Chapter 10: This Wang Hao, Impressive Indeed!

Here's the translation:

"In the pitch-black night.

Amherican, California, southern San Francisco Bay Area, Stanford University.

A second-floor office still lit up.

Professor Brian DeWitt, with his hair turning white, stared at the computer screen with great vigor.

He glanced at the time, already past ten in the evening, continuing to look at the screen without care, jotting down notes and calculations with his pen.

He was reviewing papers.

As a collaborating review editor for "Computer Mathematics and Information Engineering," Brian DeWitt was highly diligent in his work. He also enjoyed reviewing papers because he often encountered novel research and ideas within them.

Just like now.

"Algorithm Assisted Structural Data Modeling with Fourier Transform and Its Application in Data Analysis."

"One application paper, two algorithm structure papers."

"Submitted three papers..."

When DeWitt received the manuscripts from the editorial office, he felt a sense of absurdity, not directed at the content of the papers, but rather due to their sheer number.

One author, three submissions!

After carefully reading the content of the three papers, he understood why the author had submitted three papers. One of the papers dealt with the application of the Fourier transform algorithm, which could be understood as 'expanding thinking and explaining algorithm applications.'

The other two were purely algorithmically building data model analysis methods, genuine research in the field of Fourier transform application in computer algorithm research.

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

"The algorithm papers were divided into two... probably because they were too lengthy."

After a general overview, DeWitt understood the reason for dividing the papers into two parts.

Regular paper submissions rarely exceeded ten pages.

Those papers with dozens of pages were usually first submitted as research reports, ensuring the validity and significance of the findings. They might then be invited by corresponding journals for submission and eventual publication.

The contents of the two algorithm papers had been trimmed down to twenty-two pages.

After reviewing the applied direction paper, DeWitt became interested. He found the author's ideas very innovative. Some of the applied directions mentioned were things he had never even considered before, and upon closer examination, they seemed quite feasible.

Then, he began to read the algorithm papers.

Paper submissions did not entail including all the content. Even for computer algorithm papers, it was merely an overview of the main algorithm, with a brief introduction.

The papers submitted by Wang Hao mainly focused on applying the Fourier transform to construct mathematical models and methods to assist in data analysis.

Even though only the general framework was described, the core content was still very complex and not easy to understand.

DeWitt carefully studied and analyzed for over three hours, continuously taking notes and calculations. It took him three hours to understand the process of constructing mathematical models.

He made himself a cup of coffee, took a short break, and then returned to the screen, unable to help but exclaim, "Such a genius!"

"This algorithm can be applied to data analysis."

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

After a short rest, DeWitt continued to read.

After over an hour, he finished reading the remainder of one paper. Then, he looked at the time and realized it was already early morning. He did not continue but instead sent a message to the editorial office, "These three papers are very meaningful."

"I suggest they be published together in the current issue."

He also added a comment, "Genius ideas! Genius creativity and research!"

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

Meanwhile.

Wang Hao was in the small library on the top floor of the College of Science.

This library was only open to doctoral students or faculty members and contained very specialized and esoteric books.

Many of the books were not even translated, as they were too difficult for ordinary people to understand, making translation meaningless.

Wang Hao found an all-English version of "Mathematical Principles of Differential Equations" and sat down to read it earnestly. He spent more than two hours engrossed in it.

He discovered that the book's analytical treatment of mathematical fundamentals was profound and thorough.

Reading not only increased knowledge but also increased inspiration value.

This book gave Wang Hao a lot of insights. Simultaneously, the "Specific Generalized Solutions of Partial Differential Equations" task also increased by two points in inspiration value.

Two points were already a lot. The knowledge range involved in partial differential equations was very broad, and his research was among the most difficult. It involved proving the existence, uniqueness, regularity, and asymptotic properties of the geometrically involved sigma_k, q-curvature equations, curvature flow, and Monge-Ampere type equations, among others."

Every point of growth in inspiration is extremely valuable.

There is not only Wang Hao in the library.

