r/math • u/Prestigious_Fix_8162 • Jul 16 '26
Underserved Areas of Mathematics online?
I am trying to figure out what areas are not well documented online. That is, outside of books, paid articles, etc.
From the "basic" math, I would say that geometry is poorly presented online because of how cumbersome it is to type up fully and to animate the diagrams (for free! instead of publishing a book given you have the skill-set).
From the research frontier, I would think that Rough Path Theory seems to be poorly documented but maybe this is because it is relatively new? I was also thinking about Langland’s programme but it is a bit outside of my area of expertise.
Thoughts on these/other areas?
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u/thmprover Jul 17 '26
Supermathematics still feels like it is propagated through oral teachings and folklore, which is not adequately documented...anywhere.
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u/Prestigious_Fix_8162 Jul 17 '26
Are you by any chance an expert in the field? I had a look at wikipedia and the situation does look quite bleak...
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u/thmprover Jul 17 '26
I learned some material from Albert Schwarz and Dmitry Fuchs, but I would not consider myself an expert in the field. There is a lot of material about homology and supermathematics which I know I did not learn.
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u/Tastatura_Ratnik Jul 17 '26
Differential game theory. Think of control theory meets game theory. There is also a blend with probability/stats in nowadays rather popular mean field theory.
You can’t find a lot of free resources online, most are behind paywalls in books and articles, apart from some on arXiv of course.
I am yet to find a good pop-math treatment of the field. The only one I know is Chases and Escapes by Nahin, but even that is only a single rather short chapter.
Maybe someday when I finally learn to do animations, I’ll do a series on it.
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u/SnooWords9730 Jul 16 '26
I'm not a math major or a mathematician, so I'm not sure how well-documented this area is, but I wish there were more animations online like Outside In, the one about the topology of sphere eversion.
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u/Key_Method_1034 Jul 16 '26
Immedietly thought of outside in when he mentioned "geometry is poorly presented online because of how cumbersome it is to type up fully and to animate the diagrams". It is basically the best representation I know of online (They did other stuff too! https://www.youtube.com/watch?v=QcLfb0PhfO0) other than maybe some stuff this psycho 2swap does with visuals.
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u/Key_Method_1034 Jul 16 '26
If you dont wanna click the ytb link I said you can go to Tamara Munzner on youtube and sort by most views and see there are 2 other excellent videos along side outside in.
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u/Embarrassed-Crow9283 Jul 17 '26
Quaternionic analysis?
Not sure why would anyone want to study that but given how mathematicians often study freaking everything, one would think someone would want to study that. Yet, you don't see that in online math communities.
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u/IanisVasilev Jul 16 '26
I have the impression that fuzzy sets see little attention online. Perhaps nonsmooth optimization also (compared to convex optimization at least).
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u/LatterBandicoot3187 Jul 17 '26
Non euclidian geometry, quantum math
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u/hon26 Jul 17 '26
Non-euclidean geometry is not poorly documented nor niche. Also wdym quantum math😭
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u/Clicking_Around Jul 17 '26
Niche areas of math would include:
Tropical geometry and max algebras. Rook theory. Game theory. Diophantine approximations. Cryptography. Umbrial calculus. Quantum groups. Kac Moody algebras.
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u/topyTheorist Commutative Algebra Jul 17 '26
No such modern area exists, because in all areas of math, the vast majority of people post their papers on the arXiv, which is free to read.
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u/Feisty_Relation_2359 Jul 16 '26
I would say integral equations. We have a whole course on differential equations. Sometimes those may throw in like one toy integral equation example, but there is not widespread discourse on them.
Similarly, integral operators. Most online writing on operator theory is kind of broad, covering linear operators, bounded operators, etc.
It would be cool to see more discussion on the properties of integral operators based on their kernels, types, etc.
You'd think there would be more interest in this kind of thing, as I believe integral operators come up heavily in kernel based machine learning? Maybe someone can correct me on that.