--- title: "Meaning & Key Takeaway of: It (proof by contradiction) is a far…" description: "\"“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 mathe..." image: "https://sms4smile.com/quotes/i/395/g-h-hardy-2-30074_mathematics_it-proof-by-contradiction-is-a-far-finer_2967302.png" --- # It (proof by contradiction) is a far finer gambit than any… ![“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.” quote by G.H. Hardy](https://sms4smile.com/quotes/i/395/g-h-hardy-2-30074_mathematics_it-proof-by-contradiction-is-a-far-finer_2967302.png) [Download](https://sms4smile.com/quotes/i/395/g-h-hardy-2-30074_mathematics_it-proof-by-contradiction-is-a-far-finer_2967302.png) [Open image](https://sms4smile.com/quotes/i/395/g-h-hardy-2-30074_mathematics_it-proof-by-contradiction-is-a-far-finer_2967302.png) > ““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.”” [G.H. Hardy](https://sms4smile.com/quotes/author/g-h-hardy-2/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. 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. ★ ★ ★ ★ ★ No ratings yet [Mathematics](https://sms4smile.com/quotes/about/mathematics/) ## Related quotes > [By what right does White, in an absolutely even position, such as after move one, when both sides have advanced 1. e4, sacrifice a…](https://sms4smile.com/quotes/emanuel-lasker/by-what-right-does-white-in-an-absolutely-even-position-such-as-after/) [Emanuel Lasker](https://sms4smile.com/quotes/author/emanuel-lasker/) > [This sacrifice of a pawn nowadays is only played for drawing purposes. 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