Chapter 1119 Peak of the Human Mind!
In fact, even Lu Zhou wasn’t sure if he was a human being or not.
Judging from the data of his physical examination, the high tech system was not reflected in his DNA makeup. However, his cognitive ability was far beyond the level of ordinary humans.
If he recalled correctly, when he first went to Princeton around six years ago, Professor Deligne invited him to collaborate on researching the Grothendieck’s standard conjectures.
Six years had pa.s.sed since then.
There had yet to be any significant progress on this problem, until now.
Now, solving it was as easy as taking a walk.
Even though the main reason for solving this problem was due to the theoretical basis the Grand Unified Theory provided, being able to draw the conclusions using the Grand Unified Theory within half an hour was still an insanely impressive feat.
Even Lu Zhou was impressed by himself.
Lu Zhou took a deep breath and tried to calm down. He stared at the line “Lefschetz standard conjecture holds!” and spoke after a moment of silence.
“Everyone knows the Grothendieck’s standard conjectures can be divided into two parts. The first part is the generalization of the Hard Lefschetz theorem by Professor Grothendieck, what we know as the Lefschetz standard conjecture.”
“The second part is the Hodge standard conjecture.”
Lu Zhou frowned and pondered for a long time.
The venue was silent.
Everyone was waiting for him to continue.
Under the gaze of countless partic.i.p.ants, Lu Zhou suddenly relaxed and spoke in a casual tone.
“Whatever.
“Even though I was just demonstrating an algebraic geometry application of the Grand Unified Theory…
“I’ve already written so much.
“Might as well finish it.”
Lu Zhou didn’t notice the surprised looks behind him, nor did he listen to the exclaims of disbelief.
Lu Zhou walked to a blank whiteboard with a calm and relaxed look on his face. He stopped for a moment.
Grothendieck’s standard conjectures were some of the most profound propositions in algebraic geometry.
The beauty of the conjectures lied not only in its complexity but also in the inferences.
If Grothendieck’s standard conjectures were proven to be true, one could directly use it to deduce Weil’s conjecture. One could also infer that the Frobenius function on the coh.o.m.ology group of smooth algebraic cl.u.s.ters was semisimple and that the algebraic cycle, h.o.m.ological equivalence, and numerical equivalence held a closed chain relations.h.i.+p.
Everyone knew this, obviously.
Not to mention all the theories that weren’t directly related to Grothendieck’s standard conjectures.
It wasn’t an exaggeration to say that these conjectures guided the future of the algebraic geometry field.
He picked up a pen and began writing on the whiteboard.
[… When i≤n/2, the quadratic form X on A^i(X)∩ker(L^(n−2i+1))→(−1)^i·L^(r−2i ) x.x is positive definite…
[X is the smooth projection algebraic cl.u.s.ter on the domain k, while l is a prime number that is relatively prime in regard to the characteristic k, H^i(X, Ql) is the i-adic coh.o.m.ology group of X. The hyperplane of the X projection s.p.a.ce intersects the sub algebraic family of X.
[When X is an algebraic surface or a complex algebraic cl.u.s.ter, this conjecture holds true.]
However, he wanted to prove this conjecture was true for all cases of X!
Time quickly pa.s.sed by.
More and more calculations were written on the whiteboard.
The comprehension speed of the audience couldn’t catch up to Lu Zhou’s writing speed.
Perelman was sitting in the crowd with his arms crossed. He suddenly sat up straight and frowned at the whiteboard.
Schultz was sitting nearby, and he exclaimed in disbelief.
“He used the L^2 coh.o.m.ology method to obtain a topological abstract of the compact quotient of the complete manifold. This extends the Hodge theory on the compact manifolds to non-compact manifolds!
“Jesus Christ… He is a genius!”
This was a property of the L^2 coh.o.m.ology theory mentioned in the paper on discrete groups and elliptic operators published by Sir Atiyah in the Annual Mathematics in 1976.
