A Map of Mathematics | Hacker News Reader

A Map of Mathematics

mathmap.quantamagazine.org

206 pointsMitPitt40 comments

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).

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.

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

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

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

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

I prefer this one: http://www.math.wm.edu/~leemis/chart/UDR/UDR.html

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

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.

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.

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

"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.

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.

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

The OP said homotopy type theory. Homotopy theory proper is part of algebraic topology, which is certainly part of mainstream maths.

[Edit] Sorry, I originally said "you said" when it was OP who said.

> "space and quantity"

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

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.

Yeah, perhaps you're right. I was trying to delineate what gets done in maths departments from what gets done in computer science, philosophy or other departments at universities while still falling under the umbrella of mathematics.

Stuff like type theory is rarely done in maths departments (though it sometimes is).

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

I prefer this one: https://tomcircle.wordpress.com/2017/02/15/map-of-mathematic...

Yes! He also has one specifically for computer science: https://www.youtube.com/watch?v=SzJ46YA_RaA

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).

> general algebra

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

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

I don't think that's entirely correct.

> Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields.

Groups, rings and fields are abstractions of what we normally call a "number system". I think my statement is correct. That, or we're debating vague terms.

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.

Terrible presentation

Wholeheartedly agreed!

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...

This is great. It's appeared before in HN, and I'm glad to see it again.

https://news.ycombinator.com/item?id=22328516

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

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.

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

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.

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

Seems like great content but on mobile at least the presentation is utterly unusable. I hope the author can make improvements

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

Self-descriptive, I think.

works for me

Where is calculus?

Calculus comes under a bigger field called "Analysis".

It's in the diagram, but what a terrible layout!

As someone already mentioned, https://tomcircle.wordpress.com/2017/02/15/map-of-mathematic... is way better. The video is totally worth watching.

Edit: Credit to "guerilla" for the link.

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