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