Top Student at Their Peak

Zhang Shuwen's advantage in this area lies in his ability to maintain smoother academic-level exchanges with domestic colleagues. Of course, most of these exchanges are purely theoretical.

For example, he is not very familiar with the computational work that Qiao Yu is currently undertaking.

After more than an hour of explanation, this class is nearing its end. For the same seminar, Zhang Shuwen has prepared approximately three sessions.

It is not that three sessions will allow everyone to fully grasp the entire Generalized Modal Axiomatic System.

The reason is simply that, as a still-developing field of mathematics, the core ideas of the Generalized Modal Axiomatic System have already taken shape, but there still lacks a systematic, completely unified theoretical framework.

Furthermore, there is no corresponding textbook compiled yet. Given the depth and breadth of Zhang Shuwen's current research, the content can be covered in about five to six hours.

"...In summary, the core idea of the Generalized Modal Axiomatic System is to map number theory problems into high-dimensional geometric spaces, utilizing the structural relationship between point states and path evolution in modal space to geometrically and structurally transform abstract number theory problems for more intuitive description and quantitative analysis.

This method not only opens up new avenues for number theory research but also promises to provide new tools for classic problems like analytic number theory. Therefore, understanding the basic construction of modal space is just the first step.

To achieve mathematical descriptions and applications of more complex systems, we still need to delve deeper into how to modularize the Generalized Modal Axiomatic System to form more operational mathematical tools. This will be the main content of our next session.

If anyone has any questions about the content of this session or has ideas that need discussion, you can start asking them now."

As Zhang Shuwen's voice fell, someone quickly raised their hand in the audience.

"Go ahead." Zhang Shuwen pointed to the person in the audience who raised their hand. He recognized this young man as the graduate student of his colleague, Peter Sanak, who is currently focusing on L-functions research.

His teacher was also present, but seated in the back row.

"Professor Zhang, just now when you were discussing modal paths, the diagram you used, um, the animated diagram with the red curve in the three-dimensional space,

you mentioned in passing that there seems to be a certain connection between the symmetry of the path under certain conditions and the zeroes of the Riemann Zeta Function. I would like to know if this assessment is accurate?"

Zhang Shuwen smiled and replied, "If I could make an accurate assessment, I wouldn't have used the word 'seems,' which is rather imprecise. I can only say that related research is still at a relatively preliminary stage.

Whether there is a specific connection between the two still requires further rigorous proof. However, we have observed and derived some interesting symmetry phenomena.

To fully integrate the two, work in three directions needs to be done: first, we need to more precisely define the properties of the modal density function. Undoubtedly, the proposer of this theory has been lazy in this aspect.

Everyone who has come here today must have read Qiao Yu's paper, which is the main document we referenced today. Qiao Yu did not provide a precise description of the symmetry and local properties of the modal density function.

Secondly, we need to prove the relationship between the integral form under modal path symmetry and the analytic continuation of the Zeta Function. It must be understood that Pm is not arbitrary; it needs to satisfy specific geometric constraints. This point is also not clearly given in Qiao Yu's paper.

Of course, the most important thing is to construct a bi-directional mapping, which is also the most challenging part. From the perspective of number theory, we need to find a broader equivalence relationship between modal paths and prime number distribution.

From the geometric perspective, reanalyze the distribution of Zeta function zeroes through path symmetry or modal distance. Qiao Yu's paper has done part of the work, but it is not comprehensive.

In other words, if anyone is interested in this direction in the next steps, it is necessary to find a geometric structure in modal space whose symmetry perfectly matches the deep underlying patterns in number theory problems.

Here...well, I personally guess it might involve some kind of high-dimensional symmetry group or some special constraint conditions on a custom modal space.

As far as I know, Huaxia Yanbei University already has a team involved in this problem, including the introduction of group structure into modal space. I guess once this problem is solved, we will have more sufficient tools to peek into the truth of the Zeta function."

After answering this question, Zhang Shuwen briefly answered a few more questions before announcing the end of the class.

After all, today's content was only very basic and not in-depth. The part where the difficulty really increases will start from the modularization of the modal system, turning it into a usable mathematical tool.

While Zhang Shuwen was tidying up the teaching materials on the podium, the mentor of the student who had just asked a question, his colleague Peter Sanak, came over to the podium and asked, "In a hurry to go home? If not, how about grabbing a drink?"

Zhang Shuwen looked at Peter and smiled, "Forget the alcohol, a coffee would do."

"Haha, Zhang, drinking coffee in the evening is not a good habit, it will cause insomnia," Peter Sanak laughed.

"No, drinking coffee at night actually helps me sleep better," Zhang Shuwen shook his head and said.

"My god, hasn't your doctor told you that this means you might be allergic to caffeine?" Peter Sanak said exaggeratedly.

Zhang Shuwen laughed lightly, then sped up his actions, finished organizing the materials, and said, "Let's go."