Domain of Science
4 HN recommenders · recommended in 7 months, 2018–2022
11:06 · 16M views · Feb 1, 2017
An animated 11-minute tour of the whole field of mathematics as a single map, showing how pure and applied math and their sub-fields relate to each other.
Recommended to people asking how to self-learn math as a quick bird's-eye overview of the field.
8 comments from Hacker News
> shift this burden to the medium This is beautifully expressed. Knowledge consists of connections across concepts but those connections are rarely shown explicitly in textbooks. Even wikipedia, while allowing you to traverse the connections back and forth easily, does not do a great job of giving you the bird's eye view of a subject or a field. Check out this "map" of mathematics: this video Every subject needs a similar map. Besides visualizing the connections, we'd also need interactivity to the topic that helps with forming new mental models - which is the core aspect of learning. Jupyter notebooks, ObservableHQ, Mathigon are some of the good projects working on this aspect. Disclaimer: I am building the open-source project [LINK] which is attempting to build the complete map of knowledge/skills. So I too am biased against books and in favor of digital/interactive tools.
I'd start with this video to get an overview of all the topics and areas that mathematics entails (some might be unknown to you) this video . Then you go ahead and research a bit what sounds interesting to you and then you might google that topic and add "foundations" to that google search. It's just that most school/university math is heavily focused on analysis and algebra but there is so much more!
This is a good map of Mathematics to get an overview of where you can go... this video Then Giles McMullen-Klein has an awesome recommended list for data science (your mileage may vary). [LINK]
This is a much more entertaining map of mathematics in about 10 minutes this video For a history of mathematics NJ Wildberger's lectures are easy to listen to. [LINK]
I suggest this "Map of mathematics" as a starting point that gives you a reasonable birds-eye view of the field. this video