Theorems Quotes - Page 2

• The great poem and the deep theorem are new to every reader, and yet are his own experiences, because he himself recreates them.

  Jacob Bronowski

  Justice, Diversity, Culture

  Jacob Bronowski (2011). “Science and Human Values”, p.18, Faber & Faber

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• How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

  Archimedes

  Firsts, Geometry

  Archimedes (2007). “The Works of Archimedes”, p.151, Cosimo, Inc.

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• There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry.

  John Rawls

  Doubt, Variation, Moral

  "A Theory of Justice". Book by John Rawls, 1971.

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• Papers should include more side remarks, open questions, and such. Very often, these are more interesting than the theorems actually proved. Alas, most people are afraid to admit that they don't know the answer to some question, and as a consequence they refrain from mentioning the question, even if it is a very natural one. What a pity! As for myself, I enjoy saying 'I do not know'.

  Jean-Pierre Serre

  Interesting, People, Answers

  Jean-Pierre Serre (2000). “Oeuvres, Collected Papers: 1985-1998”, Springer Verlag

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• Heaven is angered by my arrogance; my proof [of the four-color theorem] is also defective.

  Hermann Minkowski

  Color, Heaven, Arrogance

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• Toward the end of his life, Gödel feared that he was being poisoned, and he starved himself to death. His theorem is one of the most extraordinary results in mathematics, or in any intellectual field in this century. If ever potential mental instability is detectable by genetic analysis, an embryo of someone with Kurt Gödel's gifts might be aborted.

  Brian L. Silver

  Intellectual, Analysis, Might

  Brian L. Silver (2000). “The Ascent of Science”, p.506, Oxford University Press, USA

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• How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon.

  Stephen Leacock

  Fall, Struggle, Math

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• I have found a very great number of exceedingly beautiful theorems.

  Pierre de Fermat

  Beautiful, Numbers, Found

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• Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.

  Ivars Peterson

  Islands, Ontology, May

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• ...contemporary physicists come in two varieties. Type 1 physicists are bothered by EPR and Bell's Theorem. Type 2 (the majority) are not, but one has to distinguish two subvarieties. Type 2a physicists explain why they are not bothered. Their explanations tend either to miss the point entirely (like Born's to Einstein) or to contain physical assertions that can be shown to be false. Type 2b are not bothered and refuse to explain why.

  David Mermin

  Science, Two, Missing

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• This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.

  Emil Artin

  Science, Important, Doe

  Emil Artin (2016). “Geometric Algebra”, p.7, Courier Dover Publications

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• 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.

  G. H. Hardy

  Science, Tasks, Raw Materials

  G. H. Hardy (2012). “A Mathematician's Apology”, p.99, Cambridge University Press

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• An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical.

  David Berlinski

  Eye, Hands, Intuition

  David Berlinski (2000). “The Advent of the Algorithm: The Idea that Rules the World”, Houghton Mifflin

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• The scientist has to take 95 per cent of his subject on trust. He has to because he can't possibly do all the experiments, therefore he has to take on trust the experiments all his colleagues and predecessors have done. Whereas a mathematician doesn't have to take anything on trust. Any theorem that's proved, he doesn't believe it, really, until he goes through the proof himself, and therefore he knows his whole subject from scratch. He's absolutely 100 per cent certain of it. And that gives him an extraordinary conviction of certainty, and an arrogance that scientists don't have.

  Christopher Zeeman

  Believe, Science, Giving

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• Humanism . . . is not a single hypothesis or theorem, and it dwells on no new facts. It is rather a slow shifting in the philosophic perspective, making things appear as from a new centre of interest or point of sight.

  William James

  Sight, Perspective, Shifting

  Dr. William James (2013). “The William James Reader”, p.102, Simon and Schuster

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• We re-make nature by the act of discovery, in the poem or in the theorem. And the great poem and the deep theorem are new to every reader, and yet are his own experiences, because he himself re-creates them. They are the marks of unity in variety; and in the instant when the mind seizes this for itself, in art or in science, the heart misses a beat.

  Jacob Bronowski

  Art, Discovery, Missing

  Jacob Bronowski (2011). “Science and Human Values”, p.18, Faber & Faber

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• That's the problem with false proofs of true theorems; it's not easy to produce a counterexample.

  Jeffrey Shallit

  Problem, Easy, Proof

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• The story does what no theorem can quite do. It may not be "like real life" in the superficial sense: but it sets before us an image of what reality may well be like at some more central region.

  C. S. Lewis

  Real, Doe, Stories

  C. S. Lewis (2002). “Of Other Worlds: Essays and Stories”, p.27, Houghton Mifflin Harcourt

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• Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems.

  Carl Friedrich Gauss

  Choices, Justified, Introduction

  Carl Friedrich Gauss (1965). “General investigations of curved surfaces”

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• When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.

  Gottfried Leibniz

  Ideas, Words Of Wisdom, Analysis

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• A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions.

  Anatol Rapoport

  Definitions, Logical, Certain

  "Various meanings of 'theory'". American Political Science Review, 52.04, 1958.

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• It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

  Henri Poincare

  Science, Thinking, Law

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• The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance.

  Edward Mills Purcell

  Education, Mean, Important

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• Professor Eddington has recently remarked that 'The law that entropy always increases - the second law of thermodynamics - holds, I think, the supreme position among the laws of nature'. It is not a little instructive that so similar a law [the fundamental theorem of natural selection] should hold the supreme position among the biological sciences.

  Ronald Fisher

  Thinking, Law, Fundamentals

  "The Genetical Theory of Natural Selection". Book by Ronald Fisher, 1930.

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• I took a break from acting for four years to get a degree in mathematics at UCLA, and during that time I had the rare opportunity to actually do research as an undergraduate. And myself and two other people co-authored a new theorem: Percolation and Gibbs States Multiplicity for Ferromagnetic Ashkin-Teller Models on Two Dimensions, or Z2.

  Danica McKellar

  Opportunity, Ucla, Years

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