7 ms·

A Map of Mathematics

206 points by MitPitt 6y ago

guerrilla 6y ago
I prefer this one: https://tomcircle.wordpress.com/2017/02/15/map-of-mathematics/ https://tomcircle.wordpress.com/2017/02/15/map-of-mathematic...
- myWindoonn 6y ago
  Yes! He also has one specifically for computer science: https://www.youtube.com/watch?v=SzJ46YA_RaA https://www.youtube.com/watch?v=SzJ46YA_RaA
nealabq 6y ago
This is great. It's appeared before in HN, and I'm glad to see it again. https://news.ycombinator.com/item?id=22328516 https://news.ycombinator.com/item?id=22328516
strathmeyer 6y ago
Terrible presentation
- ksd482 6y ago
  Wholeheartedly agreed!
amelius 6y ago
Where is calculus?
- ksd482 6y ago
  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-mathematics/ 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.
gbolcer 6y 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.
aardvarkr 6y ago
Seems like great content but on mobile at least the presentation is utterly unusable. I hope the author can make improvements
catpolice 6y ago
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 6y ago
  To what extent can you get into category theory or homotopy type theory without learning some algebra or algebraic geometry/topology?
  - jessaustin 6y 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.
- ogogmad 6y 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.
  - Ceezy 6y ago
    You can't be serious. Homotopy theory is about shape!
    - ogogmad 6y ago
      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.
  - gone35 6y ago
    > "space and quantity" That's a rather narrow view even of mainstream mathematics IMO.
gregw2 6y 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 https://space.mit.edu/home/tegmark/toe.gif (parent webpage if you want more context: https://space.mit.edu/home/tegmark/crazy.html https://space.mit.edu/home/tegmark/crazy.html).
- slowmovintarget 6y ago
  Aren't those the ones used in physics, not all of the ones there are (even in the 90s)?
- sn41 6y 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.
- laichzeit0 6y ago
  > https://space.mit.edu/home/tegmark/toe.gif https://space.mit.edu/home/tegmark/toe.gif I really like this map. Do you know of a similar map for statistics?
  - taliesinb 6y ago
    You might like https://twitter.com/xbresson/status/1271124929505714176?s=12 https://twitter.com/xbresson/status/1271124929505714176?s=12
    - mvanaltvorst 6y ago
      I prefer this one: http://www.math.wm.edu/~leemis/chart/UDR/UDR.html http://www.math.wm.edu/~leemis/chart/UDR/UDR.html
outlace 6y 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 6y ago
I like this poster: https://m.youtube.com/watch?v=OmJ-4B-mS-Y&feature=youtu.be https://m.youtube.com/watch?v=OmJ-4B-mS-Y&feature=youtu.be
sn41 6y 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 https://mathscinet.ams.org/msnhtml/msc2020.pdf
- jgwil2 6y 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.
- deleted 6y ago
  [deleted]
sillysaurusx 6y ago
“Counting holes” went to 404, sadly. I was hoping to count some holes today.
- sn41 6y ago
  Self-descriptive, I think.
- logologology 6y ago
  works for me
lamename 6y 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 https://youtu.be/OmJ-4B-mS-Y
Ceezy 6y 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).
- ogogmad 6y 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".
  - gone35 6y ago
    > Abstract algebra is basically the study of "number systems". I don't think that's entirely correct.
    - deleted 6y ago
      [deleted]
    - ogogmad 6y ago
      > 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.
  - Ceezy 6y 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 6y 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 6y 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_mathematics https://www.reddit.com/r/math/comments/l4zhxh/the_map_of_mat...
gspr 6y ago
That's a strangely low number of connections to/from algebraic topology, especially with the shapes section.

206 points by MitPitt 6y ago

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

myWindoonn 6y ago
Yes! He also has one specifically for computer science: https://www.youtube.com/watch?v=SzJ46YA_RaA https://www.youtube.com/watch?v=SzJ46YA_RaA

nealabq 6y ago

This is great. It's appeared before in HN, and I'm glad to see it again. https://news.ycombinator.com/item?id=22328516 https://news.ycombinator.com/item?id=22328516

strathmeyer 6y ago

Terrible presentation

ksd482 6y ago
Wholeheartedly agreed!

amelius 6y ago

Where is calculus?

ksd482 6y ago
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-mathematics/ 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.

gbolcer 6y 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.

aardvarkr 6y ago

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

catpolice 6y ago

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 6y ago
To what extent can you get into category theory or homotopy type theory without learning some algebra or algebraic geometry/topology?
- jessaustin 6y 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.
ogogmad 6y 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.
- Ceezy 6y ago
  You can't be serious. Homotopy theory is about shape!
  - ogogmad 6y ago
    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.
- gone35 6y ago
  > "space and quantity" That's a rather narrow view even of mainstream mathematics IMO.

gregw2 6y 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 https://space.mit.edu/home/tegmark/toe.gif (parent webpage if you want more context: https://space.mit.edu/home/tegmark/crazy.html https://space.mit.edu/home/tegmark/crazy.html).

slowmovintarget 6y ago
Aren't those the ones used in physics, not all of the ones there are (even in the 90s)?
sn41 6y 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.
laichzeit0 6y ago
> https://space.mit.edu/home/tegmark/toe.gif https://space.mit.edu/home/tegmark/toe.gif I really like this map. Do you know of a similar map for statistics?
- taliesinb 6y ago
  You might like https://twitter.com/xbresson/status/1271124929505714176?s=12 https://twitter.com/xbresson/status/1271124929505714176?s=12
  - mvanaltvorst 6y ago
    I prefer this one: http://www.math.wm.edu/~leemis/chart/UDR/UDR.html http://www.math.wm.edu/~leemis/chart/UDR/UDR.html

outlace 6y 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 6y ago

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

sn41 6y 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 https://mathscinet.ams.org/msnhtml/msc2020.pdf

jgwil2 6y 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.
deleted 6y ago
[deleted]

sillysaurusx 6y ago

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

sn41 6y ago
Self-descriptive, I think.
logologology 6y ago
works for me

lamename 6y 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 https://youtu.be/OmJ-4B-mS-Y

Ceezy 6y 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).

ogogmad 6y 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".
- gone35 6y ago
  > Abstract algebra is basically the study of "number systems". I don't think that's entirely correct.
  - deleted 6y ago
    [deleted]
  - ogogmad 6y ago
    > 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.
- Ceezy 6y 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 6y 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 6y 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_mathematics https://www.reddit.com/r/math/comments/l4zhxh/the_map_of_mat...

gspr 6y ago

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