Put to Use

Lu Guozhen gave Shen Qi a few crumpled and tattered pieces of paper, which naturally possessed the characteristics of archaeological artifacts without any special treatment.

There were two kinds of handwriting on the paper. One was extremely messy handwriting, so ugly it looked like a dog had chewed on it.

Another type of handwriting was in regular script, strong and powerful. Shen Qi recognized this handwriting; Lu Guozhen's handwriting was very beautiful.

The majority of the text was written in mathematical language, describing an algorithm. Although the logic was confusing, Shen Qi roughly understood it, which was a bounded Harmonic Analysis problem based on Fourier multipliers and Fourier integral operators.

The handwriting was ugly and the language was illogical, making it impossible for most people to understand the writer's original intention. Shen Qi was able to understand it because of two reasons: first, his exceptional mathematical comprehension, and second, the crucial role played by Lu Guozhen's annotations.

Lu Guozhen marked an "X" in red pen on a certain page, with the annotation. "Incorrect use of Lebesgue space theory, correct!"

Lebesgue, as we know him, is a mathematician whose name is often used when citing names or theorems and formulas in academic papers. This practice is also followed in Chinese versions of academic papers.

On another page, Lu Guozhen drew a strikethrough and commented. "The complex-valued rapid descent of the Schwartz function space needs to be used here, correct!"

There are twelve similar annotations, which can be summarized as follows: the writer was criticized by Lu Guozhen as utterly worthless.

Shen Qi learned from Lu Guozhen that the person who wrote the dog-chewed characters was a graduate student. He had studied at the School of Mathematics Computer Science of Anhui Normal University for his undergraduate degree, and then took the postgraduate entrance examination and was admitted to the Big Mathematics Department of Yanshan University, where he worked on a research project with Lu Guozhen.

After working with Lu Guozhen for less than half a year, this graduate student changed his major and went to the School of Environmental Science and Engineering.

These few pages became an unfinished project, and Shen Qi needed to continue with the work to complete it.

The workload was enormous. Lu Guozhen had essentially rejected all of Shen Qi's graduate student's arguments, meaning Shen Qi had to rewrite a paper.

Lu Guozhen chose a title for his thesis: "Analysis of Strong Singular Integral Operator Along Homogeneous Curves".

Shen Qi could adjust the title of his paper appropriately based on his actual arguments, as Lu Guozhen suggested.

However, the scope of the discussion should not change too much; the main problem to be solved is the boundedness of the singular integral operator in the generalized amplitude modulation space.

Lu Guozhen's twelve annotations became Shen Qi's only valuable clue. He will expand and extend the discussion around the central idea of the project, strive to write a high-quality mathematical paper, complete the project, and obtain 15 math credits ahead of schedule.

"This topic is very challenging."

Shen Qi took the few pages of paper back to his dormitory, and after his refinement, he finally condensed them into half a page.

This half-page contains the core logical structure of Shen Qi's paper, which only he himself can understand, and it is written in his notebook.

The topic given by Lu Guozhen can indeed be categorized under Mathematical Analysis, but the analytical methods will be particularly complex.

A few months ago, Sun Erxiong actually gave Shen Qi five research topics, five thesis topics derived from Problem 36 of Advanced Algebra.

In comparison, Shen Qi found that Professor Lu's "Analysis of Strong Singular Integral Operator along Homogeneous Curves" was even more difficult than the most difficult topic given by Professor Sun.

Rise to the challenge!

Shen Qi began researching materials; he needed to do a lot of preparatory work before writing this new paper.

The data sources are SCI and arXiv. The more in-depth the research and the more international the researchers become, the harder it is to find valuable Chinese materials. More than 90% of Shen Qi's materials are in English.

In order to better integrate into the process of globalization, Shen Qi upgraded his English to Level 4.

Mathematics Level 7 (288/250,000)

Physics Level 5 (40/50,000)

Physical Education Level 4 (18/10000)

English Level 4 (0/10000)

Chinese Language Level 3 (298/5000)

Chemistry Level 3 (104/5000)

Biology Level 3 (101/5000)

History Level 2 (111/3000)

Geography Level 2 (219/3000)

Political Level 2 (498/3000)

Remaining Academic Points: 90789

Upgrading my English to Level 4 only cost me a little over 4,000 academic points, which is a very small investment.

The main focus remains on mathematics, with an upgrade to the elite level (Level 8) requiring an investment of up to 250,000 academic points.

