The unification of algebra and geometry had been a topic for a long time.
In fact, this wasn't a practical research direction. It was even "contrary" to the general trend of the development of mathematics.
After all, it was common knowledge that when most disciplines moved from shallow waters to deep waters, the branches of research would be like the branches of a shrub. The more prosperous it was, the more complicated it would be.
The same was true for mathematics.
Two centuries ago, there were scholars like Gauss who were omnipotent and proficient in all fields. But now, even geniuses like Tao Zhexuan, who was an IQ 230 genius, could only be omnipotent and proficient in a limited range.
For most people, being able to master a certain field of knowledge and achieve a certain level of achievement was already enough for them to be able to hold their own in a certain field of study.
For a huge proposition like unifying algebra and geometry, except for a few geniuses who would suddenly have similar ideas, almost no one would be bored enough to think about a problem that was even more impractical than proving a mathematical conjecture, let alone use it as the opening report of the year.
However, because of this, this work that could only be done by a small number of people was precious in the long history of mathematics.
Back in the era of Descartes and Fermat, people used Cartesian coordinates to study geometric figures. This was the first time that people combined algebra and geometry.
Imagine putting a lighter in the hands of a primitive man and telling him that he only needed to press a button to replace the work he had done with a wooden stick for dozens of minutes. How surprised would he be?
Even though this was knowledge that middle school students could use, it was groundbreaking for the mathematics world at the time. Analytic geometry dominated the mathematics world for centuries, until 1857, when a genius named Riemann proposed algebraic function theory and the first absolute invariant in the history of algebraic geometry — "deficiency". Algebraic geometry was born and ended the old era.
Later on, there were still countless geniuses who devoted themselves to this great cause, constantly adding bricks and tiles to the bridge between algebra and geometry.
In the 20th century, the three major structures proposed by the Bourbaki school of thought dominated the entire structural mathematics. Any part of mathematics with structural characteristics could be defined as "algebraic structure", "topological structure", and "order structure", which were the three major structures.
The "probability theory" proposed by Grothendieck ushered in a new era of algebraic geometry. His lecture notes, "Foundations of Algebraic Geometry", were regarded as the bible of the academic community.
There were a lot of people who invented new mathematical tools, and there were also a lot of people who founded a discipline. However, very few people were able to connect these intertwined knowledge together and find the unity between them.
As everyone could clearly see, the subdivision of disciplines was the general trend. In the future, there would be more and more branches of mathematics with the development and prosperity of this discipline. It would flourish under the efforts of countless ordinary and extraordinary people.
But at the same time, the work of carrying on the past and opening up the future must be done by someone …
In fact, the new generation of mathematicians after Grothendieck's era had already made many attempts.
For example, Shinichi Mochizuki's other theory in addition to the "Universal Era Theory", "Teichmüller Theory", proposed a set of "unique and obscure" methods, which unified algebraic elements and geometric elements. Except for his students, very few people could understand what he was trying to do.
Another example was Schulz. His P-adic number and perfect space theory had become increasingly popular in recent years, and it had always been widely regarded as one of the theoretical tools most likely to unify algebra and geometry.
However, mathematical methods did not exist in isolation; they were born to solve problems.
Those mathematical conjectures were like touchstones. Only by solving the actual problems could the mathematical tools and methods be accepted by the mathematics community.
Now that the Riemann conjecture had been proven, Lu Zhou was undoubtedly the person closest to the holy grail.
Just like Fermat's Last Theorem for Wiles, the achievement of proving the Riemann conjecture had pushed him from the throne to the throne of God. If he took another step forward and touched the holy grail, he would have the hope of defining new rules for the post-Grottendieck era.
Or, renaming the new era after him would not be a problem.
At the same time, Lu Zhou speculated that if he wanted to upgrade his mathematics level to level 10 and set foot on the first step of the road to the future, it was necessary to complete this work.
Even though the system did not give any hints, he could clearly feel this.
After all, if there was any achievement that could surpass the Riemann conjecture …
This was probably the only possibility left.