Zhou Qingyuan is also there.

There are two other unfamiliar people, apparently a doctoral supervisor with a doctoral student selecting books. Although their voices are not loud, because the library is small, some sound still reaches the ears.

"Constant change method."

"Inhomogeneous ordinary differential equations."

"Annotation."

Wang Hao captured several keywords, which should be related to the content of doctoral dissertations, and it is related to the connection between the 'constant change method and inhomogeneous ordinary differential equations'.

This mathematical topic is not difficult and is suitable as a topic for doctoral dissertations.

The two were discussing.

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

Zhou Qingyuan smiled and raised his head, "You can also ask Wang Hao. He is not worse than me in differential equations."

Although this is an affirmation of Wang Hao, it is obviously a modest statement.

"This is Professor Huang Pei."

After introducing him, Wang Hao politely called out, "Professor Huang."

"Wang Hao!"

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

Sun Jian smiled shyly and glanced at Wang Hao more. Zhou Qingyuan didn't mention that he was an old professor for the time being, but he knew that Wang Hao's 'research mistake' had made the news.

In addition, Wang Hao is indeed very young, much younger than him.

Sun Jian started to speak, "I always have trouble understanding the connection between inhomogeneous ordinary differential equations and the general solution of the Riccati equation."

"It's a bit confusing..."

He scratched his head as he spoke.

Zhou Qingyuan nodded and said a few words, "The Riccati equation, ah, there should be no problem with solving the Riccati equation."

"The difficulty in connecting the Riccati equation with inhomogeneous ordinary differential equations lies in transformation and conversion..."

"There is a classic Riccati equation that can be solved using iterative methods..."

Zhou Qingyuan briefly said a few words, then asked Wang Hao, "Do you have any research on the Riccati equation and inhomogeneous ordinary differential equations?"

All three looked at Wang Hao.

"Inhomogeneous equations..."

Wang Hao did have a direction for 'solving one-dimensional inhomogeneous equations', and he had also studied the Riccati equation. So he simply said, "For ordinary, standard Riccati equations, connected with inhomogeneous equations, you only need to merge and transform normally."

"Our research is usually special cases, or those that are complicated..."

He only intended to say a few words, but then he found that one idea after another was emerging in his mind.

Then he continued speaking along that line.

"Complex Riccati equations are also very complicated to solve, and inhomogeneous equations require some other tools, other methods..."

"For example, ode45, in numerical analysis for numerical solution, you can use the fourth-order fifth-level Runge-Kutta algorithm..."

"By using algorithmic methods and superimposing some conventional solution methods for inhomogeneous equations, you can..."

Wang Hao spoke continuously.

During the discussion, ideas kept emerging in his mind. After organizing them, he continued speaking, and he even found that he was almost completing a study on 'special operations to solve Riccati equations'.

All three in the room were listening very seriously, and their looks were different.

Sun Jian's gaze was full of admiration. He didn't expect Wang Hao to talk confidently about solving specific equations in front of two professors.

Moreover, his thinking was clear.

Some of the content was definitely carefully considered and could be described as 'research', rather than knowledge found in books.

Zhou Qingyuan found that sometimes Wang Hao happened to say what he was thinking, and sometimes the content was different but equally meaningful.

In blunt terms—

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

"Could it be that Wang Hao has already surpassed me in understanding differential equations?"

Zhou Qingyuan was very surprised.

He has always known that Wang Hao is very talented, but even geniuses need to grow.

Having been engaged in mathematical research for nearly thirty years, he considered himself a top mathematician, but he was surpassed by a doctoral graduate in his early twenties.

Huang Pei and Zhou Qingyuan had similar feelings.

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

Huang Pei's face was filled with astonishment, "This Wang Hao is remarkable!"

"No wonder!"

"Even if he made a research mistake and caused huge losses to the project, Professor Zhou still strongly recommends the school to sign Wang Hao!"

"So that's it!"

"He's only in his early twenties. He's going to be incredible in the future!"