Where are the modular forms enthusiasts?

When I was doing my undergrad, I studied modular forms. I found them very interesting; they have deep connections to the frontier of mathematics and were critical to proving Fermat’s Last Theorem.

It has always bothered me that there wasn’t more discussion about them online. The internet feels so large; surely there must be a cozy little forum out there somewhere for modular form enthusiasts?

I decided to do some quick approximations to figure out how it is that almost no one on the internet discusses modular forms. How many people are thinking about modular forms, and how many of them have a presence on the web?

How many people are thinking about modular forms?

Arxiv showed 414 results for “modular form” in the last year. At a glance, I saw 7 papers out of the first 50 that seemed to be unrelated, so I took that false positive rate and got $414-((414/50)7)\approx 356$ papers.

Most papers seemed have between 1 and 3 authors. Suppose there could have been up to 10 people tangentially involved in each paper or working with the professors on modular forms.

That means 3560 people were working on modular forms in the last year. This does not account for academics who did not publish in the last year, their students, and enthusiasts who don’t publish anything on Arxiv.

How many modular forms enthusiasts have a web presence?

The first 50 results have 96 unique authors.

I selected 20 authors at random. For each author, I did a cursory google and checked if they had any active socials. This was limited to searching by name, but it’s pretty easy to find my social accounts and website, and I have no credentials, no publications, and very few views.

Unless otherwise mentioned, “Website” means a mostly-static page updated only to list recent publications. Generally, “Website” is a disappointing result; it’s the bare minimum to affirm you exist at all on the web. This is as opposed to “Blog” or some other actively-generated content like an X profile.

I’ve scrubbed the names here for anonymity, although it’s not really necessary.

Name Location Status Web Presence Notes
** South Korea Professor Website  
** China Unclear None  
** Colorado Assistant Professor Website His paper was a false positive. Nice website
** Ireland Postdoc Website  
** Switzerland Postdoc Website  
** Germany Postdoc None  
** Tennessee Postdoc Website  
** Kentucky Associate Professor Website Another false positive. He is at least mentioned on X occasionally
** French Polynesia Professor Website Nice website, looks old though
** China Assistant Professor Website, Youtube Lectures  
** Utah Associate Professor Website  
** Spain Professor Website One or two mentions on X
** South Africa Professor Website, Youtube Lectures  
** Turkey Researcher StackExchange  
** France Masters Student Github/Website False positive
** Illinois PhD Student Website, Youtube Lectures  
** India Assistant Professor Website, Youtube, StackExchange Some of the YouTube content looks good
** Hawaii Professor Website  
** Minnesota PostDoc Associate None  
** Japan Professor Emeritus Website  

So there you have it: 0/20 have any substantial web presence beyond a static website and some YouTube videos that were incidentally uploaded by their university.

Unfortunately, this makes it unclear what the actual rate is. It could be 1/20, 1/50, 1/100, or even worse. I’m not willing to do any more sampling by hand, so we can only speculate for now.

The math shows that I am alone

Supposing, optimistically, that 1 out of 20 modular form enthusiasts participates on the web at all, and given our estimate of 3560 participants in the community, that leaves $3560/20=178$ people on the web talking about modular forms.

The best case is only 178 people split across a lot of different time zones and languages.

I suspect 1 in 20 being active on the web is extremely generous. I would not be surprised at all to learn it’s more like 1/100 or worse.

Further, I wouldn’t be surprised if assuming that there exists 10 unique enthusiasts per preprint published this year is also very generous.

The lower bound is grim: if there are 5 unique enthusiasts per paper, and 1/100 are actively participating on the web, that leaves about 18 people.

Comparison with my website’s analytics

I wrote an article on the history of modular forms about five years ago. Between 01/01/2021 and 12/31/24, it got 53 views from 33 active users. That’s about 8 users per year stumbling upon my webpage.

Certainly part of the problem is accessibility. My blog post doesn’t appear in a Google search for “modular forms history”, but it’s the second result if you search on Bing.

If Google has 10x more users than Bing, and pretending they’re the two dominant forces, we can imagine that 1 in 11 modular form enthusiasts use Bing and could find my blog post, but only if they were specifically searching for the history of modular forms.

So 3560 people are thinking about modular forms. Out of those, only 323 of use Bing. I guess it’s believable that 10% of the 323 modular form enthusiasts who use Bing searched “modular forms history” in the last four years and found my website. That kinda makes sense.

