Reddit reviews Men of Mathematics (Touchstone Book)

These three sent me to grad school.

ET Bell, Men of Mathematics
http://www.amazon.com/Mathematics-Touchstone-Book-E-T-Bell/dp/0671628186/

Davis and Hersh, The Mathematical Experience
http://www.amazon.com/Mathematical-Experience-Phillip-J-Davis/dp/0395929687/

Lakatos, Proofs and Refutations
http://www.amazon.com/Proofs-Refutations-Logic-Mathematical-Discovery/dp/0521290384/

The book that really hooked me on math (I was an undergraduate math major) was G. H. Hardy's, "A Mathematician's Apology". You can find free versions online, because over 50 years have passed since publication. But the free versions I saw don't contain the introduction by C.P. Snow that the book has. So you might consider getting the book, either out of the library or from Amazon.

Two other recommendations would be:

• James R. Newman's 4-volume, "The World of Mathematics"
  
  
• E. T. Bell's, "Men of Mathematics"
  
  All three of those kept me duly inspired before and during my undergraduate years.

A classic not yet mentioned:

https://www.amazon.com/Men-Mathematics-Touchstone-Book-Bell/dp/0671628186

Dunham, Gleick, Pagels, Bell

To answer your second question, KhanAcademy is always good for algebra/trig/basic calc stuff. Another good resource is Paul's online Math Notes, especially if you prefer reading to watching videos.

To answer your second question, here are some classic texts you could try (keep in mind that parts of them may not make all that much sense without knowing any calculus or abstract algebra):

Men of Mathematics by E.T. Bell

The History of Calculus by Carl Boyer

Some other well-received math history books:

An Intro to the History of Math by Howard Eves, Journey Through Genius by William Dunham, Morris Kline's monumental 3-part series (1, 2, 3) (best left until later), and another brilliant book by Dunham.

And the MacTutor History of Math site is a great resource.

Finally, some really great historical thrillers that deal with some really exciting stuff in number theory:

Fermat's Enigma by Simon Sigh

The Music of the Primes by Marcus DuSautoy

Also (I know this is a lot), this is a widely-renowned and cheap book for learning about modern/university-level math: Concepts of Modern Math by Ian Stewart.