Young Men Should Prove Theorems, Old Men

The Mathematician Is In Much More Direct Contact With Reality. ... [whereas] The Physicist's Reality, Whatever It May Be, Has Few Or None Of The Attributes Which Common Sense Ascribes Instinctively To Reality. A Chair May Be A Collection Of Whirling Electrons.

It Is Hardly Possible To Maintain Seriously That The Evil Done By Science Is Not Altogether Outweighed By The Good. For Example, If Ten Million Lives Were Lost In Every War, The Net Effect Of Science Would Still Have Been To Increase The Average Length Of Life.

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.

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

A Chess Problem Is Simply An Exercise In Pure Mathematics.