This is the personal website of Jason Zhang.
A few days ago, I submitted my first math paper for review. I haven’t heard back yet (obviously) as the process takes quite a while. However, I want to reflect over this experience and how it different from previous projects.
Update 4/5/2026: Well, I just heard back! I don’t know the exact status yet, but they said they will get back the results within a week. I honestly don’t know how this will go, but I’m hoping for the best.
The paper itself is an exploration into an interesting set theory idea. The birth of this paper can actually be traced back to a previous blog I wrote about multiset cardinality. Since writing the ideas in there, I had found quite a bit more interesting ideas concerning the multiset cardinality developed in that respect and specifically an actual nontrivial1 theorem which made things become a lot clearer. I developed the structure of the m-cardinals \(\mathrm{MCard}\) and found an isomorphism to certain non-decreasing sequences of cardinals (which I denoted \(\mathcal{M}\)). I’ll post the preprint later.
I still am quite proud of what I was able to write, especially since I don’t have formal higher mathematical training yet. This also highlights the major difference between my previous publications/work. This latest work was completely kickstarted and managed by me, from start to finish. In a previous work, I had a mentor which guided me through the process, even if the final work was written by me. For this one, there was no guidance from a professional. There was, however, a lot of experience I had gathered throughout the years (more on this later).
Another major difference is that this is almost purely theoretical. It finds itself little to no application in any field. Maybe one day there will be something cool that applies it, but I doubt it. Anyways, this makes the style of the paper very different. I have to somehow build a cohesive story without the easy “I need XYZ so it can be applied somewhere”. Of course, this wasn’t too much of a challenge as my work is indeed motivated by actual factors. But still a major difference to highlight.
Now, I have no idea whether the journal I submitted to will reject or accept my work. Honestly, I’d put it to 50/50. The journal is targetted towards high school writters, and it is also specifically for mathematics. That is a good thing, but it can also be a bad thing. The issue I’m most concerned about is that my work is too complicated to be in a high school journal, but too amateur to go beyond that. There isn’t a fantastic place this fits right into, especially considering the time constraints I am subjected to and the circumstances of my work. I’m hoping for the best with the current journal I’m submitting to, it seems like the best fit and honestly I just want to be done with this project.
Regardless of reject/accept, I would probably point to this as my “high school capstone” (silly as a concept, but it illustrates the point). This really has been the culmination of my high school experience, and it nicely captures a lot of aspects of my high school life. Or more generally, my pre-college life.
I started this paper last year in December 2025. However, this is certainly NOT where the journey to publish started. The exact starting point is a bit debatable, but I think the most arguable starting point is almost exactly two years ago (spring break 2024).
There were many reasons why I wanted to start writing an actual math paper. Obviously, there was external motivation, but a large part of it genuinely came from my own interests. I already had some prior experience to what math papers should look like. However, I was still not well equipped for what I was going to face. It is a bit embarrasing to think about now. It was shocking how little I knew back then, which is a funny thing to say considering I still know next to nothing today. But the knowledge I had back then was somehow even less. Just to demonstrate how little I knew, I didn’t even use \(\LaTeX\) to make the thing. I am not going into the contents of the paper for my own sanity, although maybe one day I’ll overcome this fear and share out.
After taking an extended break, I came back with twice the mathematical knowledge that I had and I tried to rewrite my old paper. Soon, I quickly realized that what I was writing was not of quality and all and decided to completely restart. My second attempt focussed on a new idea altogether. This one made it much further than before, but it suffered from the issue of not having a clear central motivation. It was just a string of true statements in which the central purpose was weak. This one eventually got scrapped as well, although I might be able to save it one day. Finally I had started this paper, which I ended up submitting. Yay! Throughout this entire process, I had experienced a sort of stress that I suppose is similiar to writer’s block. It really stalled my progress and it is why this dragged out so much.
Anyways, I am getting tired from all of this. The journey isn’t even over yet, there is a high chance that the first few journals will hit me with a bunch of rejections. I hope not. I hope this can be a one and done thing. We will see. I’ll keep this updated.
Nontrivial of course depending on who you ask. I’m sure more experienced mathematicians could see the idea quite quickly. However, it was nontrivial to me and also it wasn’t just a restatement of pre-existing work. At least to my knowledge. ↩