Chapter 262 - 247: To the Next Generation, Good Luck

Chapter 262: Chapter 247: To the Next Generation, Good Luck

Who is Carlson?

James Carlson. He’s one of the veteran members of the Clay Mathematics Institute’s (CMI) Scientific Advisory Board and its former director. He led the institute from 2003 to 2012.

And what is the Clay Mathematics Institute?

In 2000, that private mathematical foundation announced seven "Millennium Prize Problems."

The Riemann Hypothesis, P vs NP, the Hodge Conjecture, the Poincaré Conjecture, Yang-Mills Existence and Mass Gap, the Navier-Stokes Equations, and the Birch and Swinnerton-Dyer Conjecture.

Each problem carries a prize of one million US dollars.

So far, only Perelman has solved the Poincaré Conjecture, and he refused the prize money.

The other six remain unsolved.

As a member of the Clay Mathematics Institute’s board, Wiles was qualified to recommend new "candidate problems" to the institute.

He believed Li Dong’s conjecture was worthy of being added to that list.

Wiles looked away from Li Dong and added,

"All I’m doing for now is submitting a formal recommendation, but..."

"In my personal opinion, your conjecture is very likely to become the eighth great problem, following the seven Millennium Prize Problems."

Everyone present was stunned, but no one objected. They were all experts in the field...

Li Dong said nothing.

Wiles looked at Li Dong and asked again,

"It’s your conjecture. What do you think?"

Li Dong suddenly smiled.

He looked back at Wiles and said,

"Professor Wiles, I have no problem with that."

"But please pass on a message to Mr. Carlson for me. Tell him not to be in a rush to prepare the million-dollar prize."

Wiles froze for a second.

Then, the old man, who rarely ever smiled, broke into the biggest grin Li Dong had ever seen from him.

"Alright, I’ll pass that along."

A hush fell over the room.

Liu Ruochuan finally noticed that the hand holding his teacup had been trembling for some time.

Qiu Chengtong, however, narrowed his eyes slightly.

He and Wiles were old friends; he could read between the lines of what Wiles had just said.

Wiles genuinely believed that this "Li’s Conjecture" had the potential to be ranked alongside the seven Millennium Prize Problems.

That was why he wanted to "give it a push."

He wanted to get it onto the list of problems for the next generation of mathematicians, and the generation after that.

And as for Li Dong...

’This young man is truly audacious,’ Qiu Chengtong marveled internally. ’And I don’t mean that in a bad way. It’s his confidence.’

After all, if the CMI were to officially list his conjecture, only for it to be proven or disproven within a few years, it would become a massive joke.

...

Just as the tense atmosphere in the room began to ease, Professor Levan suddenly spoke.

To be honest, he hadn’t said much up to this point.

It wasn’t that he didn’t want to join the conversation, but when it came to the Langlands program, he was a step behind Wiles, Penrose, and Liu Ruochuan.

His specialty was applied mathematics, after all.

In this room, he felt he had the least authority to speak.

But at this moment, he simply couldn’t hold back any longer.

His tone unconsciously took on a note of respect.

"Mr. Li Dong... may I ask you a question?"

Li Dong quickly waved his hand dismissively.

"Professor Levan, please, don’t be so formal. Go ahead."

Levan took out a tablet and pulled up an image.

It was a diagram illustrating spectral inversion.

The horizontal axis represented energy, and the vertical axis represented the eigenvalue density of a certain operator.

There were three peaks on the graph.

The first peak was clear and sharp.

The second peak was barely discernible.

The third peak was just a blurry smear.

Levan’s voice was tinged with urgency.

"My main field is applied mathematics, but I’ve been keeping up with pure mathematics as well."

"Last night, I read your paper twice, and I think I found something."

"Your technique of ’using the convergence interval of the correlation function F_π(α) to constrain the upper bound of the ramification index’... it’s almost a mirror image of a class of ill-posed operator inversion problems I’ve been wrestling with for the past two years."

Li Dong’s brow twitched slightly.

Levan continued,

"I’m working on a class of spectral inversion problems where the kernel of the forward operator is incomplete."

"We can only extract partial information from certain segments of experimental data."

"And we need to invert this incomplete data set back into what should be a clean tensor."

"In theory, all we need is Tikhonov regularization."

"However, when we expand the basis functions into three different bases, they interfere with each other."

"The phase from each basis is off by an error approaching π, which leads to... well, what you see on the graph."

He pointed at the screen. "The third peak is always just a smear."

...

Finally, Levan took a deep breath. "In other words, in our physics problem, there might also be something analogous to your ’ramification index’."

"As long as that ’something’ isn’t explicitly constrained, the basis functions will pull each other apart."

"But your technique uses the zeros of the correlation function to constrain the upper bound of the ramification index."

"My intuition tells me it could be adapted to constrain the upper bound of this hidden variable, and in doing so, pull the position of the third peak out from that blurry mess."

"But..." He gave a wry smile. "I can’t formulate it, because I don’t understand the details of your proof. I can only say, based on gut feeling, that it should work."

The room fell silent. It was a rare scene.

A top applied mathematician had just sniffed out an interdisciplinary connection in a paper on pure number theory.

Even more remarkably, Professor Levan had dared to voice this speculation in this room without even fully grappling with the details of the proof.

Li Dong was stunned for a few seconds.

To be honest, he was a little baffled himself.

He had to admit, he hadn’t fully delved into the world of applied mathematics yet.