I wrote it in Korean first and I rewrote it in English.

I cannot remember where I saw the link (probably Facebook or LinkedIn). Someone made a toolkit for writing a paper that checks references and writing at the same time. While I agree that AI could greatly shape one’s point of view, I am highly skeptical of relying on generative AI to write a paper.

Writing a mathematics paper is a writing between poetry and a novel. It needs to be concise, like poetry, and explained well so the reader can understand the problem’s key difficulty. Although mathematics research paper is nonfiction, it needs a sort of elegance in elaborating the logic and it should contain some logical thinking so that people can be touched.

Many of the great papers that I read were in that category. For instance, the famous Landau damping paper by Mouhot and Villani clearly explains why this problem is important and elaborates on its key difficulties. Also, they explain the whole strategy for managing all difficulties. Another reason that I like this paper is that it appreciates people who discuss the problem with them. Creating a new language to explain the mysterious phenomenon can be achieved through fruitful discussions with people, not from a single brilliant mind. Moreover, this paper also explains potential different directions so that future researchers can get some benefit.

I also like the fundamental paper due to J. Leray written in 1934, Sur le mouvement d’un liquide visqueux emplissant l’espace. It explains many efforts by engineers, physicists, and mathematicians to understand the motion of viscous fluids. After Navier introduced the model, J. Leray sought to justify it by introducing a new framework. This is now called the theory of weak solutions. In this paper, he proved the global existence of turbulent solutions (now it is called the Leray-Hopf weak solution). To show this, he invented a revolutionary idea to construct a weak solution. Not only for constructing this solution, but he also investigated a limitation of this solution by introducing an epoch of regularity. While this paper was written 90 years ago, I can see how he thought about this problem, and his perspective amuses me. Modern PDE theory did not deviate that much from this paper.

I heard that someone created a review website for an AI paper from Stanford. If the user uploads the paper as a PDF, the AI will evaluate it and provide feedback. Link

It seems this tool was created because publishing a paper on AI is too competitive. I don’t know how to think. I believe that humankind chose to be destructive. Now we have lost lots of critical thinking, and many writings have become homogeneous.

90% of research papers will be forgotten. Many people will not listen to how to write a good paper in the extreme era of publish-or-perish.

Now I kept thinking how to write a good article to touch the reader. That’s why I kept reading literature these days to get some idea.