screen is extremely distorted, yet it still appears flat; such a thing is not seen in real life.
Shen Qi: "This is the 'S-type characteristic surface,' please observe it carefully."
The surface rotates continuously around the origin, which is not theoretically the center.
Suddenly, new twisted surfaces were generated. After twisting to their extremes, they covered the complex plane, one page, two pages, N pages. They rotated around the origin in an irregular manner, more and more, faster and faster.
A sapling can instantly grow into a vast forest; this is the mathematical forest, whose properties can be precisely described using algebraic expressions through the SLW system.
The guests' eyes were dazzled, but no one was willing to close them.
Shen Qi calmly stated, "This mathematical forest comprises Algebraic Geometry, topology, and Mathematical Analysis. To fully describe the mathematical model shown on this slide, approximately 700,000 algebraic expressions are required. Theoretically, it can explain all problems in Algebraic Geometry, topology, and Mathematical Analysis. It is SLW."
The guests fell silent, not daring to speak.
"Do you think this is all there is to mathematics?" Shen Qi raised his voice, his words ringing out in a resounding self-answer, "No, no! We still need one last seed—number theory! Algebraic Geometry + topology + Mathematical Analysis + number theory—this is the true Mathematical Grand Unification. When it arrives, even the gods will tremble."
Whether God trembled or not is unknown, but many people present had already begun to tremble, shaking with excitement.
"This animation is addictive..." Lu Guozhen closed his eyes; he couldn't bear to look at the screen.
"What I'm showing you today is only a preliminary research result. The road ahead is long, or perhaps not so long." Shen Qi ended the animation and switched to the next slide.
Call...
A strange breathing sound filled the room, a mixture of extreme exhaustion and intense stimulation.
"The last part, please look at this expression, which I call the S-type characteristic surface) expression. It represents another algebraic form of the Hodge conjecture. Undoubtedly, in the SLW system, H^2p(X, Q)alg=H^p, p(X)∩H^2p(X, Q), so the Hodge conjecture is a correct proposition."
"Thank you again to Princeton, Yenching University, and the Morning Star Mathematics Center for their strong support of this project. Thank you to all the guests for listening patiently. Thank you, that concludes my presentation!" Shen Qi bowed in thanks and left through a special passage.
The guests were stunned for a full minute; the lecture hall was as quiet as a tomb.
Suddenly someone shouted at the top of their lungs, "Professor Shen succeeded! He proved the Hodge conjecture! A truly brilliant speech; even the gods would tremble before it!"
The atmosphere erupted in cheers and applause. The entire hall was filled with shouts and thunderous applause.
"Where is Professor Shen?" Suddenly, everyone realized something: Professor Shen was gone; he'd run off after showing off.
"Professor Shen went to change his clothes, he'll be back later," someone said.
"No, he won't. Let's call it a day and see what the official IMU news is in a few days." Lu Guozhen shook her head. You guys are all too young.
Shen Qi did not go on stage again as expected. He had already said, "Thank you, my report is finished," so listen carefully to the report and pay attention to the details.
After Shen Qi's special report meeting, he provided IMU with the original PDF version of "Systematization and Hodge Conjecture" as well as a printed copy.
IMU immediately convened hundreds of mathematics experts to conduct in-depth discussions on "Systematization and Hodge Conjecture".
Princeton provided the venue and all logistical support, and IMU's validation work was carried out on the Princeton campus.
Two weeks later, IMU officially announced:
"Professor Shen Qi proved the Hodge conjecture. More importantly, Shen Qi Team established a system, namely the 'Shen-Lu-Wu System' (SLW). To view the relevant papers, please go to link XXX. We thank Shen Qi Team for their tremendous contributions. We have every reason to believe that a new era in mathematics is about to begin."