For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems.
There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down.
In any non-trivial axiomatic system, there are true theorems which cannot be proven.
It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations,' are simply the notes of our observations.
We often hear that mathematics consists mainly of 'proving theorems.' Is a writer's job mainly that of 'writing sentences'
A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.
The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.
A Mathematician is a machine for turning coffee into theorems.
Beginning from a few intuitive postulates, far reaching consequences could be derived, and I took immediately to the sport of proving theorems.
Economists often like startling theorems, results which seem to run counter to conventional wisdom.
Young men should prove theorems, old men should write books.
A mathematician is a device for turning coffee into theorems.
I have found a very great number of exceedingly beautiful theorems.
All great theorems were discovered after midnight.
The Mean Value Theorem is the midwife of calculus not very important or glamorous by itself, but often helping to delivery other theorems that are of major significance.