The submission process is everything but familiar to me. While I did submit to the arXiv, the arXiv is not a peer-reviewed journal, unlike many other mathematical journals. Over the past two months I have been working carefully on a paper that relates closely to the topic in On Finite Fields and Higher Reciprocity , and I was debating whether to submit it to the American Mathematical Monthly (AMM) - a prestigious journal for expository articles that is well-respected in the math community - or another journal such as the Mathematics Magazine (MM). After much thought and revision (as well as some much-needed guidance), I decided that my article was not novel enough to warrant a place in AMM, but that it would perhaps be suitable for MM. So, today (or rather yesterday), I submitted my article to MM.

Here are some thoughts that I have. First, I do not have incredibly high expectations for the publication of this article. While I know that MM is perhaps on the lower end of journals in general (despite featuring incredibly expository work), it still has a lower standard based in originality and novelty. While I think my paper certainly is interesting and would be appropriate to the readership of MM, I am not entirely sure. I guess we’ll see. Second, publication takes a long time. The website for MM indicates that, on average, the first decision regarding an article will be 19 days. Now, this is kind of arbitrary - it can take far longer or far less time. Looking back at previously published articles, it seems that people took anywhere from a few weeks to an entire year to publish. That’s a long time. I guess we’ll see how long this takes!

If the paper is rejected from MM, I can still possibly publish in a different undergraduate journal - we’ll see. Either way, I’m going to post this paper on the arXiv at some point. I will update this page if anything happens.

(2 October, 2024)

The paper is now informally available on this website. I am still awaiting notice from MM. A pdf (v1) is available here, and the arXiv preprint is here.

(11 October, 2024)

This journey has reached an important milestone. It seems that my paper has been “reviewed favorably” by Mathematics Magazine, and after completing minor revisions, it will go on to publication. In this post, I’ll cover a little bit of the timeline of the journey this paper has taken and some of my thoughts.

Timeline picture

The above shows a sort of timeline of events in the submission process (I’ll update it later when more stuff happens, but for now, I have until 18 April, 2025 to revise and resubmit for eventual publication).

Here are some initial thoughts. The publication process seems like something really exciting, but in reality, it’s mostly waiting. Just waiting. And a lot of it. This should be pretty clear from the timeline shown as evidenced by the 4 month gap between submission and decision, but it really isn’t put into perspective until you’re in it. I found myself refreshing that page for a while until I eventually gave up - each step in the process felt like an eternal wait, so reaching a point with some more certainty is a great feeling. If I have any more thoughts or any interesting comments about referee comments on my paper, maybe I’ll write more here. For now, it’s just some revisions.

(5 March, 2025)

Revisions only took about two weeks, and the paper will now be re-examined. Hopefully it takes just a couple weeks. I will post an updated version (v2) to the arXiv before publication, and will update that page accordingly. Thank you to everyone who has contributed to this and helped me throughout the process. As promised, here is an updated timeline.

Timeline picture

(17 March, 2025)

The article was returned on 19 June, 2025, with a few brief revisions (typos and punctuation) and one minor remark about an assumption made, as well as a guarantee of acceptance and publication after resubmitted. I made these changes quickly and added a remark to address the assumption, and now I guess I wait until either the paper is sent back out to reviewers (which I would find to be unnecessary because so little has been changed, but it’s not up to me) or accepted by the editor. I think that the two scenarios have a very different timeframe… Either way, here is the timeline updated again. Until later!

Timeline picture resubmit

(20 June, 2025)

As of today, 26 June, 2025, this article has been accepted for publication. There was a minor round of revisions from the editor that mostly pointed to punctuation and rephrasing of some sentences which I managed quickly. Mathematics Magazine indicates an average of 45 days from acceptance to online publication, but I don’t know what to expect—I guess it depends on how close 26 June is to any individual 5-times-a-year publication. Below is the final timeline.

Timeline picture accepted

I suppose now that this project has come to its end, I should talk a bit about what this means to me for eventually pursuing research and doing more like this. At the end of the day, this result is a stepping stone. Yes, I am happy that I completed it, and I am happy that it has been accepted, but there’s a bit of melancholic sadness—it’s like when you’ve achieved something you wanted for a long time and initially feel content, but internally you know that to achieve what you really want, there will be many more seconds, minutes, and hours spent working, doubting, and revising. Those seconds, minutes, and hours seem far away, but they really aren’t—years are now conscious fractions of our lives, and all that we do, whether to advance our career or personal interests, will eventually shape us.

I can’t get ahead of myself. The next decade of my life decides really how I want to diversify my specialty—a bit of an oxymoron, but I think this concept of being specialized yet flexible and interdisciplinary is exactly what the remaining three-quarters of this century demands—and achieve whatever it is I want to achieve. There is work to be done.

When the article is published, I will include a link here; I expect the updated article to appear on the arXiv as well.

Also I now officially endorse using em-dashes.

(26 June, 2025)