Mathematics Quote by G.H. Hardy
““It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.””
About This Quote
Source Essay: A Mathematician's Apology, 1940
Contradiction is a powerful logical strategy, more subtle than a chess sacrifice, allowing mathematicians to win by proving impossibility.
In simple terms: Contradiction wins by showing something cannot be true.
Key Takeaway
Use proof by contradiction to reveal hidden truths.
Themes
logic
strategy
mathematics
Mood
analytical
inquisitive
Type
philosophical
inspirational
When to use this quote
- research
- problem solving
- teaching
- debate
Key Concepts
proof by contradiction
game theory
Questions to Reflect On
- When have you used a contradiction to solve a problem?
- Can a contradiction ever mislead?
A Different Perspective
It may be hard to grasp for beginners lacking formal training.
![“Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we…” quote by Jean le Rond d'Alembert](https://sms4smile.com/quotes/img-quotes/0d9/jean-le-rond-d-alembert-26487_able_geometry-which-should-only-obey-physics_6945.jpg)
![“Even a pure mathematician may find his appreciation of this geometry [applied geometry] quickened, since there is no mathematician so pure that he feels no interest at all in the physical world; but, in so far as he succumbs to this temptation, he will be abandoning his purely mathematical position.” quote by G.H. Hardy](https://sms4smile.com/quotes/img-quotes/84c/g-h-hardy-2-30074_applications_even-a-pure-mathematician-may-find-his-a_1015722.jpg)
