G. H. Hardy — A Mathematician’s Apology
34 published claims from this book.
- A mathematician’s apology for mathematics doubles as a self-defense.
- Academics reject wealth not from caution but from ambition for lasting fame.
- All of Hardy’s major mathematical work came from two collaborations
- Applied mathematicians must discard their finest ideas for failing to match reality
- Applied mathematics selects maps that fit physical facts
- Beauty is the first test of mathematics and ugly mathematics has no permanent place
- By the utilitarian test even great mathematicians wasted their lives
- Chess players’ appreciation of beauty proves widespread taste for mathematics
- Even Russell’s greatest logical work may be forgotten in a century.
- Hardy finds his only justification in having created something of intrinsic worth
- Ideas wear less with time than words do, making mathematical patterns more durable
- Justifying a life requires separating value from motivation.
- Mathematical facts are true independently of human thought
- Mathematical fame can reward errors and mediocrity
- Mathematical patterns outlast artistic ones because they are built purely out of ideas
- Mathematical proofs gain beauty through economy and lack of variation
- Mathematical work is valuable as a memorial in the same way art is
- Mathematicians value uselessness because science serves evil in war
- Mathematics is among the most specialized of human talents.
- Mathematics is more popular than music but fear of the name masks this
- Mathematics offers its practitioners refuge from a mad world
- Mathematics spans from before Pythagoras to beyond Einstein
- Newton’s mathematical creativity had ended by age forty.
- No major mathematical advance has ever been initiated past age fifty.
- Permanent creations like geometrical theorems exceed ordinary human powers
- Physical reality fails to match common sense, while mathematical reality does not
- Pure geometries depict no physical reality of the world
- Pure mathematics cannot be turned to warlike purposes
- Pure mathematics proves more useful than applied mathematics
- Purely mathematical theories can gain unforeseen practical applications
- Puzzle-column curiosities fail as serious theorems because they admit no generalization.
- The reductio ad absurdum risks an entire proof in one move
- Useful mathematics tends to be aesthetically dull
- Useful subjects are not useful for most people to learn