What surprised Schultz wasn’t Lu Zhou’s ingenuity, but how easily Lu Zhou applied these mathematical tools.
It was like Lu Zhou knew these mathematics tools like the back of his hand.
Perelman stared at Schultz and spoke.
“Yes, obviously.”
Nearby in the venue.
Two old men sat there, staring at the whiteboard.
When Lu Zhou successfully expanded the Hodge theory on compact manifolds to non-compact manifolds, Professor Deligne suddenly broke the silence.
“What do you think?”
Faltings was sitting next to him, and he remained silent.
After 10 seconds, he shook his head.
“I need some time to think about this… Maybe I’m getting too old.”
Deligne looked at the stage with a dignified look on his face.
This was the first time he heard old man Faltings talk about his age.
Hearing the old man admit it himself was a little saddening…
On the other hand, another conversation was happening inside the venue.
Qiu Chengtong had asked a question to Professor Tao.
As an expert in a wide range of mathematics fields, he was probably one of the only people that could keep up with Lu Zhou’s speed.
He had to give it everything he got.
Even he found it challenging to keep up with Lu Zhou’s pace.
“His thinking speed is way too fast… It’s like how normal people think in the speed of cars, I’m thinking in the speed of a s.p.a.ce-X rocket, but he’s thinking in the speed of light. Before I catch up to his train of thought, he has already solved the proposition.”
Because Tao Zhexuan’s wife worked at NASA, he often liked to make aeros.p.a.ce a.n.a.logies.
Old Qiu ignored Tao Zhexuan as he continued to stare at the whiteboard.
After a while, he clenched his fist and muttered, “Sensational.”
…
There was no doubt that this was the most glorious moment in the history of Chinese mathematics.
No, not just Chinese mathematics.
It was the most significant moment in the history of mathematics, period.
Not only did he stand at the top of the mathematics pyramid, but he also represented the pinnacle of the human mind.
In front of the whiteboard that connected the human mind to the universe, things like nationality, race, and cultural background paled in comparison.
Trivial details like those became meaningless.
Lu Zhou wrote down the last symbol.
The venue was dead silent.
In fact, minutes ago, a handful of people knew this was going to happen.
Lu Zhou took two steps back and looked at his writing, almost like it was a piece of art.
A few minutes went by before he turned around and spoke to the silent audience.
“That’s my proof of Grothendieck’s standard conjectures. Quod erat demonstrandum.”
The entire stadium was silent.
Not a single sound could be heard.
No one spoke.
No one clapped.
The solemn and emotional expressions were replaced by exhaustion and shock.
Lu Zhou looked at the crowd and spoke.
“The Grand Unified Theory is the subject of this report.
“The proof of the Grothendieck’s standard conjectures is only an example. I hope it inspires future explorations.
“What we witnessed together is the proof that the universe perfectly aligns with mathematical beauty.
“Are there any questions?”
The crowd stayed silent.
No one spoke.
Lu Zhou relaxed his shoulders.
It was almost like a thousand kilograms had just been lifted off his shoulders. He suddenly had a pleasant smile on his face.
The smile was nothing out of the ordinary, but it resonated with every listener’s heart.
“If there are no questions, I’m going to end the report.
“I will be here for the next three days, so if anyone has any questions, you can find me.
“Thank you.”
The applause sounded like a thunderstorm.
Completely flooding the gymnasium.
Lu Zhou could see the shock and surprise in people’s eyes.
It was almost like someone had unmuted the world.
The staff members standing on the sides of the venue, as well as the security guards, looked confused.
They obviously didn’t understand what was going on.
Not everyone understood the beauty of mathematics.
However, for those that did, the beauty shocked and resonated with the deepest part of their souls.
The applause was like a song.
In the midst of the thunderous applause, Lu Zhou placed his marker on the podium, took a step back, and gently bowed. He then turned around and walked off stage.
The era of the Grothendieck’s standard conjectures had ended.
From now onward, the world was entering a new era of mathematics!