In May 2017, I convinced myself I had solved a niche but stubborn problem in ergodic theory. I spent three weeks obsessing over the LaTeX, making sure every lemma was perfectly labeled, and then I did the bravest thing a mid-tier mathematician can do: I submitted it to Inventiones Mathematicae. I felt like a god for about four hours. Then the waiting started. I waited 14 months. For 426 days, my paper sat in a digital void. When the rejection finally came, it was three sentences long. The reviewer basically said the result was ‘fine’ but not ‘surprising.’ I cried in a stall in the basement of the math building. It was pathetic.
That’s the reality of the ‘best’ journals in mathematics. We pretend they are these objective bastions of truth, but they’re mostly just gated communities with very long wait times. If you’re looking for a list of where to send your work—or what to read if you want to see the ‘pinnacle’ of the field—you have to start with the Big Four. But don’t expect them to be nice to you.
The Ivory Tower: The Big Four
If you ask any math professor at a cocktail party (which is a miserable place to be, trust me), they’ll tell you the same four names. Annals of Mathematics, Inventiones Mathematicae, Journal of the American Mathematical Society (JAMS), and Acta Mathematica. These are the gold standards. If you get a paper in here, you’re basically tenure-track royalty.
Annals is the king. It’s published by Princeton, and it’s where Wiles published the Fermat’s Last Theorem proof. It’s legendary. But here is my hot take: JAMS is actually the hardest one to read because the formatting is hideous. I know people will disagree and say the content is what matters, but JAMS papers look like they were typed on a haunted typewriter from 1984. The margins feel claustrophobic. It’s like reading a legal summons for a crime you didn’t commit. I genuinely find it hard to focus on the beauty of a proof when the font choice feels so aggressive.
Acta Mathematica is different. It’s Swedish, it’s old, and they only publish a handful of papers a year. It’s like a boutique hotel that only has three rooms and they’re all booked by people who won Fields Medals twenty years ago. It’s prestigious, sure, but it’s so slow that by the time a paper comes out, the subfield has usually moved on to something else. Total lag.
The ones that actually work
What I mean is—actually, let me put it differently. If the Big Four are the Ferraris you can’t afford, there are journals that are like a reliable Honda Accord. They aren’t ‘flashy,’ but they are where the real work of mathematics happens.
- Duke Mathematical Journal: High prestige, but feels slightly more ‘human’ than Annals.
- Journal of the European Mathematical Society (JEMS): These guys are doing great work. They seem to actually care about the breadth of math, not just the trendy stuff.
- Crelle’s Journal (Journal für die reine und angewandte Mathematik): It’s the oldest math journal in the world. There’s something cool about publishing where Gauss and Cantor published.
I once tracked the review times for 14 papers in my specific subfield across these ‘second tier’ journals. The average was 310 days. Still long, but compared to the 500+ days you often see at Inventiones, it feels like a sprint.
Takeaway: If you aren’t trying to win a Fields Medal, aim for a top-tier specialized journal instead of the Big Four. You’ll keep your sanity.
The ‘Nature’ Problem
I’m going to say something that might get me blocked by some of my former colleagues. I refuse to respect mathematics published in Nature or Science. There, I said it. These are general science journals. They want ‘impact.’ They want ‘narrative.’ Math doesn’t always have a narrative. Sometimes math is just a very difficult proof about a shape that doesn’t exist in the physical world.
When math gets into Nature, it’s usually because it has some tenuous connection to biology or ‘big data.’ It’s math for people who want to look smart at parties. It’s physics-lite. If your proof needs a ‘discussion’ section that explains why it matters to society, it’s probably not the kind of pure, soul-crushing math I care about. I know that sounds elitist. I don’t care. Real math belongs in math journals, not sandwiched between an article about penguin migration and a study on melting glaciers.
Anyway, I digress. My point is that ‘impact factor’ is a metric for people who don’t actually understand the papers they are publishing. In math, we use the IMU (International Mathematical Union) rankings, or we just rely on the ‘vibe’ of the editorial board. It’s a vibe-based economy.
The rise of the ‘Free’ stuff
I used to think that if a journal was free and online-only, it was probably garbage. I was completely wrong. My perspective changed when I realized how much Elsevier and Springer are bleeding university libraries dry. It’s a scam. We write the papers for free, we review them for free, and then they charge our libraries $5,000 for a subscription. It’s a velvet rope that we helped build.
Now, I have an irrational loyalty to the Electronic Journal of Combinatorics. It’s diamond open access. No fees to publish, no fees to read. It’s run by mathematicians who actually give a damn about the community. Is it as prestigious as Annals? No. But I can actually send a link to my mom and she can click it without hitting a $40 paywall (not that she’d read it, but still).
I’ve reached a point where I actively tell my friends to avoid the mid-tier commercial journals. If it’s not a ‘top’ journal and it’s owned by a massive corporation that treats research like a commodity, why bother? Just put it on the ArXiv and send it to a society-run journal.
Does any of this actually matter?
I left academia three years ago. I work in ‘general’ now (data stuff, mostly). I still check the ArXiv every morning while I drink my coffee. My chair at my current job is much more comfortable than the one I had in the department—that one had a broken hydraulic lift so I was always slowly sinking toward the floor while trying to understand Perelman’s work.
Looking back, the obsession with ‘best’ journals feels a bit like a fever dream. We spent so much time worrying about the masthead on the PDF. But when I think about the papers that actually changed how I think, they weren’t all in Annals. Some were in weird, defunct journals from the 70s. Some were just preprints that never got published because the author got bored or died.
Is the peer review system a corpse we keep dressing up in a suit? Maybe. I still don’t know if there’s a better way to filter the noise. If we didn’t have the prestige of the ‘Best Journals,’ we’d just be drowning in a sea of mediocre PDFs. But the current system is definitely broken.
I still wonder what happened to that reviewer who rejected my 2017 paper. I hope they’re doing well. I hope they’ve found something ‘surprising’ lately.
Submit to the ArXiv first. Everything else is just ego.
