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Does a graphical representation of mathematics, its fields and subfields, exist ?

Meaning, for instance a graph where vertexes are fields of mathematics (e.g convex geometry, Lie algebra, Kahler geometry ...) at different scales or something ?

Or maybe by concepts ?

Even if it seems rather difficult, and probably any "decent" graph representing mathematics at a given scale is not quite planar but still, I guess it would be quite interesting to try drawing a "big picture" (actually drawing :) ).

The only thing I know off is some videos online called "The Map of Mathematics", which is nice, but very incomplete and coarse of course.

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  • $\begingroup$ The two big issues I see are the vastness of possible subfields to include and, more importantly, where do we put some of the fields? How do we split Geometry for example? Even just talking major subfields there are dozens, ranging from algebraic to symplectic to analytic, etc. $\endgroup$ – Brevan Ellefsen Oct 2 '18 at 18:28
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    $\begingroup$ For sure any representation will be highly criticizable, for reasons you evoke @BrevanEllefsen, but it would still be at least entertaining, and still informative for many. What do you mean Christian Blatter, that this topic will be closed soon ? $\endgroup$ – Gericault Oct 2 '18 at 19:35
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    $\begingroup$ As a start sprinkle the tags of this site on a tree/graph identifying origin/spread/specialization . $\endgroup$ – Narasimham Oct 4 '18 at 3:46
  • $\begingroup$ There's also a similar question on MathOverflow, with several interesting-looking pictures. $\endgroup$ – Calum Gilhooley Oct 16 '18 at 15:02
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If I recall correctly I saw this "map" quite some time ago on T. Tao's blog

If I recall correctly I saw this "map" quite some time ago on T. Tao's blog.

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    $\begingroup$ And, where is the jungle of sets? $\endgroup$ – Carlos Jiménez Oct 3 '18 at 0:38
  • $\begingroup$ Apparently Henry Whitehead said "Combinatorics is the slums of topology"!! (got this I think from Cameron's book on combinatorics he mentions it on this blog ) $\endgroup$ – Mehness Oct 3 '18 at 9:10
  • $\begingroup$ I think this is the original source of the map: youtu.be/XqpvBaiJRHo $\endgroup$ – Michael Greinecker Oct 3 '18 at 10:45
  • $\begingroup$ Recreative but very nice ! thank you $\endgroup$ – Gericault Oct 3 '18 at 15:11
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How about this excellent question on meta which features an interactive graph of MSE.

The direct link to the interactive graph is here.

created by user @piotr migdal, chapeau bas!

EDIT: here is a picture of MSE for example using the second link: enter image description here

...and here is MO (difficult to read best visit link if interested) enter image description here

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  • $\begingroup$ (btw any rep accruing to this ideally will find a way to transfer to the actual author of the graphs if that's possible in case anyone worries abt these things, just think they're great and not a bad proxy for the OP, hence the mention, would have posted comment but for the pictures) $\endgroup$ – Mehness Oct 3 '18 at 8:56
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    $\begingroup$ Precisely what I had in mind ! Thank you so much. I might get on to create my own graphic, I will post it there if anyone interested (scrapping arXiv looks like a good first step) $\endgroup$ – Gericault Oct 3 '18 at 15:12
  • $\begingroup$ sounds good look forward to it! - do check out the links you can click on the nodes and drill down etc, good effort on the part of the author! - actually maybe misremembered the drilldown bit, but fyi here's another one with topic inclusions to make a directed graph $\endgroup$ – Mehness Oct 3 '18 at 15:33
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I found the following visual which establishes the relationship to mathematics as a whole: enter image description here

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    $\begingroup$ This tongue-in-cheek answer made my day and the day of all those I've shared it with XD $\endgroup$ – Brevan Ellefsen Oct 3 '18 at 0:25
  • $\begingroup$ Haha, I felt I would get something like that as my subset of mathematical fields was quite odd .. It was just to give an idea of the scale I was looking for (meaning not Mathematics = Topology, Geometry, Analysis, Algebra nor = Union of mathematical articles from Euclide to the last update of arxiv). Made me laugh though $\endgroup$ – Gericault Oct 3 '18 at 15:09
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This video may be of help, although it is relatively broad: https://youtu.be/OmJ-4B-mS-Y

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    $\begingroup$ That's the video I was referring to :) $\endgroup$ – Gericault Oct 3 '18 at 15:11
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    $\begingroup$ Had same idea. Good choose $\endgroup$ – Krzysztof Myśliwiec Oct 4 '18 at 17:10

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