Chapter 285: Chapter 118: Inspiration as Wonderful as a Volcano_3

Finally waiting for this sentence, Pan Jingyuan pulled out a printed document from the materials he carried with him and handed it to Danis.

This was something he had prepared specifically.

In fact, it was just a translated version of the report that Yuan Zhengxin forwarded to him, supplemented with some additional content, mainly including Qiao Yu’s usual skepticism about the rigor of the paper during their WeChat exchanges.

Danis glanced at Pan Jingyuan, then took the printed sheet, and instead of continuing to walk, stood there reading it.

The doubts Qiao Yu raised lacked concrete examples, so it was not long, but Danis read it very carefully. They stood there for about five minutes before Danis looked up from the document.

After handing the printout back to Pan Jingyuan, Danis slowly said, “If these are indeed questions that a sixteen-year-old came up with after studying the paper and thinking, I have to say he is gifted beyond measure.”

Pan Jingyuan nodded and replied, “In fact, he is indeed exceptionally gifted. You can tell just from his paper. It’s said that from the time he decided to independently use the theory of quasi-complete spaces to study the upper bound of rational points of curves, to writing that paper, it took only about twenty days.

What’s even more astonishing is that he had been exposed to Professor Schulz’s mathematical ideas and a series of tools for just over a month. It’s said that he started studying Schulz’s papers because of a recommendation from another teacher.”

Danis nodded, and if the genius Pan Jingyuan spoke of had questioned a different proposition, he might have been more interested in chatting with Pan about that Qiao Yu.

But the doubts were precisely about their topic.

Danis shook his head and said, “The questions he raised are indeed very interesting. We all know how important structural consistency is to the conclusions we provide. This is indeed a hard-to-refute skepticism, but it’s not based on the rigor of the proof itself.

The interaction among multiple papers does increase the complexity of verification. Demonstrating that the systematic analytical tools we use throughout the proof process can ensure the strict consistency of the designed geometric objects, algebraic structures, and related properties is a very complex and immense task.

But frankly, I can somewhat understand how you feel. His questions even make me feel a bit uneasy. But you see, he hasn’t been able to find a counterexample yet. This at least indicates that our argument is rigorous, or at least relatively rigorous, as counterexamples are not so easily found.”

Pan Jingyuan smiled wryly and nodded, then asked softly, “What if he finds one? Perhaps at some point in the future.”

Danis let out a long breath, shrugged, and said, “Then we can only revisit the issue and re-examine the proof process of the paper. That would mean our work has to continue.

Otherwise, what choice do we have? At least I won’t give up on this proposition. It would just be a matter of addressing the opponent’s proposed counterexamples, which I’m certain won’t be harder than starting from scratch! Wouldn’t you agree, Pan?”

Pan Jingyuan rather liked Professor Dennis’s openness, which was probably one of the reasons he was determined to choose Danis as his mentor back then, so he nodded and said, “Understood, I will continue as well.

Oh, by the way, the two best universities in Huaxia have organized a series of seminars specifically on the Geometric Langlands Conjecture. I’ll attend this conference too after I return home in a couple of days. I guess Qiao Yu might also bring up his questions at the meeting. Is there anything you’d like me to convey to him?”

Danis pondered for a moment and replied, “I was going to let you give him my email so that we could communicate directly, which might be very interesting. But considering that I’m still reviewing his paper, this isn’t the right time to do so; let’s wait until the final review opinion of his paper comes out.

But if there’s any fresh perspective at this conference, please email me at any time. Certainly, if that Qiao Yu really, as he imagines, finds a counterexample, you can call me directly. Although I think the possibility should be small. And of course, I’m not just referring to the seminar period.”

Pan Jingyuan nodded and agreed.

“Do you know why I added the last sentence? Because people like Schulz often have a terrifying mathematical intuition, especially when they are not deeply involved in mathematical research. How to put it, young people are always adept at creating mathematical miracles, which is also why I enjoy mentoring students.”

Danis explained a bit, then raised his hand and patted Pan Jingyuan on the shoulder, jokingly saying:

“Alright, let’s go eat now. Don’t look so worried. I think you should be happy that there’s another math genius in Huaxia. Even if you feel uneasy, I think it should be Schulz, because his unique genius position is being challenged.”

Hearing this, Pan Jingyuan also smiled, but then felt a tinge of bitterness in his heart.

Indeed, his mentor was a second-generation rich kid, without the need to rely on the salary of a professor for a living, and pursued mathematics purely out of interest, so he viewed fame and fortune more lightly than others.

But to be honest, Pan Jingyuan still aspired to win an award in the international mathematical community.

In a way, people like Schulz and Qiao Yu, who are naturally gifted, are the arch-rivals of mathematicians worldwide. Others’ lifelong efforts might not compare to a few months of their research.