I’ve missed more than $9000$ shots in my career. I’ve lost almost $300$ games. $26$ times I’ve been trusted to take the game winning shot and missed. I’ve failed over and over and over again in my life. And that is why I succeed. —Michael Jordan

Study actively. Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?-Halmos

To be a mathematician you must love mathematics more than family, religion, money, comfort, pleasure, glory.-Halmos

“A man must love a thing very much if he not only practices it without any hope of fame or money, but even practices it without any hope of doing it well.” – G.K. Chesterton

"Many people say that it is the intellect which makes a great scientist. They are wrong: it is character." -- Albert Einstein

A person who never made a mistake never tried anything new.--Albert Einstein

In mathematics you don’t understand things. You just get used to them.-John von Neumann

A mathematician is a blind man in a dark room looking for a black cat which isn’t there!-Charles Darwin

We must know — we will know!---David Hilbert

"Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty"- Archimedes

The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it-Carl Friedrich Gauss

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.-Henri Poincare

The memory of God will not come to the selfish man. - Vivekananda

A sign of a great mathematician is that you can actually read and understand their proofs.

“Ever tried. Ever failed. No matter. Try again. Fail again. Fail better.” - Beckett

It’s also good to remember that professional mathematics is not a sport (in sharp contrast to mathematics competitions). The objective in mathematics is not to obtain the highest ranking, the highest “score”, or the highest number of prizes and awards; instead, it is to increase understanding of mathematics (both for yourself, and for your colleagues and students), and to contribute to its development and applications. For these tasks, mathematics needs all the good people it can get.- Terence Tao

Write down every definition, every theorem, and every proof. The definitions and theorems should be produced verbatim from the book since it is important to ensure that your understanding of the rigor is correct. However, the proofs should be written in your own words. -AD

Life is like a boxing bout.You are not lost when you fall down, you are lost when you refuse to get up.- Muhammad Ali