"I'm still short nearly 160,000 academic points. Where can I get them? By the way, will the five papers I've already published be enough to earn 160,000 academic points?"

Based on his experience, Shen Qi knew that he could only receive the academic excellence points as a reward from the system after his paper was officially published.

Just wait and see, what can we do?

But one thing is certain: the higher the quality of the paper, the more prestigious the journal in which it is published, the more outstanding the achievement, and the more academic points a top student will receive.

Is it about quantity or quality of papers?

This is a problem.

The best-case scenario is to publish a large number of high-quality papers. In the first quarter, publish three to five in the * Annals of Mathematics *; in the second quarter, publish seven or eight in *Acta Mathematica Journal of Mathematics *; and in the third and fourth quarters, shift your focus to *Inv- Inventiones Mathematicae * and JAMS. Achieving dozens of publications annually in the four major international Journal of the American Mathematical Society journals would likely generate an annual income of millions, even tens of millions, of academic credits.

Keep striving towards this goal, young man!

Shen Qi set a small goal and then threw himself into the battle.

First, complete the mathematical analysis project assigned by Professor Lu.

Collecting references is a time-consuming task, and the collection path reflects the core thinking of a paper author.

Casting a wide net and downloading whatever comes to mind indicates that the paper's author is completely clueless and lacks a clear direction.

Never mind, I'll just start writing. I'll write as I go, with a Mac in my left hand, a tablet in my right, and a Wi-Fi hotspot at my feet. I'm writing my paper while simultaneously researching. It's a very amateurish approach; I seem busy as a dog, but in reality, it's incredibly inefficient.

Shen Qi is, after all, a professional with a Level 7 math certificate; he can't be so amateurish. His direction is clear: three keywords—strong singular integrals, amplitude-modulated spaces, and homogeneous curves—and searching for information in these directions is the right thing to do.

With the direction for reference collection determined, the rest is just a matter of time.

"JKFalls, who is this guy? Oh, from Princeton. His doctoral dissertation is pretty good. I'll save it."

"T. Nakata, is he a Japanese guy, from the Todai? Only one formula in his entire paper works. I'll save it for later. I can directly use this formula and prove it myself, which will take at least a month."

"Gong, CW, this is my senior from MIT, that's right, it's my senior, Gong Changwei. This paper... I'll save it for now. Senior Gong specializes in number theory. I'm saving it out of friendship, you might need it later."

"SWHawking, Cambridge University, the author of this paper is... Stephen Hawking!"

As Shen Qi searched, he came across a mathematics paper written by Hawking.

Hawking was a physicist and mathematician. This mathematical paper he wrote was included in the British Mathematical Abstracts in 1987, the year before the publication of A A Brief History of Time.

During that period, Hawking could only move two fingers with difficulty, and he communicated with his assistants using a speech synthesizer.

Hawking's assistant was a learned person who understood Hawking very well.

The drafting of Hawking's papers and popular science books after his illness was mainly done by his assistants. Hawking provided the core ideas, which were then transmitted to his academic assistants through a speech synthesizer. There might be more than one assistant; it could be a team.

"The Chinese translation of Hawking's mathematical paper should be something like, 'Boundedness of the Commutator of the Riesz potential operator Related to the Schrödinger Operator'? Hawking is truly a master; even the title of his paper is breathtakingly complex."

Shen Qi collected Hawking's mathematical paper. Hawking's mathematical foundation was also solid; he used mathematics as his sole tool to describe the universe, time, and physics.

Not out of friendship, Shen Qi astutely discovered that Hawking's 1987 mathematical paper, based on the Schrödinger operator and the Riesz potential operator, contained at least one proof that could be cited in his new paper.

Shen Qi understood Hawking's proof, but it took a lot of brainpower to figure it out.

Shen Qi couldn't understand the remaining important proof and the core formula.

If you don't understand it, you can't quote it; otherwise, you'll make a fool of yourself.

This also verifies Professor Shing-Tung Yau's view. "Good mathematical papers are inevitably cited very little because most people cannot understand them. Therefore, the impact factor (IF) of mathematics journals is generally low."

Regardless, Shen Qi at least understood a mathematical proof that Hawking had made at the peak of his academic career, demonstrating a comprehension ability superior to most of his peers.

Good papers rely on good citations, and good citations require the ability to understand and utilize them. Shen Qi highlights this point: a mathematical proof by Hawking, which is cited.