Advice for journey through mathematics

No.12946531 ViewReplyOriginalReport
Hello

I have made this thread to receive guidance

To anyone who is now a mathematics undergraduate / graduate, what advice would you give to a 16 year old who plans to study mathematics at University.

Some books I have read include Calculus (Spivak), Counterexamples in Analysis, How to Solve It (Polya), and some ancient texts involving the study of finding solutions of differential equations.

Of course, I studied these equations for around 3 months, as I found them intrinsic and interesting in their own right. However, I came to learn from a more modern text that, in practice, they are solved mainly through numerical approximations by computer.

I would appreciate any advice, reads, or anything else you can offer that would be a stepping stone towards the higher realms of mathematics, which seem quite impenetrable at the current moment.