Chapter 10

The pitch-black night.

In America, California, in the southern part of the San Francisco Bay Area, at Stanford University.

The lights were still on in a second-floor office building.

Professor Brian DeVic, with his graying hair, stared intently at the computer screen, full of energy.

He glanced at the time; it was already past ten in the evening. He paid no attention and continued to look at the screen, constantly taking notes and doing calculations.

He was reviewing a paper.

As a co-editor of "Computational Mathematics and Information Engineering," Brian DeVic was very conscientious and responsible. He also enjoyed the work of reviewing papers because he could always find some novel research and ideas in them.

Just like now.

"Fourier transform auxiliary framework data model, and an algorithm for data analysis?"

"A practical paper, two algorithm framework papers?"

"Three submissions..."

When DeVic saw the manuscripts sent by the editorial department, he felt a sense of absurdity, not because of the content of the papers, but because of the sheer number of them.

One author, three paper submissions!

After carefully reading the three papers, he understood why the author had submitted three manuscripts. One of the papers was about the application of Fourier transform algorithms, which could be understood as an "expansion of thinking and algorithm application explanation."

The other two were purely about the analysis methods of constructing data models using algorithms, solid research in the field of Fourier transform application to computer algorithms.

The three papers were completed together, and their contents were interconnected.

"The algorithm papers are split into two... probably because of the page count."

DeVic took a general look and understood why the later papers were split.

For ordinary paper submissions, it was already very difficult to pass the review if they were more than ten pages.

Those papers that published dozens of pages at once were usually first presented as research reports, confirming the authenticity and significance of the results, and then might be invited by the corresponding journal to submit and publish all of them.

The two algorithm papers in front of him, even after being simplified, still reached twenty-two pages.

After reviewing the narrative paper on the application, DeVic became very interested. He found that the author had very innovative ideas, and some of the application directions were things he had never thought of, but upon careful consideration, they did have a certain feasibility.

Then, he started reading the algorithm papers.

Paper submissions did not include all the content, even for computer algorithm papers, they only explained the main algorithm and introduced the direction.

The main content of the paper submitted by Wang Hao was the application of Fourier transform to construct mathematical models and the method of using these models to assist in data analysis.

Even just introducing the general framework, the main content was very complex and not easy to understand.

DeVic read carefully, studied meticulously, and continuously followed the calculations with a pen. It took him three hours to understand the process of constructing the mathematical model.

He made a cup of coffee, took a short break, and then returned to the screen, couldn't help but exclaim, "What a genius!"

"This algorithm can be applied to data analysis."

"For large-scale data analysis, the more data, the more efficient this method becomes..."

After resting for a while, he continued reading.

It took him more than an hour to finish the latter part of the paper. He then looked at the time and realized it was already midnight. He didn't continue reading but sent a message to the editorial department, "These three papers are very meaningful."

"I suggest they be published as the core of the current issue."

He added a comment, "A genius idea! A genius's creativity and research!"

"It is a brand new application of Fourier transform, very valuable for large-scale data analysis. In the future, it might even change the framework of high-end data analysis—"

At the same time.

Wang Hao was in a small library on the top floor of the science building.

This small library was only open to doctoral students or faculty members, and it contained very specialized and profound books.

Many of the books were not even translated, directly purchased from abroad, because ordinary people couldn't understand them, and there was no market for them, so translation was meaningless.

Wang Hao found an English version of "Mathematical Principles of Differential Equations" and sat down to read it seriously, reading for more than two hours.

He found that the book provided a very deep and thorough analysis of the basics of mathematics.

Reading books could increase knowledge, and similarly, it could also increase inspiration points.

This book made Wang Hao feel that he had gained a lot, and the inspiration points for the task "General Solution of Specific Partial Differential Equations" increased by two points.

Two points were already a lot.

Partial differential equations involved a wide range of knowledge, and his research was also very challenging, requiring the proof of sigma_k, Q-curvature equations, curvature flow, and Monge-Ampere type equations, and their existence, uniqueness, regularity, and asymptotic behavior...

And so on.

Every point of inspiration was very valuable.

Wang Hao was not the only one in the library.

Zhou Qingsheng was also there.

