Check out

https://www.amazon.com/Mathematics-Its-History-Undergraduate...

which goes through the history of maths while actually _doing_ some maths at undergraduate level.

Also the lectures based on it by N J Wildberger

E.g. https://www.youtube.com/watch?v=HRD9X-2Bmdw&t=2692s

The article is a very interesting popular account of the Fermat-Wiles Theorem and the discovery of the flaw in Wiles's first attempted proof of the theorem. I was glad to see that the article makes the timeline of Fermat's writings on the topic sufficiently clear to support the historical statement that Fermat himself surely didn't have a proof for the full theorem: "Fermat himself had given a proof for n = 4." (Writing marginal notes in the book about number theory he was reading was something that Fermat did early in his amateur study of mathematics, while doing his professional work as a lawyer. Fermat later "published" many proofs in the manner of his era by writing letters to other scholars. Fermat's son published the marginal notations in an edition of the book Arithmetica published only after Fermat's death. If Fermat actually had a proof for the theorem known as his last theorem, he had plenty of opportunity in his lifetime to find other pieces of paper on which to write it down.) I recall that the current textbook Mathematics and Its History by John Stillwell[1] reviews the history of this topic pretty well.

[1] http://www.amazon.com/Mathematics-Its-History-Undergraduate-...

Can you now teach me how I (~20 year old) can be interested in math?

The popular books by mathematician Ian Stewart

http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&...

are very interesting and mathematically accurate. Some readers also like the books by Keith Devlin,

http://www.amazon.com/Keith-Devlin/e/B000APRPC6/ref=ntt_athr...

one of which I am reading right now.

I like almost every book by John Stillwell

http://www.amazon.com/John-Stillwell/e/B001IQWNS2/ref=ntt_at...

and especially recommend the latest edition of Mathematics and Its History

http://www.amazon.com/Mathematics-Its-History-Undergraduate-...

as a book you should try to obtain from a library to see what a book with challenging, interesting, but accessible problems looks like.

Many people like the videos that feature Edward Burger

http://www.thegreatcourses.com/tgc/professors/professor_deta...

or Arthur Benjamin lecturing about math in the Great Courses (Teaching Company) video lecture series, which you may be able to find at a library.

AFTER EDIT: Here is a link for Calculus Made Easy, a book recommended by another participant here.

http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...

You would like Mathematics and its History by John Stillwell

http://www.amazon.com/Mathematics-its-History-John-Stillwell...