I Was At My Best

A Chess Problem Is Genuine Mathematics, But It Is In Some Way "trivial" Mathematics. However, Ingenious And Intricate, However Original And Surprising The Moves, There Is Something Essential Lacking. Chess Problems Are Unimportant. The Best Mathematics Is Serious As Well As Beautiful-"important" If You Like, But The Word Is Very Ambiguous, And "serious" Expresses What I Mean Much Better.

If A Man Is In Any Sense A Real Mathematician, Then It Is A Hundred To One That His Mathematics Will Be Far Better Than Anything Else He Can Do, And That He Would Be Silly If He Surrendered Any Decent Opportunity Of Exercising His One Talent In Order To Do Undistinguished Work In Other Fields. Such A Sacrifice Could Be Justified Only By Economic Necessity Of Age.

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

The Fact Is There Are Few More Popular Subjects Than Mathematics. Most People Have Some Appreciation Of Mathematics, Just As Most People Can Enjoy A Pleasant Tune.

A Mathematician ... Has No Material To Work With But Ideas, And So His Patterns Are Likely To Last Longer, Since Ideas Wear Less With Time Than Words.