Pitch dark night.

Ameriken, Stanford University, Southern San Francisco Bay Area, California.

The second floor of an office building is also lit up.

Gray-haired Professor Brian Dweck stared at the computer screen in high spirits.

He looked up at the time, it was already more than ten o'clock in the evening, and he continued to look at the screen absently, and kept recording and calculating with his pen.

He is reviewing the paper.

As a co-editor of Computer Mathematics and Information Engineering, Brian Dweck is very conscientious, and he also enjoys reviewing papers because he always sees new developments and ideas in them.

Just like now.

"Fourier transform assists in constructing data models and algorithms for data analysis?"

"One application paper, two algorithm architecture papers?"

"Voted for three ......"

When Dweck saw the manuscript sent by the editorial department, he had a very ridiculous feeling, not only for the content of the paper, but because there were too many papers.

One Author, Three Paper Submissions!

After carefully reading the contents of the three papers, he realized why the other party submitted three papers, one of which was the application of the algorithm of the Fourier transform, which can almost be understood as 'expanding thinking and algorithm application instructions'.

The other two are analysis methods that purely use algorithms to build data models, which are real research in the field of Fourier transform application computer algorithms.

The three papers were completed together, and the content of them was linked.

"The algorithm paper was divided into two parts...... It should be too many pages. ”

Dweck took a general look at it and knew why the latter paper was split into two parts.

It is difficult to pass the review of an ordinary paper submission of more than 10 pages.

For those papers that publish dozens of pages in one go, they will first make a report on the results, and after confirming that the results are true and effective, and very meaningful, they may be invited by the corresponding journals to submit and publish all of them.

The content of the two algorithm papers in front of me has been streamlined and condensed, and it has reached 22 pages.

After reviewing the narrative paper on the application direction, Dweck immediately became interested, and he found that the author of the paper was very thoughtful, and some of the application directions in it were all unexpected, and if you think about it carefully, there is indeed a certain degree of implementability.

Then, he looked at the algorithm paper.

Paper submission is not to write all the content, even if it is a computer algorithm paper, it is only to explain the subject of the algorithm and make an introduction in the direction.

The main content of Wang Hao's paper is to apply the Fourier transform to the construction of mathematical models, as well as the methods of assisting in data analysis under the framework of mathematical models.

Even if you only introduce the general framework, the main content is very complex and not so easy to understand.

Dweck looked carefully, studied carefully, and continued to follow the calculations with his pen for three hours before he understood the process of constructing a mathematical model.

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

"This kind of algorithm can be applied to data analysis."

"The kind of analysis of very large-scale data, the more data there is, the more efficient this method will be......"

Dweck took a break and continued watching.

It took me more than an hour to read the back part of a paper, and then I looked up at the time and found that it was already early in the morning, so I didn't continue to read it, but sent a message to the editorial department, "These three papers are very meaningful." ”

"The proposal is the core of the current issue and is published together."

He made a comment in passing, "Genius idea! Genius creativity and research! ”

"It's a new way of application for Fourier transformation, which is very valuable for hyperscale data analysis, and in the future, it may even change the framework model of high-end data analysis."

Meanwhile.

Wang Hao was staying in the small library on the top floor of the laboratory building of the Faculty of Science.

This small library is only open to PhDs or faculty members, and it is full of very specialized and esoteric books.

Many books are not even translated, they are purchased directly from abroad, because ordinary people can't understand them at all, there is no market, and translation has no meaning.

Wang Hao found an all-English version of "Analysis of the Mathematical Principles of Differential Equations", sat on a chair and looked at it seriously, and it took more than two hours to look at it.

He found that the analysis of the mathematical basis was very in-depth and thorough.

Reading books can increase knowledge, but also increase inspiration.

This book made Wang Hao feel that he had gained a lot, and at the same time, the task of 'solving the common properties of specific partial differential equations' also increased the inspiration value by two points.

Two points, it's already a lot.

Partial differential equations involve a wide range of knowledge, and his research is also very difficult, which needs to demonstrate the existence, uniqueness, regularity and asymptotic properties of sigma_k, Q-curvature equations, curvature flow and Monge-Ampere equations involved in geometry......

Wait a minute.

Every bit of inspiration is valuable.

Wang Hao is not alone in the library.

