Chapter 451: Chapter 148 This Isn’t Paranoia, It’s Confidence_3
However, as the discussion deepened, he truly found it difficult to keep up. Qiao Yu’s questions always pinpointed the core of the issue and even led him to consider more profound concepts.
The deeper the discussion went, the more oppressive it felt. The next day when he planned to confront the young challenger’s ideas, the framework was presented directly before him, leaving him unsure how to evaluate it.
Therefore, he was quite happy to let Tao Xuanzhi become aware of this as well.
"What you said makes me really want to communicate with him. If he is also focused on prime number issues, I wonder if he would notice our paper and what his evaluation might be," James Maynard said with a smile.
For people like them who have already spent so much effort on prime number research, who wouldn’t wish to be the first to solve these puzzles that have baffled people for hundreds of years?
"Yes, Professor Zhang, maybe you can help me contact Qiao Yu. I’m very interested in his concepts, and if possible, perhaps we could collaborate,"
Tao Xuanzhi suddenly said.
Having just done some simple deductions in his mind based on Zhang Yuantang’s explanation, he suddenly realized Qiao Yu’s ideas indeed had the potential to succeed.
There were some issues he still didn’t know how Qiao Yu would solve, but there’s no doubt that this was a brand new mathematical thought.
A more unified mathematical expression could make the process of proving number theory clearer, eliminating the need to construct a complex system for a specific problem, instead using various types of modal spaces to represent different issues...
Qiao Yu was ambitious! He wanted to build a grand unified theory of mathematics in his own way. Tao Xuanzhi even suspected Qiao Yu wanted to replace the Langlands Program, yes, using his modal space theory as a substitute.
This did not seem impossible because, while Qiao Yu’s method was abstract, it wasn’t as difficult to understand as the Langlands Program.
Especially the geometrization of number theory issues, making some obscure number theory problems more intuitive in modal spaces.
"I can ask, but that child, although only sixteen... how to say it, he doesn’t resist communication, but he does have his own way of choosing collaborators."
Zhang Yuantang said with a peculiar expression.
In fact, ever since learning about Qiao Yu’s topic, he has been following the related progress, and of course, the results surprised him.
"Stubbornness?" Harvey Gus, who had remained silent on the Qiao Yu issue, inquired.
He knew the least about Qiao Yu, having only heard about some incidents that happened at the World Algebraic Geometry Conference, so he hadn’t commented until now.
"Not stubbornness, to be precise, it’s confidence. I think he believes he can complete this project on his own. Thus, when choosing collaborators, he prefers those with a closer relationship rather than those who are beneficial to the project."
Zhang Yuantang shook his head, correcting the statement.
Well, that’s understandable, one might even say that this self-confidence is something geniuses commonly possess.
Tao Xuanzhi also laughed and joked, "Indeed, if the main framework can be proven on one’s own, the rest is just minor verification work, and a high-level collaborator isn’t really needed."
"But I’m very much looking forward to seeing what results he can achieve. Professor Zhang, you might make it so I can’t sleep well for a while, especially considering if someone could really solve many complicated number theory problems in one go."
Zhang Yuantang smiled slightly, offering no reply.
Not only him, but the other two also felt a sense of urgency.
If someone indeed proved a series of difficult problems about prime numbers in an unprecedented way, it wouldn’t be entirely welcome news for many mathematicians who have been studying prime numbers.
After all, nobody wants to be a mere bystander—if you don’t believe it, you can ask Sam and Frank.
"No worries, let’s first inquire. I haven’t had any interactions with Qiao Yu, and abruptly sending him an email might be somewhat presumptuous. I’m counting on you, Professor Zhang."
Tao Xuanzhi contemplated for a moment and said.
Zhang Yuantang chuckled and nodded in agreement.
Presumptuousness was just an excuse; geniuses are often proud.
...
Huaxia, Yanbei University.
At this moment, Qiao Yu was indeed working on what the professors across the ocean were concerned about.
He could ignore the verification work, but certain tasks he needed to perform ahead of time.
The work Qiao Yu was engaged in at the moment was transforming a series of problems he intended to solve using the modal space framework from classical expressions to modal space expressions.
For instance, the classical expression of the twin prime conjecture is that there are infinitely many prime pairs (p, p+2), where both p and p+2 are prime numbers.
So, under the multi-modal space expression, it needed to be converted into three problems.
1. In Modal Space M, there are infinitely many pairs of modal points (r_p, r_p+2), where the modal distance d_m(r_p, r_p+2), satisfies fixed constraints.
2. The modal density function ρ_m(r) accumulates infinitely in the region of modal space satisfying the twin prime condition.
3. The distribution of twin prime pairs forms equidistant points on the modal path Γ, demonstrating periodicity and symmetry within the modal space.
Simply put, a classic number theory problem was decomposed into three geometric problems.
If he could prove these three geometric problems in modal space, it would mean he had completed the proof of the twin prime conjecture.
Of course, the premise is that his generalized modal number theory axiom system could gain widespread recognition in the mathematical community, and that it could be proven this axiom system indeed allows interconversion between geometry and number theory while maintaining verifiability at all times.