The Academic Superstar's Research Summoning System

As he walked back to his dormitory after dinner, the cool autumn breeze on his face finally calmed his feverish head.

Having solved Gödel's incompleteness theorems in the first part, his attention naturally shifted to the second part.

[Noncommutative geometric solution to the Riemann Hypothesis].

The moment Lu Feng saw those words, he felt as if an invisible hand was gripping his brain.

The Riemann Hypothesis.

This top-level problem, hailed as the "jewel in the crown of mathematics," has perplexed the mathematical community for over a century and a half.

Countless geniuses have devoted their entire lives to this cause, yet none have been able to shake it in the slightest.

The solution provided by the system was completely unheard of.

Noncommutative geometry.

This is an extremely abstract branch of mathematics that developed at the end of the 20th century, attempting to describe geometric space using the language of operator algebra.

Could it be used to solve the Riemann Hypothesis?

This line of thinking is even more absurd than explaining love using quantum mechanics.

Lu Feng tried to construct a Hilbert space in his mind, linking the non-trivial zeros of the Riemann Zeta function with the spectrum of a specific operator.

But when he got to the second step, his thinking got completely stuck.

How should this operator be constructed? And how should its noncommutative property be connected with the distribution pattern of prime numbers?

I have absolutely no clue.

It feels like a primary school student who has just learned addition, subtraction, multiplication, and division is suddenly thrown at them with a calculus problem that they can't even understand.

Riemann.

The name suddenly flashed through Lu Feng's mind.

One of the greatest mathematicians in 19th-century Germany, a direct disciple of Gauss, and a genius who died young.

If anyone in the world is closest to the truth of the Riemann Hypothesis, it can only be Riemann himself, who proposed the hypothesis.

Lu Feng's heart skipped a beat.

He quickly scrolled through the list of big shots' information database, his fingertips slid rapidly among those shining names, and finally stopped on a slightly unfamiliar gray avatar.

Bernhard Riemann.

it's him!

Lu Feng took a deep breath without the slightest hesitation.

"System, summon Riemann."

[Confirmed Summon: Bernhard Riemann?]

[Cost: 10000 Learning Points + 1000 Emotion Points]

confirm.

The learning value and emotion value were instantly reduced by more than half.

In the center of the panel, golden light shone brightly, and the gray portrait representing Riemann was instantly illuminated.

[Summoning successful! Enter the inner space immediately?]

Enter.

The dormitory corridor in front of me instantly disappeared, replaced by an extremely simple space.

It lacks Tesla's futuristic laboratory and Newton's classical 17th-century study.

Here, there is only a simple wooden desk, a chair, and a huge blackboard that stretches into the distance.

A young man dressed in a simple scholar's gown, with a slender build and a gentle face, stood somewhat awkwardly in front of the blackboard, holding a piece of chalk in his hand, seemingly unsure of what to do.

When he saw Lu Feng appear, he instinctively took a half step back, his blue eyes filled with a hint of shyness and unease.

"Hello...

His voice was soft, with a strong German accent.

Just as rumored.

Riemann was shy, gentle, and even a little socially anxious.

Faced with such an introverted genius, Lu Feng knew that any formalities and preambles would be superfluous.

He must get straight to the heart of the matter.

Lu Feng strode forward and walked straight up to Riemann, a gentle smile on his face.

"Hello, Mr. Riemann."

He bowed slightly, then got straight to the point.

"I'm trying to prove your conjecture about the zeros of the Zeta function using noncommutative geometry, but I've encountered some problems. Would you be willing to offer some guidance?"

Riemann was completely stunned.

A moment of bewilderment flashed in his clear blue eyes, which was then replaced by an incredulous shock.

My own guess?

How would he prove it using a "noncommutative geometry" that he had never heard of before?

Moreover, this person in front of me, who looks even younger than me, already has his own ideas?

Riemann's somewhat introverted personality was completely overwhelmed at this moment by pure academic curiosity.

He rubbed his hands together excitedly.

"I'd like to hear more details!"

Lu Feng smiled. Instead of describing it in words, he took the piece of chalk from Riemann's hand and turned to walk towards the huge blackboard.

"My idea is to construct a Dirac operator D that acts on the L²(R) space, whose spectral closure should completely coincide with the set of nontrivial zeros of the Zeta function."

The pen tip swept across the blackboard, leaving behind rows of exquisite mathematical symbols.

Riemann followed behind him, his gaze fixed intently on the formulas.

When Lu Feng wrote about how to transform the set of prime numbers P into a semigroup acting on the Hilbert space H, his pen stopped.

"It is here that I cannot prove a natural isomorphism between the operator algebra of this semigroup generation and the Dirac operator D."

Riemann stared at the definition of the semigroup and fell into a long silence.

He didn't speak, but took the chalk back from Lu Feng and wrote a new arithmetic operation below Lu Feng's formula.

He introduced an additional torsion factor, which is related to the Dirichlet trait in number theory.

Lu Feng looked at the revised formula, and his mind instantly cleared.

That's it!

By introducing Dirichlet features, the commutative number theory problem is forcibly transformed into a non-commutative operator algebra problem!

This idea is simply a stroke of genius!

Lu Feng let out a long breath.

He turned around, looked at the somewhat shy mathematical genius in front of him, and said sincerely, "Sir, thank you for your guidance."

Riemann waved her hand, her cheeks slightly flushed, as if she were a little embarrassed.

"Now," Lu Feng said with a mysterious smile, "please allow me to introduce you to two new friends."

Riemann was taken aback.

Before he could react, Lu Feng had already sent two messages in the public chat channel.

[Lu Feng]: @Isaac Newton @Nikola Tesla, let's meet a newcomer.

He replied almost instantly.

[Isaac Newton]: Coming right away.

[Nikola Tesla]: Oh? Another newcomer?

In the center of Riemann's study, ripples appeared in the air, and two light doors of completely different styles appeared out of thin air.

From the door on the left, Newton emerged, dressed in his seventeenth-century court attire and holding half an apple.

From the door on the right, Tesla, dressed in a well-tailored modern suit, walked out with his hands in his pockets, whistling.

The air in the study seemed to freeze instantly.

Riemann was completely dumbfounded as she looked at the two men in front of her, whose styles were so different.

What's going on?

"Oh? This is our new friend?" Tesla spoke first, circling Riemann and stroking his chin.

Newton, on the other hand, appeared more scholarly. He walked up to Riemann and bowed slightly.

"Hello, I am Isaac Newton."

Riemann felt like his brain had crashed.

Isaac Newton?

I feel that my faith has been challenged.

"This is Mr. Bernhard Riemann, an outstanding mathematician," Lu Feng said, stepping in to defuse the situation.

"A mathematician, a kindred spirit?" Newton's eyes lit up. "Perfect timing! I've recently been researching a problem about the geometrization of gravitational fields; perhaps we can discuss it..."

"Come, Mr. Riemann, let me show you my newly designed unified field theory model, which is the ultimate mystery of the universe!" Tesla squeezed in and grabbed Riemann's arm, trying to drag him into his own space.

"Let go! I was here first!"

"Your theory can't even be verified experimentally; it's pure fantasy!"

The two bigwigs started arguing right in front of Riemann.

Caught in the middle, Riemann's delicate face changed from bewilderment to terror, and finally, a blush crept onto her cheeks.

He felt like he was about to be set on fire by these two overly enthusiastic guys.

Lu Feng looked at the chaotic scene and shook his head with a smile.

He silently took two steps back, turned around, and walked into the still-open door of light.

The rest is up to you to build relationships yourselves.

I hope Mr. Riemann will still be well when I come tomorrow.