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My knowledge in math sums up to several university level courses and a lot of self-study. Sometimes it feels like Mathematics is a huge subject with a lot of different areas which some of them correlate with each other. I've tried to find some sort of knowledge map, or interaction map between different areas inside math, but could not find. I'm asking for this kind of map, paper, or anything which will be a kind of a big picture about current mathematics development, including all current areas and the known interaction between those. Also, it will be great to see a sketch, map or something about math pyramid. i.e. a map which describes Reliance between math areas and the existence of areas based on other. THANK YOU!

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If you try to map out every branch I'd imagine it would look like a very ugly blob rather than an attractive pyramid of sorts. –  Vincent Aug 18 at 20:05
    
I see math as a tree that have different branches that all have the same origin. The core of this tree is set theory, not the naive set theory but the one concerned about the foundation of mathematics. For the rest I let your imagination speak, cheers! :) –  Math Gems Aug 18 at 20:11
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Google for Dave Rusin's Mathematical Atlas. –  ioannis galidakis Aug 18 at 20:12
    
Similar question on mind maps: math.stackexchange.com/q/124709/43100 –  Victor Wang Aug 18 at 22:48
    

6 Answers 6

Here is one map of mathematics that's been getting some attention lately:

enter image description here

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That's a really nice illustration, thanks for sharing! :) –  Math Gems Aug 18 at 20:08
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This is the video it comes from youtube.com/watch?v=XqpvBaiJRHo (it actually discusses some of the relationships between different areas of mathematics in a 'big picture' way, so might be of interest to @Ido4848 –  jfhc Aug 19 at 8:29
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This is sort of pretty but has close to zero informational value. –  Jack M Aug 19 at 11:36

At one point, I got frustrated with always lacking the math to understand the things I read about and made a cheeky poster expressing my frustration. With that format, I tried my best to cluster more related topics together.

(I could add that thinking about the possible hierarchy made me ask this question. Later I started an online notebook, working out that structure myself, and a couple of math concepts -not subjects- can be viewed on this graph.)

My question on how to put the topics in disk form became a populat question on Mathematics.SE.

For an incomprihensble big picture, essentially unordered, there is a list of "all" math subjects here.

enter image description here

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Have you ever seen a river delta? At the root there is a river (logic) which splits into several streams (analysis, topology (geometry), algebra etc.). But these streams merge and split (algebraic geometry, differential topology, etc.). There isn't a single sequence of reliances that you could follow. It isn't necessary to go into the depths of logic for example to understand calculus.

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Mathematics - Form and Function by Saunders Mac Lane is a great book which tries to give some kind of "big picture".

As a bonus, some of the chapters also contain "map-like" sketches of various areas of mathematics (IIRC), but that's not why I'm recommending the book.

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enter image description here

Stumbled across this just now. Not sure of the source to give the appropriate credit. If someone knows where it is from please add a comment.

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I also saw this here: math.stackexchange.com/q/124709/43100 –  Victor Wang Aug 18 at 22:48
    
Interesting. I hadn't seen that thread yet. –  Vincent Aug 19 at 2:10
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I believe te original comes from here: arxiv.org/pdf/gr-qc/9704009v2.pdf –  chaosflaws Aug 19 at 20:40

Have you seen the cool "MSE-driven" graphs of maths (well ... of MSE question tags) posted on meta? They only include the 64 most popular tags, so a lot of more advanced and/or specialised areas are left out, but I still think they provide some insight.

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