Zhou Qingyuan is also there.

There are two other people I don't know, it seems that a doctoral supervisor brought a doctoral student to select books, and the sound they made was not loud, but because the library was small, some voices still reached the ears.

"Constant Variation."

"Nonhomogeneous Ordinary Differential Equations."

"Annotation."

Wang Hao captured a few key words, which should be related to the content of the doctoral dissertation, which is related to the 'constant variation method to connect with non-homogeneous ordinary differential equations'.

This mathematical topic is not very difficult, and it is suitable as a topic for doctoral dissertation.

The two were discussing.

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

Zhou Qingyuan raised his head with a smile, "You can also ask Wang Hao, he is no worse than me in differential equations." ”

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

"This is Professor Huang Pei."

After he finished speaking, he introduced a sentence to Wang Hao.

Wang Hao shouted politely, "Professor Huang." ”

"Wang Hao!"

Huang Pei smiled and nodded to Wang Hao, and then looked at the doctoral students under him, "This is Xiao Sun, Sun Jian." ”

Sun Jian smiled shyly and glanced at Wang Hao a few more times, Zhou Qingyuan is an old professor aside, he knew that Wang Hao's 'scientific research mistakes' were on the news.

In addition, Wang Hao's age is indeed very small, much younger than him.

Sun Jian still said, "I just don't understand the non-homogeneous ordinary differential equations and the general solution of the Riccati equation. ”

"It's a bit ...... around"

He said and scratched his head.

Zhou Qingyuan nodded and said a few words, "The Rikati equation, there should be no problem in solving the Rikati equation, right?" ”

"The difficulty of connecting the Ricati equation with non-homogeneous ordinary differential equations lies in the transformation and transformation......"

"There is a classical Ricati equation that can be solved using the iterative method......"

Zhou Qingyuan said a few words briefly, and then asked Wang Hao, "Do you have any research on the Ricati equation and the non-homogeneous ordinary differential equation?" ”

All three of them looked at Wang Hao.

"Nonhomogeneous equations......"

Wang Hao has the inspiration direction of 'solving one-dimensional non-homogeneous equations', and has also studied the Ricati equation, so he simply said, "The conventional and standard Ricati equation, in connection with the non-homogeneous equation, only needs to be merged and transformed normally." ”

"Our studies are generally exceptional, or those that are complex......"

He only planned to say a few words, but he found that one after another 'inspirations' kept coming to his mind.

And then just go on and on.

"The complex Ricati equation is also very complex to solve, while the non-homogeneous equation requires some other tools and other means......"

"For example, ode45, to do numerical solutions in numerical analysis, you can use the fourth-order and fifth-order Runge-Kutta algorithm......"

"Using algorithmic means and superimposing some conventional methods for solving non-homogeneous equations, you can ......"

Wang Hao said a lot in a row.

In the process of discussing, ideas kept popping up in his head, and he continued to talk about it, and he even found that he was almost complete a study on 'solving the special operation of the Ricati equation'.

The three people in the room listened very carefully, and their eyes were different.

Sun Jian's eyes were full of admiration. He didn't expect that Wang Hao would be able to talk eloquently about the solution and connection of specific equations in front of the two professors.

Moreover, the idea is clear.

Some of the content is definitely carefully thought out, and can be described as 'research', rather than knowledge that can be seen in books.

Zhou Qingyuan found that Wang Hao sometimes happened to say what he thought in his heart, and sometimes, the content of what he said was different, but it was also very meaningful.

To put it bluntly -

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

"Could it be that in the understanding of differential equations, Wang Hao has surpassed me?"

Zhou Qingyuan was very surprised.

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

After nearly 30 years of mathematical research, he thought he was already a top mathematician, but he was surpassed by a Ph.D. in his early twenties?

Huang Pei and Zhou Qingyuan's feelings are very similar.

Whenever he thought of a content, Wang Hao could easily say it, and Wang Hao could also say other questions that he hadn't thought of.

Huang Pei's face was full of shock, "This Wang Hao, it's amazing!" ”

"No wonder!"

"Even if there is a scientific research mistake and a huge loss to the project, Professor Zhou still strongly recommends that the school sign Wang Hao!"

"I see!"

"He's only in his early twenties, and he's going to be amazing in the future!"