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Proof Quotes

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Proof Quotes

“I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions - they are not just repetitions of each other.”

ThinkingShouldSaidTwoDifferentReasonLawTenWeaknessShould HaveMathematicsProofRepetitionReciprocityDifferent DirectionsTheoremsStrength And WeaknessQuadratics
Author:Michael Atiyah
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“The man who has learned that three plus one are four doesn't have to go through a proof of that assertion with coins, or dice, or chess pieces, or pencils. He knows it, and that's that. He cannot conceive a different sum. There are mathematicians who say that three plus one is a tautology for four, a different way of saying "four" ... If three plus one can be two, or fourteen, then reason is madness.”

IfsKnowsMenWayTwoDifferentReasonThreeNumbersPiecesFourHe ManMadnessMathematicsProofChessDifferent WaysPlusMathematicianCoinsPencilsAssertionFourteenDiceTautologyChess Pieces
Book:The Book of Sand and Shakespeare's Memory
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“The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.”

StatesGoalStepsObjectsArgumentMathematicsPropertyDefinitionsVariousProofStatementsMathematicalReasoningIntroducingJustifiedConvincingPresentingTheoremsSmall Steps
Author:IU?. I. Manin
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“I don't think there's a problem. First of all, I don't think music turns people into social liabilities. Because you hear a lyric - there's no medical proof that a person hearing a lyric is going to act out the lyric. There's also no medical proof that if you hear any collection of vowels and consonants, that the hearing of that collection is going to send you to Hell.”

PeopleIfsThinkingFirstsPersonsProblemTurnsSocialHellAtheismHearingPositive AtheismProofMedicalCollectionsLiabilityVowelsConsonants
Author:Frank Zappa
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“Trust, like love, is a word that has great power Everybody deserves their own space, in their own time. You are even entitled to keep secrets. But it is not secrets that destroys things, suspicion does. For it may take many years to build trust, sometimes.. all it takes is suspicion, you don't even need proof to destroy trust. So, if you say you can trust someone, you're admitting to something that is even greater than love. Trust, like love, is a word that has great power.”

IfsNeedsYearsMayDoeSometimesSpaceLove IsSecretGreaterTrustDeserveProofSuspicionEntitledGreat PowerAdmittingLike LoveTrust Love
Author:Rita Zahara
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“You can be a thorough-going Neo-Darwinian without imagination, metaphysics, poetry, conscience, or decency. For 'Natural Selection' has no moral significance: it deals with that part of evolution which has no purpose, no intelligence, and might more appropriately be called accidental selection, or better still, Unnatural Selection, since nothing is more unnatural than an accident. If it could be proved that the whole universe had been produced by such Selection, only fools and rascals could bear to live.”

IfsStillsWholeMightPoetryPurposeUniverseImaginationNaturalDealsMoralFoolBearsEvolutionConscienceIntelligenceAccidentsProofSignificanceMetaphysicsSelectionDecencyUnnaturalThoroughNatural SelectionRascalsAppropriateness
Author:George Bernard Shaw
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“If any doubt has arisen as to me, my country [Virginia] will have my political creed in the form of a "Declaration &c." which I was lately directed to draw. This will give decisive proof that my own sentiment concurred with the vote they instructed us to give.”

IfsGivingCountryFormPoliticalMy OwnDoubtDrawsVoteProofSentimentsCreedsDeclarationVirginia
Book:The Works of Thomas Jefferson: Correspondence 1771 - 1779, the Summary View, and the Declaration of Independence
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