Recommendations

This blog (link) by Prof. Terrence Tao can be very helpful at times. In particular, the section titled "Career Advice" has helped me a lot. He also includes links to articles by other mathematicians.

Approach Zero is a math search engine, which supports Latex based searches. 

AMS Open Math Notes.

MathStackExchange(MSE) is a great platform to ask any questions in mathematics.

MathOverflow (MO) is a platform for research-level questions. Many top-level mathematicians use this site regularly. It is fun to read old questions and answers as we can quickly sort them using the available tags [examples of a few tags of general interest are: soft-question, career, mathematics-education etc]. Some example posts are:

• How do you not forget old math? link 

• Examples of commmon false beliefs in mathematics. link 

• Open problems with monetary rewards. link 

• Proofs without words. link 

• Journals and other sources with "easy reading" papers. link 

The man who loved only numbers by Paul Hoffman is a biography of mathematician Paul Erdos. It is a good introduction to the world of a mathematician for young students.

Logicomix: An Epic Search for Truth is a graphic novel about the foundational quest in mathematics, written by Apostolos Doxiadis and Christos Papadimitriou. 

Grabiner, Judith V. "Why did Lagrange “prove” the parallel postulate?." The American Mathematical Monthly 116.1 (2009): 3-18.