Top Student at Their Peak Chapter 449: 148 This Isn't Paranoia, It's Confidence

Chapter 449: Chapter 148 This Isn’t Paranoia, It’s Confidence

At the University of California, Los Angeles, Tao Xuanzhi is hosting three mathematicians from Massachusetts and Oxford University: Harvey Gus, Jas Maynard, and Zhang Yuantang.

It’s evident that these three guests are prominent figures in academia.

Especially Jas Maynard, who recently won the Fields dal three years ago for his contributions to analytic number theory, particularly his research on pri numbers.

Moreover, Tao Xuanzhi was also one of the youngest Fields dal winners ever, and if it weren’t for Peter Schultz, he would still be the youngest Fields dal recipient.

Thus, this eting is high-profile, with at least two Fields dal winners present.

The reason for today’s gathering of the four is the recent pre-release of a paper by Harvey Gus and Jas Maynard titled, “New Progress in Large Value Estimates of Dirichlet Polynomials.”

According to Tao Xuanzhi, this paper represents a significant breakthrough in the field of analytic number theory and makes substantial progress along the long path to proving the Riemann Conjecture.

More importantly, Tao Xuanzhi believes this is the first substantial breakthrough on the Riemann Conjecture problem in decades, providing new tools and perspectives for its study.

Undoubtedly, this is a very high evaluation, even though the paper is still under peer review. As a result, both authors were invited to discuss it.

Zhang Yuantang’s presence is due to his achievents and stature in pri number research. Discussions among mathematicians of this caliber have always been happening in smaller circles. After all, eting in person is relatively convenient.

The four of them just experienced a brainstorming session for over three hours, primarily with Tao Xuanzhi and Zhang Yuantang raising questions, followed by explanations or even revisions from the two authors.

For instance, in sections 7 and 8, on page 63, an equation that previously didn’t exist was cited, Lemma 12.3 was missing a reference, a suddenly appearing function lacked a definition in the paper, and a certain step was missing a valid justification…

Alright, so of these problems seem ludicrous, but anyone who has written a paper on a computer knows that so small flaws are hard to avoid.

As long as they are not logic-level mistakes, many errors are hard to avoid, especially in number theory papers, which often require repeated revisions due to the authors’ state at the ti, making it normal to miss a few formulas.

This is also why many paper reviewers often have back-and-forth interactions with the authors, mostly because of the rigorousness inherent in the scientific paradigm.

Especially in mathematics, generally pointing out flaws in key steps of the paper counts as a challenge. Identifying such minor issues is more of a discussion.

Just like when Wiles was proving Fermat’s Last Theorem, the editorial office arranged for six reviewers, who found nurous issues during the review process. Fortunately, most were small issues Wiles could quickly clarify; if he couldn’t, they would be major problems.

The sa was true when Perelman proved the Poincaré Conjecture; it had many issues when first released, with so feeling it wasn’t explained clearly and needed more detailed proofs, which later led to so controversies.

In short, theoretical mathematics is like this; it is one of the reasons it demands exceptionally high talent.

Mathematics allows mathematicians to disregard real-world constraints, freely define anything, and build theories from any starting point as long as they are logically consistent.

However, it simultaneously demands an extrely high level of rigor in the proof process. Any slight logical contradiction or omission can potentially overturn an entire theory.

…

“Speaking of new tools and fraworks, one has to ntion Qiao Yu. By the way, you all should know Qiao Yu, right?”

After discussing serious academic topics, Zhang Yuantang shifted the topic towards Qiao Yu.

The other three prominent figures nodded simultaneously.

Editions of Tao Xuanzhi receiving a Ph.D. from Princeton University at the age of 21 are widely known to anyone familiar with Princeton University’s graduation standards and how challenging it is.

The key is that Tao Xuanzhi’s talent has never been limited to one specific direction.

He has conducted top-tier research in harmonic analysis, partial differential equations, combinatorial mathematics, analytic number theory, and representation theory, demonstrating mastery across more than a dozen fields of mathematics.

By age 31, when he received the Fields dal, he had already published over eighty highly influential papers across major mathematical journals.

Among these, the most important was proving the Green-Tao theorem, which laid a new path for research on the Twin Pri Conjecture.

In a sense, Tao Xuanzhi, Peter Schultz, and Qiao Yu are the kind of first-tier geniuses who exhibited mathematical talent from a young age, naturally attracting attention.

“Of course, Peter Schultz even emailed , specifically ntioning Qiao Yu. He holds this young man in high regard. I’ve read his papers, and how should I put it… he is the most ticulous young mathematician I have ever seen.”

Tao Xuanzhi remarked.

Upon hearing this evaluation, the other two mathematicians nodded as well. Actually, this nod didn’t signify agreent but was more a sign of respect for the evaluation.

Zhang Yuantang smiled and said: “It’s not just about rigor; more importantly, his ideas are incredibly imaginative. Really, as I was saying earlier, he proposed an entirely new frawork.

If he succeeds, he will not only integrate the existing tools of number theory but also perfectly combine number theory problems with geotry. Most importantly, after reviewing his ideas, I believe he stands a good chance of succeeding.”