…
After the report, there was a Q&A session.
Because many people hadn't finished reading their theses, even after listening to Lu Zhou's explanation, they still needed time to digest the huge amount of information.
Other than Tao Zhexuan and Schulz who stood up and asked a few interesting questions, most of the scholars in the research field were very quiet and cautious. Even when they stood up to ask questions, they only asked questions that were not related to the Riemann conjecture itself.
For example, what did he mean by unifying algebra and geometry at the end of the report? Did he already start researching this topic, or was he just casually talking about it?
However, Lu Zhou did not want to answer these questions. Not to mention that this had nothing to do with the proof of the Riemann conjecture. Therefore, most of the questions were brushed off by him.
Honestly speaking, Lu Zhou was quite surprised. He had been at the ICM conference for so many days, but he did not see Professor Tao there.
Of course, he didn't know that after Professor Tao saw the preprint on arXiv, he rushed over from Los Angeles. Before this, he had no intention of coming to St. Petersburg at all …
The Q&A session did not last long; it ended much faster than expected. In the midst of the applause, Lu Zhou bowed and ended this groundbreaking report.
This was also the end of this historic moment.
Before the applause stopped, Professor Holden, the secretary-general of the International Mathematical Union, walked on stage with a bottle of champagne and handed it to Lu Zhou.
"This is a gift from the Corinthia Hotel, and it's a gift from all of us. Open it, this century-long journey has finally come to an end, and we should celebrate with wine. And this historical glory belongs to you! "
Lu Zhou took the champagne and nodded sincerely.
"Thank you."
"You're welcome … Oh yeah, if you plan on publishing your results, I recommend Inventiones Mathematicae. In fact, I sincerely recommend you to do this. You've already published enough articles in Annual Mathematics. If you continue like this, three of the top four journals will be removed. "
Professor Holden spoke in a voice that only the two of them could hear. He sounded like he was joking.
Lu Zhou paused for a second and spoke with a smile.
"I'll think about it."
Under everyone's gaze, Lu Zhou followed Professor Holden's instructions. He shook the bottle vigorously and opened the champagne. The fragrant foam seemed to have grown wings as it sprayed up to the ceiling and splashed onto the audience sitting in the front row.
Lu Zhou originally wanted to apologize to these unfortunate guys, but he saw that they were not angry. Instead, they were happy because they were sprayed on. They stood up and showed off their wet chests to their friends. On the other hand, the professors who were not sprayed had looks of envy and regret on their faces.
Therefore, there was no need for Lu Zhou to apologize.
The atmosphere at the venue reached its peak.
Lu Zhou poured a glass of champagne into a glass of champagne and toasted the audience. He then returned the glass and champagne to Professor Holden and walked out of the venue.
The reporters waiting outside the lecture hall had been waiting for a long time.
If it weren't for the security guards blocking the entrance, they would have rushed in the moment they heard the applause and whistles coming from the lecture hall.
Therefore, when the door of the lecture hall opened and Lu Zhou appeared at the door, the group of reporters were like sharks that smelled blood.
"Professor Lu Zhou, has Riemann's conjecture been proven?!"
"Will you go to the Institut de France to receive the million-dollar prize money from the Clay Institute? What will you do after receiving the prize money? Will you donate it to someone in need? "
"I heard that your research was influenced by your student, Vera Pulyuy, is this true?"
"Does the Riemann's conjecture mean that the rules of modern cryptography will be rewritten? Are our bank cards and social media accounts no longer secure? "
"Professor Lu Zhou …"
Lu Zhou didn't answer a single question. He was escorted by a group of burly men as he walked toward the elevator.
A few minutes ago, the hospital transfer had been arranged.
The visa and other procedures had been completed.
If everything went smoothly, Vera would be able to take the transfer flight from St. Petersburg to Beijing, where the experts at 301 Hospital would take care of her.
Lu Zhou's flight back to China was tomorrow morning before the closing ceremony.
Compared to answering those boring questions, there were still many things waiting for him to deal with …
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