If only I had discovered that list back when I was still an undergraduate. The hardest part about finding a good research area seems to be knowing it exists in the first place.
I'm not sure why they don't start with the navigation map, instead of the wonky scrolling experience. You have to hunt for the map, but the link to it is just below the title screen. The map is actually well designed!
Their classification is curious. It seems similar to Wikipedia's list of Quantity (Numbers), Structure (Algebra), Space (Geometry), and Change (Analysis). And yet, they put geometry under "Numbers" and don't really seem to address Algebra at all.
A more realistic taxonomy would be discrete (number theory, graph theory), continuous (geometry, analysis), and discrete properties of continuous things (topology, applications of analysis to number theory).
Oh, that's interesting. Do you have a more detailed version of this taxonomy you could point to?
The thing I like about Wikipedia's version is that the high-level concepts are sufficiently abstract while still providing an intuition as to how the different disciplines can be applied.
I like that the related Quanta articles are linked from each concept. The idea of teaching maths as an ontology of concepts and tools is very appealing because it creates a "why," for each aspect. It's as though code did for math what the blues scale did for music, where suddenly a lot of amateurs could string a few ideas together and make something useful and good.
I'm working through "Content, Methods, and Meaning" now and what makes it great is it starts with what necessitated the invention of methods. The model in the Quanta map has a lot of potential.
I'd say this is part of the mainstream move from an "industrial" society (with mostly human robots and computers) to an "information" society (with mostly human modelers and architects, as robots and computers are now machines).
We now start with the "why", see where knowledge fits in the puzzle of reality, where it plugs and how to find it; then only on a need-to-basis do we go deeper into the 'how'.
I love this map of mathematics, but in explaining concepts, the website shows unfurling images that scrolljack[0]. The inability to scroll back up makes me feel trapped in the content.
I recommend this a lot "A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover Books on Mathematics)" by Michael Crowe. It's a page turner.
It not specifically about history, but I found it nice how it builds up concepts from first principles, e.g. "We had problem X, so we invented math concept Y to help with problem X, and then extended the idea concept Z that handles more general class of problems."
2. Mathematics 1001: Absolutely Everything That Matters About Mathematics in 1001 Bite-Sized Explanations Hardcover by Richard Elwes, 2010. (non free)
This one doesn't go into any details on any topics, but it gives you a bird's eye overview of many topics and based on the "sampling" I did for the few concepts that I know, I found the bite-size explanations to be fairly good (i.e. mathematician explains things in plain language, and not science journalist simplistic analogy).
“A Concise History of Mathematics” by D.J. Struik apparently (I have read only a tiny part of it) is good, but being 70+ years old, it is getting more and more dated.
It also doesn’t discuss the mathematics itself in much depth; it more connects topics and has references (plenty of them) for those who want to learn about those topics.
“The World of Mathematics” by J.R. Newman isn’t a history, but more a sample of pure and, mostly, applied (“How to hunt a submarine” is the title of a chapter on operations research) mathematics.
I think it is worth mentioning, though, certainly for “tourists” who aren’t aiming for full coverage of the subject, but just want to visit nice viewpoints.
Also, I think it’s quite readable for non-mathematicians, as it doesn’t do much ‘real’ math (Stillwell's _Mathematics and its History_, mentioned elsewhere, has more of that in its first 25 pages than this 1000+ page work), and its chapters can be read in isolation.
For a very informal tour, The Three Body Problem by Cixin Liu is a science fiction novel where the history of mathematics, physics, and computation play a large role. So much so that I think it puts many people off the book and its entire trilogy.
I don't know how helpful it is to the common reader, L.E Dickson's 3-volume 'History of the Theory of Numbers' is mentioned frequently as a definitive history of that branch of Mathematics.
"A Cultural History of Physics" by Karoli Simonyi is a brilliant book on the history of Science and math from antiquity to recent past. Even though the title reads as history of physics, the book touches upon everything from Math to Philosophy as they were all under one umbrella until recent past.
Nature and Growth of Modern Mathematics by Edna Kramer. If you love history and mathematics, this is a good combination from what I remember, sort of alternating between historical placements and biographies with actual mathematical content explained.
I read this decades ago before I learned advanced mathematics and I found it enlightening and inspiring at the time though I have not revisited it since though it is a cherished memory. The book's age prevents it from covering the many modern innovations since.
Hand-drawn cartoon map of a conceptual arrangement are very hard to get to grips with. Is there's an actual structure there that could be modeled by a Voronoi diagram, or is it just an elaborated doodle? OK, all conceptual maps are arbitrary to some extent, but the nice thing about the one int he OP is that the relationships are discrete.
While mathematics is often motivated by physical phenomenon, it's epistemologically misleading to present physics as math or vice versa. All too common pet peeve.
You are in a maze of twisty little passages, all alike.
Agreed. But I was pleasantly surprised to find the map is built out of a HTML table and extremely simple js, and longer I looked at it the more I liked it.
I'd go so far as to say it's the back button that needs to change, rather than the site. By that I mean, it's often rather useful to have a stack-based history of your explorations around a map (like this, or a deep dive into Wikipedia, or...), but it'd also (obviously) be nice to pop the whole stack for this site and jump back to HN in a single step.
After all, why are browser history and bookmark navigation so linear when the way we use the web is not? It's like being forced to use turtle graphics or turn-based navigation to connect places on a geographic map. The bookmark manager in browsers is super primitive and hasn't really evolved in 20 years.
Likewise, think about when you have a plethora of open tabs; I've had as many as 400 at times, spread across 7 or 8 windows, with heavy insite overlap (ie I might have 10 tabs pointing at different books or products, multiple tabs going to a specific news outlet, multiple tabs pointing to different Wiki and Git pages etc.). Yet my open tabs are arranged in highly linear fashion along the top of each browser window, and there's no simple way to pull back from looking at the individual pages to looking at the map of my page universe.
tl;dr We use the web in a nonlinear way, like jumping around a dynamic tree, but the browser limits us to an ant-like perspective where leaves are privileged over the tree.
I might indeed. I am not a big fan of console driven applications, but it's intriguing so I am installing it on my linux box now. Thanks for the suggestion!
https://cran.r-project.org/web/classifications/MSC-2010.html
It is arguably less useful for someone who is not a mathematician, but does illustrate how difficult the problem of classifying all of mathematics is.
Both "maps" have their uses.