A Chess Problem Is Simply An Exercise

No Mathematician Should Ever Allow Himself To Forget That Mathematics, More Than Any Other Art Or Science, Is A Young Man's Game

If Intellectual Curiosity, Professional Pride, And Ambition Are The Dominant Incentives To Research, Then Assuredly No One Has A Fairer Chance Of Gratifying Them Than A Mathematician.

I Have Never Done Anything 'useful'. No Discovery Of Mine Has Made, Or Is Likely To Make, Directly Or Indirectly, For Good Or Ill, The Least Difference To The Amenity Of The World... Judged By All Practical Standards, The Value Of My Mathematical Life Is Nil; And Outside Mathematics It Is Trivial Anyhow. I Have Just One Chance Of Escaping A Verdict Of Complete Triviality, That I May Be Judged To Have Created Something Worth Creating. And That I Have Created Something Is Undeniable: The Question Is About Its Value.

In [great Mathematics] There Is A Very High Degree Of Unexpectedness, Combined With Inevitability And Economy.

The Primes Are The Raw Material Out Of Which We Have To Build Arithmetic, And Euclid's Theorem Assures Us That We Have Plenty Of Material For The Task.