Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination. 

"A mathematician is a device for turning coffee into theorems" (P. Erdos)
Addendum: American coffee is good for lemmas. 

An engineer thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care. 

Old mathematicians never die; they just lose some of their functions. 

Mathematicians are like Frenchmen: whatever you say to them, they translate it into their own language, and forthwith it means something entirely different. -- Goethe 

Mathematics is the art of giving the same name to different things. -- J. H. Poincare