In high school nowadays most mathematics you learn is fairly 'old'. You have your geometry, all of which (taught in high school) was known to the Greeks more than 2 thousand years ago. You have medieval trigonometry and algebra. You also have 17th century calculus, and that's about it for most high schools.
Now for somebody seriously interested in mathematics, it is hard to decide where to continue your studies after completeling the high school curriculum. Of course you could just start reading about a certain field you are particularly interested in and disregard the other fields as much as you can, but this might give you gaps in your knowledge. You could just learn more advanced calculus, like people usually do, but you'll get the same dilemma after finishing multivariable calculus.
So what I've been doing is reading about the history of mathematics and just reading the major developments in chronological order. Pre-Greeks there was some mathematics, but almost all of it is extremely trivial for a high schooler, and there are no proofs, so the Greeks is where I started. What I'd then do is just read some of their works very selectively, just the most revolutionary stuff. For example:
- Euclid's proof of the infinitude of primes
- Proof of existence of irrational numbers
- Archimedes proof of the area of a sphere
These are just some of the things off the top of my head, usually not taught in high school, which come to mind. And you keep progressing in time, quickly reaching the 17th century . My question is; would it be smart and logical to approach mathematics in this way? As an aspiring physicist, the 17th century is just where it begins to get complicated and I was wondering if it would be smart to keep on doing it like this up until around the 20th century. In my opinion, it flavours up the learning process, it is much more fun than reading a boring text book, it also shows the motivation, and of course reading from the original author themselves in some cases is beneficial (and if it isn't, there are a billion explanations online).