Actually, though, the number of people who found my page on modular forms by searching is probably lower than 33. 77% of my overall website traffic comes from direct links, while 14% comes from organic search, but one page that went viral biases the data heavily towards direct links. I’d guess around 50% of the 33 users or less actually found the page by searching. The others were probably directly linked to the page by me.

Overall, though, I think the takeaway here is that getting indexed higher in Google could potentially 10x my views, but it seems unlikely that the target audience for my modular forms article is larger than a few hundred people.

Academia is hogging all the writers

I doubt that many of the authors with preprints on Arxiv feel intellectually isolated. Academia does a good job of connecting academics that share niche interests, and there’s never a shortage of eager students who want to be brought on board for whatever research you happen to be doing.

Unfortunately, prospects are grim outside the academic sphere. There are no casual readers looking for modular forms content. Realistically, even academics probably aren’t interested in unpublished rants on personal blogs with no credentials, especially articles dealing with math history rather than frontier mathematics. Similarly, writing their own blog posts will do little to further their career.

I don’t claim that the approximations done here are irrefutable or even particularly accurate. I think it’s more of a cathartic experience for me.

I don’t really think about modular forms any more, but for few years after college, I had this fantasy that, one day, someone would find my work and invite me into a sphere of like-minded individuals. I imagined a global network of enthusiasts digging into the history of mathematics, sharing their findings, and writing for each other without the institutional pressure of academia.

The reality is that there are very few people with such interests, the vast majority of them are already in academia, and most academics don’t have a digital presence outside of their academic publications.

There is still a lingering question of “why?” Why aren’t more people like me? 29,013 math degrees were awarded in the US in 2022. There must be hundreds of thousands of people with degrees in mathematics. What are they all thinking about? Where are their blogs? I do not know the answer to this.

What am I supposed to do?

I have changed the subject matter of my writing over time to try and appeal to a larger audience. I talk about machine learning, LLMs, computer science, and statistics. I’ve also worked on interactive web apps like Caravan and Astral Fugue.

These pages have been objectively more successful, but it’s an uphill battle to get any meaningful engagement. It’s nice to see the “views” number go up in my analytics, but that’s just a proxy to what I really want. I want to have discussions with people who like my ideas and have ideas of their own. On this front, I have been wildly unsuccessful.

The only page which has ever really generated spontaneous discussion is my article on Bernoulli diffusion. I had several academics reach out for clarification or to make corrections. It was awesome, and it felt good, even if it was only very surface level stuff. In fact, that page still gets a disproportionate amount of engagement, and people really read it. They spend a substantial amount of time on the page. More so than any other article on the website.

I have reason to believe that some of the people who truly read the Bernoulli diffusion article were using it to assist in writing their own academic publications. Some readers used the derivations in their own works, which they then published without citing me or even contacting me.

When I realized this, I was excited that my work was finally being used for something, even if it wasn’t how I imagined. But now, I am still here, with nothing to show for all of it except a conspiracy theory that my blog is being plagiarized by academia.

My pivot to more broadly accessible writing has been ongoing for 3 years. It’s still niche content. I’m not denying that. But the articles tend to be less dense, they’re shorter, they have more pictures, and the subject matter is more variable. What does my audience look like now? What kind of best-case engagement should I expect? It’s tough to say. The diversity of content doesn’t lend itself to this analysis.

Enough rambling. Wrap it up.

I don’t have any prescriptive claims to derive from this article. I already had a loose strategy, and I’m continuing to adhere to it. I’ll keep writing about interesting shit, some of which involves mathematics. I’ll keep the articles brief and think about keeping readers engaged. I’ll dip into other kinds of media like web apps. I will look for other people like me publishing content on the web.

I don’t expect things to get better. I’m learning to make peace with it. I do wish I understood why it’s not working. Does my shit just suck? Does nobody care about this stuff? Is it the search providers? Is it some kind of institutional problem? Am I not advertising enough? Where are the other blogs like mine?

Anyways, I am proud of the things I’ve written, even if they are inaccurate and messy, and even if no one reads them. I try to convince myself that the personal narrative of developing my own unique understanding has inherent value. Nobody thinks about exactly what I’m thinking about. That’s cool, and I should be proud of it. At the end of the line, I will be someone that no one else is.

Maybe it’s a mistake to conflate one’s need for intellectual development with one’s need for community. When you decouple the two, they are each available in surplus. I dunno. At least I have a beautiful wife. Thanks for reading.