A Map of Mathematics

I'm not usually one to poke fun at these things but my friends who study formal logic/model theory/category theory/homotopy type theory/etc. will be excited to learn that they are not in fact doing mathematics.

dmch-1• 5 years ago

To what extent can you get into category theory or homotopy type theory without learning some algebra or algebraic geometry/topology?

jessaustin• 5 years ago

"Algebra" by itself doesn't appear on this map. Clicking through and reading some of the descriptions, my impression is that this was not created by mathematicians.

ogogmad5• 5 years ago

Those areas aren't part of mainstream mathematics. More like "theoretical computer science".

Mathematics (in the mainstream sense) is the study of space and quantity.

Ceezy3• 5 years ago

You can't be serious. Homotopy theory is about shape!

gone352• 5 years ago

"space and quantity"

That's a rather narrow view even of mainstream mathematics IMO.

catpolice2• 5 years ago

This is a very strange claim. Just off the top of my head, this definition of "mainstream mathematics" would exclude, for instance, Gödel's more famous theorems, a good bit of Grothendieck, some of the Bourbaki collective, and a huge amount of work from rather high profile mathematicians working today.

gregw2• 5 years ago

Interesting. I still prefer the clarity of the map of mathematical structures I ran across in the late 90s from Max Tegmark... Perhaps it might interest some of you who are reading this discussion: https://space.mit.edu/home/tegmark/toe.gif

(parent webpage if you want more context: https://space.mit.edu/home/tegmark/crazy.html).

sn413• 5 years ago

Thank you for that link. This is really interesting. I am used to thinking in terms of "removing" features in order to get to more abstract notions. But it is good to have most such structures in one map.

slowmovintarget• 5 years ago

Aren't those the ones used in physics, not all of the ones there are (even in the 90s)?

laichzeit0• 5 years ago

https://space.mit.edu/home/tegmark/toe.gif

I really like this map. Do you know of a similar map for statistics?

taliesinb• 5 years ago

You might like https://twitter.com/xbresson/status/1271124929505714176?s=12

outlace• 5 years ago

I'm not getting much out of the visualization but if you click each topic it has a nice little lay-person summary which is great.

auroranil• 5 years ago

I like this poster: https://m.youtube.com/watch?v=OmJ-4B-mS-Y&feature=youtu.be

sn413• 5 years ago

Semi-literate nonsense - I think it only shows the "little knowledge" of the mapmaker.

What about dynamical systems? Theoretical computer science? Mathematical Logic? If you want to have a look at the classification used by the American Mathematical Society, here is what their "map" looks like (151 pages):

https://mathscinet.ams.org/msnhtml/msc2020.pdf

jgwil2• 5 years ago

Doesn't include calculus either - I think perhaps it's not meant to be exhaustive.

EDIT: it has been pointed out elsewhere that calculus falls under analysis, which does appear in the map.

sillysaurusx• 5 years ago

“Counting holes” went to 404, sadly. I was hoping to count some holes today.

sn413• 5 years ago

Self-descriptive, I think.

logologology• 5 years ago

works for me

lamename• 5 years ago

The educational youtube channel Domain of Science has a pretty wide-scope Map of Mathematics, depending on your background https://youtu.be/OmJ-4B-mS-Y

gbolcer• 5 years ago

That's really cool, but after poking around, I can't find set theory, logic, and graph theory. Am I just missing it? It seems kind of tainted toward physics.

Ceezy3• 5 years ago

At this point it looks more like trolling. No mention of the operator theory. No general analysis no general algebra. ZERO math applied to physics (discretisation, stats).

ogogmad5• 5 years ago

general algebra

They've got a bunch of stuff on "number systems" and "group theory". Abstract algebra is basically the study of "number systems".

gone352• 5 years ago

Abstract algebra is basically the study of "number systems".

I don't think that's entirely correct.

Ceezy3• 5 years ago

Yes but that's far from enough, you need at least to study kernel ring and module and EV to go somewhere in math. No holomorphic functions, complex number quaternions... I'm also not sure on how you would do modern cosmology without studying connection, and differential geometry.

systemvoltage• 5 years ago

I like boring diagrams.

  - Static with zero animations
  - Connections are always visible (no need to hover over)
  - Logically laid out, not randomly placed and drawing connection lines all over
  - SVG or PNG format, I can copy it and save it on disk

speters• 5 years ago

At first I thought this was a random student attempting something. Would have never guesses that this was actually from quanta.

Here is the discussion from /r/math: https://www.reddit.com/r/math/comments/l4zhxh/the_map_of_mat...

gspr• 5 years ago

That's a strangely low number of connections to/from algebraic topology, especially with the shapes section.

A Map of Mathematics

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