In a mathematical examination ... the examiner is not allowed to content himself with testing the competence and the knowledge of the candidate; his instructions are to provide a test of more than that, of initiative, imagination, and even of some sort of originality. And as there is only one test of originality in mathematics, namely the accomplishment of original work, and as it is useless to ask a youth of twenty-two to perform original research under examination conditions, the examination necessarily degenerates into a kind of game, and instruction for it into initiation into a series of stunts and tricks.

— G. H. Hardy

These [mathematics] contests are a bit like spelling bees. There is some connection between good spelling and good writing, but the winner of the state spelling bee does not necessarily have the talent to become a good writer, and some fine writers are not good spellers. If there was a popular confusion between good spelling and good writing, many potential writers would be unnecessarily discouraged.

— William Paul Thurston

Professional mathematics is not a sport. In particular, whether one is “better” than one’s peers is not really the right thing to focus on; the more important thing is to ensure that one can do good mathematics in one’s chosen research area.

— Terence Tao

What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant.

— Laurent Schwartz

There was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates, almost by sleight of hand, the most forbidding subjects.

— Alexander Grothendieck

The most profound contributions to mathematics are often made by tortoises rather than hares.

— William Timothy Gowers

I tend to be slower than most mathematicians to understand an argument.

— Sir Andrew Wiles

Problem-solving should never be practiced for its own sake; and particularly tricky problems must be excluded altogether.

— André Weil

In one way I think my early involvement with Mathematical Olympiads and suchlike has damaged my mathematical taste: I still have this feeling that short, elegant problems should have short, elegant solutions, and that one should be able to do mathematics without absorbing a lot of difficult stuff first. Unfortunately, this is all false.

— Gareth McCaughan

I was never interested in artificial puzzles.

— Goro Shimura

I was never fascinated by puzzles or intellectual games.

Introduction to Finite and Infinite Series and Related Topics by J. H. Heinbockel

http://www.amazon.com/Elliptic-Curves-Function-Geometry-Arithmetic/dp/0521658179/ref=sr_1_3?s=books&ie=UTF8&qid=1419509745&sr=1-3#customerReviews

Elementary Applied Topology Ghrist

Bill Burke, Div, Grad, and Curl are Dead

http://www.amazon.com/Handbook-Analysis-Foundations-Eric-Schechter/dp/0126227608