Scholar's Advanced Technological System

1031 Future of Number theory

On stage.

Seven whiteboards were fully written!

The eight whiteboards were dragged on stage. There was no doubt Lu Zhou would complete the proof.

His calculations and clear thinking, as well as his deep understanding of mathematical tools, were impressive to everyone sitting in the audience.

Who knew a complex function proposition could turn out to be so convoluted.

The concepts of a complex plane and differentiable manifolds seemed to be completely different things, yet they were unified by the Riemann zeta function.

Lu Zhou’s pen was like Beethoven’s baton; the disordered prime numbers came to life, creating a song for the audience.

Just like Schultz had said, it seemed like this was something from another universe, it didn’t belong to this world.

The audience wished that the report would never end.

They wanted Lu Zhou to continue to perform until all of the secrets of the universe were revealed to them...

Molina was sitting in the crowd as she bit her lip and clenched her fists. Her eyes were filled with stubbornness.

The problem that troubled her for years felt insignificant under Lu Zhou. Lu Zhou didn’t even stop and think for a second. He kept on writing.

This feeling of powerlessness made her frustrated.

Even though she wasn’t qualified to make a conclusion on whether or not the proof was correct, judging from the atmosphere in the lecture hall, the result was obvious.

After all, the feeling of enlightenment was obvious.

Even herself was convinced Lu Zhou was correct...

Sitting next to Molina was her former mentor Sophie Morel, a mathematics professor. Sophie looked at her former student and spoke in a soft voice.

“In my opinion, there’s an 80% chance he is correct... What do you plan on doing?”

Molina went silent for a while and looked down.

“I don’t know, maybe go for a vacation back home.”

She spent the past decade trying to solve this proposition.

Even though she didn’t want to believe what she was seeing, the reality was often cruel.

She lost.

Sophie sighed and tried to comfort Molina.

“You shouldn’t feel too bad about yourself, there are plenty of other propositions worthy of being solved.”

Molina went silent for a while and spoke.

“Maybe.”

...

That was right.

There was no suspense at all.

When the eighth whiteboard was being written, Professor Faltings squinted.

At that moment...

It was like a gate opened in his heart. He was seeing a brand new world that he had never seen before...

He forgot when was the last time he felt something like this.

He just remembered it was a long time ago, back when Grothendieck was alive. Back when he wrote a “naive” letter to the king of algebraic geometry...

Professor Deligne was sitting next to him. Deligne stared meticulously at the whiteboard.

He suddenly asked, “Do you think he did it?”

Professor Faltings was caught off guard. He composed himself and gave a conservative answer.

“90% certain he did.”

Professor Deligne smiled and asked, “When did you start to speak with uncertainty in mind?”

Faltings didn’t care for the joke made by his old friend. He spoke calmly, “After all, it’s Riemann’s hypothesis, so we have to be cautious. Besides, what do you think?”

Professor Deligne went silent for a while and spoke.

“I can’t find a counterexample to disprove his theory, just like I can’t find a non-trivial zero beyond the critical line...”

Professor Deligne spoke confidently.

“I can only say that his proof is logically consistent.”

Professor Faltings looked slightly surprised.

Even though Faltings didn’t say anything, Deligne knew what Faltings was thinking.

Being logically consistent basically meant the proof was correct...

People sitting on the other side of the venue were also talking.

When Fefferman saw Lu Zhou write down a crucial formula, he turned to Tao Zhexuan and asked, “You’re better versed in number theory... What do you think?”

Professor Tao had a flash of excitement in his eyes. However, before he could speak, a man sitting nearby stood up with excitement and spoke.

“That’s it!”

The man ignored the dirty looks from the scholars sitting around him.

It was as if the man were at a football game, not a mathematics conference.

Tao Zhexuan looked at Professor Fefferman and shrugged.

“Looks like... Someone answered the question for me.

“I feel the same way as him.”

...

The last row of equations was written.

The whiteboard marker was put down.

The venue was dead silent.

Not a single sound in the entire venue.

Lu Zhou took two steps back and took a look at the neatly written equation on the whiteboard. He spent thirty seconds reminiscing about his journey, as well as each step he took to get to where he was today...

This also gave the audience a chance to digest the information.

Lu Zhou cleared his throat, turned toward the audience, and spoke.

“It is obvious that we have found the distribution of non-trivial zeros on the Riemann zeta function. Which is, all non-trivial zeros of the Riemann zeta function on the complex plane Re(s) = 1/2 lie on a straight line.

“The proof is completed. However, the journey has only just begun, there are still many questions that the world has yet to find an answer.

“For example, the analytical extension of the Dirichlet L series; are all non-trivial zeros of the Dirichlet L function also located on the straight line of the complex plane Re(s) = 1/2? And what about the automorphic L function? We still don’t have an answer to these profound questions.

“History tells us that whenever we solve a problem, there are two more difficult problems waiting for us.”

Lu Zhou paused for a second and spoke.

“There are some things I wanted to say after the academic community makes an evaluation of my proof, but... I don’t think it matters.”

The venue was silent.

Lu Zhou could feel the tension from the audience. He nodded and spoke in a louder voice.

“First of all, let’s answer the previous question, what is next for analytic number theory?

“My answer is, this ancient discipline will become revitalized and become more prosperous than ever.

“As for myself, maybe I will research the Dirichlet L function and Generalized Riemann hypothesis... Or maybe I’ll research the non-trivial zero-point correlation function for the Riemann zeta function.

“However, there is a bigger proposition waiting for me.”

Lu Zhou paused for a few seconds and looked around the audience. He soaked in the atmosphere and took a deep breath.

“Which is, unifying algebra and geometry!”

The second Lu Zhou finished speaking, the audience was shocked!

Unifying algebra and geometry!

People were shocked, doubtful, curious, confused...

“Unifying... algebra and geometry? Oh my god.”

“That sounds ridiculous.”

“The academic community hasn’t even made a judgment on his proof, and he’s already so arrogant!”

“If anyone can do it, it would be him...”

There was a huge commotion in the audience.

Academician Wang’s eyes widened. He couldn’t believe Lu Zhou would propose something this crazy.

Molina looked shocked; unifying algebra and geometry was undoubtedly a taller mountain than Riemann’s hypothesis. She didn’t know why he was making such a big claim, right after proving Riemann’s hypothesis.

Faltings was also surprised.

However, he was surprised at something else.

The old man stared at Lu Zhou as he muttered to himself, “I can’t believe this...”

Unifying algebra and geometry...

That was the last thing Faltings wanted to do before he retired.

He didn’t expect Lu Zhou to have the same idea as him.

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