Mathematics Quotes - Page 29

• On the basis of my historical experience, I fully believe that mathematics of the 25th century will be as different from that of today as the latter is from that of the 16th century.

  George Sarton

  Believe, Historical, Different

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• Ask not what's inside your head but what your head's inside of.

  William Mace

  Asks

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• Why, for example, should a group of simple, stable compounds of carbon, hydrogen, oxygen, and nitrogen struggle for billions of years to organize themselves into a professor of chemistry? What's the motive?

  Robert M. Pirsig

  Struggle, Simple, Oxygen

  Robert M. Pirsig (1991). “LILA An Inquriry into Morals”

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• I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.

  Roger Penrose

  Plato, Ideas, Mind

  Roger Penrose (1999). “The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics”, p.554, OUP Oxford

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• From nothing I have created another entirely new world.

  Janos Bolyai

  World, New World

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• A peculiarity of the higher arithmetic is the great difficulty which has often been experienced in proving simple general theorems which had been suggested quite naturally by numerical evidence.

  Harold Davenport

  Simple, Arithmetic, Difficulty

  Harold Davenport (1970). “The higher arithmetic: an introduction to the theory of numbers”

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• Success is the result of hard work.

  Thomas A. Edison

  Hard Work, Results, Hard Work Pays Off

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• The purpose of life is to conjecture and prove.

  Paul Erdos

  Purpose, Life Is, Conjecture

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• It saddens me that educated people don't even know that my subject exists.

  Paul Halmos

  People, Educated, Subjects

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• The heart of mathematics is its problems.

  Paul Halmos

  Heart, Problem

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• If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof.

  G. H. Hardy

  Sorry, Sorrow, Would Be

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• The student is best taught who is told the least

  Robert Lee Moore

  Taught, Students

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• One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory.

  Hermann Weyl

  Men, Numbers, Quality

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• Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

  David Hilbert

  Ontology, Vitality, Connections

  "Mathematical Problems". Lecture delivered before the International Congress of Mathematicians at Paris, translated by Maby Winton Newson, mathcs.clarku.edu. 1900.

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• Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.

  David Berlinski

  Lying, Logic, Arithmetic

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

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• An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In the best of circumstances, the relationship is clear enough so that the mathematician can submit his or her reasoning to an informal checklist, passing from step to step with the easy confidence the steps are small enough so that he cannot be embarrassed nor she tripped up.

  David Berlinski

  Steps, Assuming, Enough

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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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• For the most part, it is true, ordinary men and women regard mathematics with energetic distaste, counting its concepts as rhapsodic as cauliflower. This is a mistake-there is no other word. Where else can the restless human mind find means to tie the infinite in a finite bow?

  David Berlinski

  Mistake, Mean, Men

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

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• Computation involves going from a question to an answer. Mathematics involves going from an answer to a question.

  Peter Hilton

  Answers, Computation

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• The best therapy for emotional blocks to math is the realization that the human race took centuries or millennia to see through the mist of difficulties and paradoxes which instructors now invite us to solve in a few minutes.

  Lancelot Hogben

  Block, Math, Emotional

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• University President: Why is it that you physicists always require so much expensive equipment? Now the Department of Mathematics requires nothing but money for paper, pencils, and erasers . . . and the Department of Philosophy is better still. It doesn't even ask for erasers.

  Isaac Asimov

  Money, Philosophy, President

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• Mathematics, the non-empirical science par excellence . . . the science of sciences, delivering the key to those laws of nature and the universe which are concealed by appearances.

  Hannah Arendt

  Nature, Keys, Law

  Hannah Arendt (1981). “The Life of the Mind”, p.23, Houghton Mifflin Harcourt

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• Analytic It is clear that the definition of "logic" or "mathematics" must be sought by trying to give a new definition of the old notion of "analytic" propositions.

  Bertrand Russell

  Giving, Trying, Definitions

  Bertrand Russell (2009). “The Basic Writings of Bertrand Russell”, p.155, Routledge

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• Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".

  Bertrand Russell

  Facts, Logic, Study

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• When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong. Perhaps the adjective 'elderly' requires definition. In physics, mathematics, and astronautics it means over thirty; in the other disciplines, senile decay is sometimes postponed to the forties. There are, of course, glorious exceptions; but as every researcher just out of college knows, scientists of over fifty are good for nothing but board meetings, and should at all costs be kept out of the laboratory!

  Arthur C. Clarke

  Mean, College, Elderly

  Profiles of the Future ch. 2 (1962).

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