CHAPTER 481: CHAPTER 155 UNDER THE SPOTLIGHT

Scientists, or the highly educated demographic, are a very special group. They may not have a lot of wealth, but to some extent, much of society’s wealth growth is built on their efforts.

If you must make an analogy, they are like the engine of social wealth growth, doing the hardest work in fields invisible to the public.

It’s like how after a normal family buys a car, besides maintenance or repair, no one would purposely open the hood every day to check the engine.

Yes, everyone knows the engine is important, but when there’s nothing wrong, no one bothers to look at it.

Because most ordinary people do not know how the engine works or understand its principle. They only need to know that it still works and hasn’t broken down.

Mathematicians are like the engine of the academic world, doing the hardest and most tiring work, yet public awareness of mathematics is mostly limited to whether there are any handy tools to use.

Even when applying for research funding, the funds for mathematical research are often less than those for other sciences.

Things like physics and chemistry, as the latter require various experiments. Lab investments and various instruments require money...

So in a sense, the spotlight moments for mathematicians are actually quite rare.

Only a few can create the ultimate romance with just a pen and paper.

The vast majority can achieve something by making improvements on others’ research results.

Yes, Chen Zhuoyang has no need to feel ashamed.

Because the nature of mathematical research dictates that major breakthroughs are not common.

Ninety percent of mathematicians’ work is refining existing theories or solving local problems, not that these seemingly insignificant results are unimportant.

Because this accumulation might someday spark a genius inspiration.

For various reasons, for most mathematicians, being able to present for sixty minutes at a significant conference is already a highlight of their lives.

After all, this is not a subgroup session, and the given time is quite long. Moreover, there are many people present today, seemingly even more than the last World Algebraic Geometry Conference.

Fortunately, Qiao Yu is already accustomed to being a thought leader among the crowd.

"Prime number distribution is one of the core issues in number theory, and the gap problem has always been an unsolved mathematical challenge. In actual research, mathematicians have proven that the upper limit of prime number gaps can be restricted to a specific range.

Professor Zhang Yuantang’s pioneering work lowered this gap upper bound to 70 million and, with the efforts of mathematicians worldwide, decreased it to 246. Today, what I will report on is a new geometric method derived from the generalized modal number theory axiom system to solve related problems.

By mapping prime number distribution to modal space and utilizing modal density functions, modal paths, and modal convolutions, we have proven that the bounded distance between prime numbers can be further reduced to an upper bound of 6..."

The beginning is a simple introduction.

First, I must let everyone know how this work unfolded. Without Lott Degen’s cooperation, this part would be very troublesome.

Because the summary "derived a new geometric method according to the generalized modal number theory axiom system" could confuse countless people in the audience.

But now, without saying it all, at least more than eighty percent of the attendees would not be confused.

Since it was published yesterday at noon in Ann.Math, the well-prepared organizers have already begun to act.

Over two thousand printed papers were distributed by the session hosts before dinner through each sub-session.

Ensuring that every registered member of the Mathematics Society has a copy. Those with no interest in the topic give the paper directly to interested parties.

Some even borrowed the paper to print a copy.

Hotels hosting such academic conferences thoughtfully arrange for printing services. If internal resources are overwhelmed, there are dedicated people who deliver outside for printing.

Although a night’s time might not be enough for all attendees to fully understand the paper, at least most people have a rough concept and preliminary understanding.

Simultaneously, a sixty-minute duration, for a top-tier conference academic report, is already the longest time, but it still isn’t enough for Qiao Yu to popularize the generalized modal space framework to everyone. So, after briefly discussing the abstract, Qiao Yu directly got to the point.

"...The modal path Γ∗ is a continuous curve in modal space, used to describe the distribution trajectory of prime numbers in geometric space. To reduce the modal point distance, the following optimizations to the path are needed:

As everyone can see from the formula on the big screen, where T is the path period, used to ensure the periodic repetition structure of the path in modal space."

"From the above, it can be seen that the curvature and distribution of path Γk are driven by the local high-value regions of the modal density function ρM(r), Γk passes through the local extreme points of the modal density function, ensuring path coverage of high-density areas.

Modal paths have geometric symmetry, assuming a symmetric mapping ϕ:M→M, satisfying:

Through the above optimization construction, the high-density, periodicity, and symmetry of the modal path Γ∗ can be ensured..."

...

"Did you understand?" Zhang Yuanling, who was lost in thought, was interrupted by Shen Chongxing beside her.