Reddit mentions of The Mathematical Experience

https://www.amazon.com/Mathematical-Experience-Phillip-J-Davis/dp/0395929687

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 Mathematical Experience is really a collection of essays, so it doesn't bog you down, and you can easily skip the ones that don't interest you. It covers some actual mathematics, but is mostly focused on what it means to do math, what it is like to be a mathematician, and philosophy of math topics. If you liked A Mathematican's Apology, this is a good bet.

Mathematical Literature is a genre I don't think many people are aware of, I'm glad you're interested.

The Mathematical Experience is a great survey of mathematical ideas. This book toes the line perfectly - someone not knowledgable of advanced mathematics can follow easily yet the book does not dumb down complicated ideas. This is my top recommendation for anyone thinking about studying mathematics.

If you love geometry, then check out Geometry Revisited by H.S.M Coxeter. Coxeter is one of the greatest mathematicians of his time - he single handedly brought geometry back into vogue as a serious study.

Maybe for lighter reading, Ian Stewart has a bunch of good Mathematical survey books for the "layman" - I'd recommend if you have minimal mathematic knowledge.

There's a yearly collection of mathematical writings that you might like too. I've only bought and read the 2010 edition, but I assume the followups have been great. The essays collected vary from finance, game theory, geometry, social sciences, literature, etc. with connections to mathematics.

Hope you have a fun time with math, good luck!

I've currently been absolutely loving The Mathematical Experience. It's an amazing book thus far, and is blowing my mind more and more every day.

http://www.amazon.com/Mathematical-Experience-Phillip-J-Davis/dp/0395929687

This is one of the best philosophy of math books I've ever encountered. It's not exactly short like you wanted, but it covers a lot and it's very readable.

Sadly, no. I feel Lockhart's essay is unique in spirit. A different kind of resource on the similar topics would be this book. I's a very well written and understandable account of some topics in the philosophy of Mathematics.

The Mathematical Experience