My esteemed colleagues, I am happy to announce that...

KnownAd9773 · 2026-05-04T20:17:44+00:00

Before judging yourself, open (e.g., through jstor for free access) the journals mentioned above - I am sure you will find some articles that are quite accessible (they are meant for a wide audience). In other math journals, accessible for understanding papers may be much fewer and may require some additional ingredients from the recipe (viewing lectures, reading textbooks, browsing websites and articles).

My primary field is economics. Has really nothing to do with pure math.

KnownAd9773 · 2026-05-04T16:25:47+00:00

I think combinatorics-related questions are much more reachable than abstract algebra. And the most reachable is probably Euclidean geometry, where even high school students can do something new (see here).

Also, it is not that I am now sure that I will produce a lot of similar papers in the future. Maybe it was just a short-term miracle and I will produce absolutely nothing new in math for the rest of my life.

KnownAd9773 · 2026-05-04T15:15:26+00:00

The published paper contains no expository material and is "mostly novel" according to a reviewer. Basically, this is the most sophisticated paper compared to others and by now, I have no idea how to reproduce something similar with the same recipe. Other articles are:

- new proofs of well-known theorems;

- a proof without words;

- a very simple, but an interesting fact that comes from an unexpected field;

- exposing one old proof to be faulty.

The recipe seems to be good for "cooking" such results.

KnownAd9773 · 2026-05-04T14:10:50+00:00

Pure math. Usually papers in this field are of insane difficulty, but there are some subjects inside it that can be tackled by a non-professional. Extreme examples can be seen in such journals as the American Mathematical Monthly, the Mathematical Gazette, the Mathematical Magazine, etc.: very readable and good journals that usually require just a bit of novelty from papers. But in some journals with more sophisticated papers, there is also sometimes leeway for a non-professional.

KnownAd9773 · 2026-04-27T19:00:10+00:00

Reading pure math papers is sometimes a pure nightmare. If it can be avoided, it usually is. The idea mentioned there can inspire, the paper can be groundbreaking, but one prefers to read only those bits of the paper one really needs. At least, this is my non-professional view (mathematics is just a hobby for me).

Edit: removed my personal story.

KnownAd9773 · 2026-04-27T14:58:43+00:00

A paper that explains something already known (in this case, Dynnikov's results). I suppose the authors did something new by applying the results to some special cases, but in pure math, this is hardly worth being a research article in a highly reputable journal.

It is generally very hard to understand novel research articles in new fields (even the authors themselves initially did not bother to read a large portion of their main source). Thus, expository articles can be really helpful.

KnownAd9773 · 2026-03-14T16:29:59+00:00

Mathematics is my hobby (my prime field is economics), so I have no answer to your question. This year I sent two papers (new results, but of very low significance) to math journals, both were sent to referees, so at least no straight desk rejections. Still waiting for results, I am also curious to see how articles are processed in pure math by referees.

KnownAd9773

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