Sanjoy Mahajan's The Art of Insight in Science and Engineering (available online, https://mitpress.mit.edu/books/art-insight-science-and-engin...). Takes a very pragmatic look to doing mathematics, while not pulling many punches on how advanced the mathematics gets. Would have appreciated this a lot, math books are usually split into dry theory where you have to already know math to be able to properly read them and books that are simplified to death for people who are forced to study math and don't want to.

Tim Gowers' Mathematics: A Very Short Introduction is a popular book on doing mathematics. Not a textbook that teaches you mathematics, so wouldn't give this as the only book, but popular "what's the field like" books could be very interesting to a high schooler.

Also, not suitable for the only book, Penrose's The Road to Reality. It gets very advanced and probably can't be fully tackled without additional mathematical education, but it tries to be an honest exposition of the math needed for modern physics from the ground up without explicitly resorting to external knowledge. I would have loved a "this will teach you all of the math if you can get through it" book like this even if I never did manage to get through it.