List of G. H. Hardy Quotes

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.

I Do Not Know An Instance Of A Major Mathematical Advance Initiated By A Man Past Fifty

As Littlewood Said To Me Once [of The Ancient Greeks], They Are Not Clever School Boys Or "scholarship Candidates," But "fellows Of Another College."

I Propose To Put Forward An Apology For Mathematics; And I May Be Told That It Needs None, Since There Are Now Few Studies More Generally Recognized, For Good Reasons Or Bad, As Profitable And Praiseworthy.

Bradman Is A Whole Class Above Any Batsman Who Has Ever Lived: If Archimedes, Newton And Gauss Remain In The Hobbs Class, I Have To Admit The Possibility Of A Class Above Them, Which I Find Difficult To Imagine. They Had Better Be Moved From Now On Into The Bradman Class.

It Is A Melancholy Experience For A Professional Mathematician To Find Himself Writing About Mathematics. The Function Of A Mathematician Is To Do Something, To Prove New Theorems, To Add To Mathematics, And Not To Talk About What He Or Other Mathematicians Have Done. Statesmen Despise Publicists, Painters Despise Art-critics, And Physiologists, Physicists, Or Mathematicians Have Usually Similar Feelings: There Is No Scorn More Profound, Or On The Whole More Justifiable, Than That Of The Men Who Make For The Men Who Explain. Exposition, Criticism, Appreciation, Is Work For Second-rate Minds.

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.

There Is Always More In One Of Ramanujan's Formulae Than Meets The Eye, As Anyone Who Sets To Work To Verify Those Which Look The Easiest Will Soon Discover. In Some The Interest Lies Very Deep, In Others Comparatively Near The Surface; But There Is Not One Which Is Not Curious And Entertaining.

[regarding Mathematics,] There Are Now Few Studies More Generally Recognized, For Good Reasons Or Bad, As Profitable And Praiseworthy. This May Be True; Indeed It Is Probable, Since The Sensational Triumphs Of Einstein, That Stellar Astronomy And Atomic Physics Are The Only Sciences Which Stand Higher In Popular Estimation.

A Chess Problem Is Simply An Exercise In Pure Mathematics.

Chess Problems Are The Hymn-tunes Of Mathematics.

As History Proves Abundantly, Mathematical Achievement, Whatever Its Intrinsic Worth, Is The Most Enduring Of All.

A Month's Intelligent Instruction In The Theory Of Numbes Ought To Be Twice As Instructive, Twice As Useful, And At Least 10 Times As Entertaining As The Same Amount Of 'calculus For Engineers'.

It Is Rather Astonishing How Little Practical Value Scientific Knowledge Has For Ordinary Men, How Dull And Commonplace Such Of It As Has Value Is, And How Its Value Seems Almost To Vary Inversely To Its Reputed Utility.

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.

The Public Does Not Need To Be Convinced That There Is Something In Mathematics.

[i Was Advised] To Read Jordan's 'cours D'analyse'; And I Shall Never Forget The Astonishment With Which I Read That Remarkable Work, The First Inspiration For So Many Mathematicians Of My Generation, And Learnt For The First Time As I Read It What Mathematics Really Meant.

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

In These Days Of Conflict Between Ancient And Modern Studies, There Must Surely Be Something To Be Said For A Study Which Did Not Begin With Pythagoras, And Will Not End With Einstein, But Is The Oldest And The Youngest Of All.

I Count Maxwell And Einstein, Eddington And Dirac, Among "real" Mathematicians. The Great Modern Achievements Of Applied Mathematics Have Been In Relativity And Quantum Mechanics, And These Subjects Are At Present At Any Rate, Almost As "useless" As The Theory Of Numbers.

No One Should Ever Be Bored. … One Can Be Horrified, Or Disgusted, But One Can’t Be Bored.

I Wrote A Great Deal During The Next Ten [early] Years,but Very Little Of Any Importance; There Are Not More Than Four Or Five Papers Which I Can Still Remember With Some Satisfaction.

... Philosophy Proper Is A Subject, On The One Hand So Hopelessly Obscure, On The Other So Astonishingly Elementary, That There Knowledge Hardly Counts.

Most People Have Some Appreciation Of Mathematics, Just As Most People Can Enjoy A Pleasant Tune; And There Are Probably More People Really Interested In Mathematics Than In Music. Appearances Suggest The Contrary, But There Are Easy Explanations. Music Can Be Used To Stimulate Mass Emotion, While Mathematics Cannot; And Musical Incapacity Is Recognized (no Doubt Rightly) As Mildly Discreditable, Whereas Most People Are So Frightened Of The Name Of Mathematics That They Are Ready, Quite Unaffectedly, To Exaggerate Their Own Mathematical Stupidity