There were two others he didn't recognize, seemingly a doctoral supervisor and a doctoral student, browsing books. They didn't make much noise, but because the library was small, some sounds still reached his ears.

"Variation of parameters."

"Non-homogeneous ordinary differential equations."

"Annotations."

Wang Hao caught a few keywords, which, when connected, seemed to be about a doctoral thesis, related to "the variation of parameters method for non-homogeneous ordinary differential equations."

This mathematical topic was not very difficult and was suitable as a doctoral thesis topic.

The two were discussing.

The doctoral supervisor suddenly said, "Professor Zhou is here, an expert in differential equations. If you have any questions, you can ask Professor Zhou."

Zhou Qingsheng smiled and lifted his head, "You can also ask Wang Hao. He is as good as I am in differential equations."

Although it was a compliment to Wang Hao, it was clearly a modest statement.

"This is Professor Huang."

He introduced Wang Hao to him.

Wang Hao politely greeted, "Professor Huang."

"Wang Hao!"

Huang Pei smiled and nodded at Wang Hao, then looked at his doctoral student, "This is Xiao Sun, Sun Jian."

Sun Jian smiled shyly and glanced at Wang Hao a few times. Zhou Qingsheng was an old professor, but he knew about Wang Hao's "research error" that made the news.

Moreover, Wang Hao was indeed very young, much younger than him.

Sun Jian still spoke up, "I'm having trouble understanding the connection between non-homogeneous ordinary differential equations and the general solution of Riccati equations."

"It's a bit confusing..."

He scratched his head as he spoke.

Zhou Qingsheng nodded and said a few words, "Riccati equations, right? There shouldn't be any problem with solving Riccati equations, right?"

"The difficulty in connecting Riccati equations with non-homogeneous ordinary differential equations lies in the transformation and conversion..."

"There's a classic Riccati equation that can be solved using an iterative method..."

Zhou Qingsheng briefly explained and then asked Wang Hao, "Do you have any research on Riccati equations and non-homogeneous ordinary differential equations?"

The three of them looked at Wang Hao.

"Non-homogeneous equations..."

Wang Hao had an "inspiration direction" for solving one-dimensional non-homogeneous equations and had studied Riccati equations, so he spoke up, "For standard Riccati equations connected to non-homogeneous equations, you just need to normally combine and transform them."

"Our research is usually about special cases or more complex ones..."

He only intended to say a few words, but then he found that a series of "inspirations" kept emerging in his mind.

So he continued.

"Complex Riccati equations are also very complex to solve, and non-homogeneous equations require some other tools and methods..."

"For example, ode45, which uses the fourth-order fifth-stage Runge-Kutta algorithm for numerical solutions in numerical analysis..."

"By combining algorithmic methods with conventional solutions for non-homogeneous equations, you can..."

Wang Hao spoke a lot.

As he explained, ideas kept emerging in his mind, and he continued. He even found that he was almost completing a study on "special computational solutions for Riccati equations."

The three people in the room listened very attentively, and their gazes were different.

Sun Jian looked at Wang Hao with admiration. He didn't expect Wang Hao to be able to discuss the solution and connection of specific equations so confidently in front of two professors.

Moreover, his thoughts were clear.

Some of the content was definitely well-thought-out and could be described as "research," not just knowledge from books.

Zhou Qingsheng found that Wang Hao sometimes said exactly what he was thinking, and sometimes said something different but equally meaningful.

To put it bluntly—

What he thought of, Wang Hao also thought of; what he didn't think of, Wang Hao still thought of.

"Has Wang Hao's understanding of differential equations already surpassed mine?"

Zhou Qingsheng was very surprised.

He had always known that Wang Hao was excellent, but even geniuses need to grow.

After nearly thirty years of mathematical research, he considered himself a top mathematician, but now he was being surpassed by a doctoral graduate in his early twenties?

Huang Pei had a similar feeling to Zhou Qingsheng.

Whenever he thought of something, Wang Hao could easily say it, and Wang Hao could also mention other things he hadn't thought of.

Huang Pei's face was full of shock, "This Wang Hao is extraordinary!"

"No wonder!"

"Even with a research error that caused significant losses to the project, Professor Zhou still strongly recommended that the school sign Wang Hao!"

"Indeed!"

"He's only in his early twenties, and he will be extraordinary in the future!"