Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. Whereas mathematics began merely as a calculational tool for computation and tabulation of quantities, it has blossomed into an extremely rich and diverse set of tools, terminologies, and approaches which range from the purely abstract to the utilitarian.
Related subjects include: Statistics and Probability, Computer Science and Engineering, History and Philosophy of Science, Leisure Reading — Science and Technology.
Related topics include: Your Scholarly Identity (ORCID), Designing Documents with LaTeX, Research Data Services, Scholarly Communication, Open Access Publishing at Notre Dame.
One readable magazine about all things mathematical is The Mathematical Intelligencer.
The most accessible encyclopedia, with definitions, is Wolfram Math World. Another authoritative source, although very technical, is the Encyclopaedia of Mathematics, edited by M. Hazewinkel. Print volumes may be requested from the Hesburgh Libraries Annex.
Improving Your Proofs
There are a number of books on writing better mathematical proofs. Here are two that may help:
One of the best sources for biographies of mathematicians is the MacTutor History of Mathematics Archive.
Careers in mathematics are discussed in depth in the Bureau of Labor Statistics' Occupational Outlook Handbook's group of Math Occupations.