Quotes

*‘Uitspraken’-blogs*

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Carl Friedrich Gauss

  • I have had my results for a long time: but I do not yet know how I am to arrive at them.

 

Georg Cantor (Duits wiskundige)

  • A set is a Many that allows itself to be thought of as a One.

Over zijn bewijs dat het lijnstuk [0,1] evenveel punten bevat als de hele n-dimensionale ruimte:

  • Ik zie het wel, maar ik geloof het niet.

 

Isaac Newton

  • It is the glory of geometry that from so few principles, it is able to accomplish so much.

 

Henri Poincaré  (Frans wiskundige)

  • It is through science that we prove, but through intuition that we discover.
  • Mathematics is the art of giving the same name to different things.

 

Bertrand Russell (Brits wiskundige)

  • Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
  • Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture.
  • Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as a sensible intelligible world.

 

Martin Gardner (Amerikaans schrijver van  populaire wiskundeboeken)

  • All mathematicians share a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.

 

Abraham Robinson (Ontdekker van de niet-standaard analyse)

  • As far as I know, only a small minority of mathematicians accept the idea that there may be mathematical facts which are true but unknowable.

 

David Armstrong  (Filosoof)

  • Mathematics is concerned with “all possible worlds”.

 

Janos Bolyai (Hongaarse wiskundige; ontdekker van een niet-Euclidische Meetkunde)

  • Out of nothing I have created a strange new universe.

 

Godfrey Hardy  (Brits wiskundige)

  • The Greeks first spoke a language which modern mathematicians can understand. So Greek mathematics is ‘permanent’, more permanent even than Greek literature.
  • Reductio ad absurdum [bewijs uit het ongerijmde] is one of a mathematician’s finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

 

Edward Lorenz  (Wiskundige, meteoroloog)

  • Mathematicians seem to have no difficulty in creating new concepts faster than the old ones become well understood.

 

Josiah Willard Gibbs (Amerikaans natuurkundige)

  • The human mind has never invented a labor-saving machine equal to algebra.

 

David Burton  (Schrijver van The History of Mathematics)

  • The advance in algebra that proved to be the most signicant was the introduction of better symbolism.
  • The liberation of algebra from the necessity of dealing only with concrete examples was largely the work of the French mathematician Francois Viète, who initiated using consonants to represent known quantities and vowels for the unknowns. This one step marked a decisive change, not only in convenience of notation but also in the abstraction of mathematical thought.

 

Dirk-Jan Struik (1894-2000)  (Wiskunde hoogleraar aan het M.I.T)

  • Vaak zijn nieuwe resultaten ontdekt als gevolg van een verbeterde notatie. Een voorbeeld is de invoering van de Hindoe-Arabische cijfers, een ander voorbeeld is Leibniz’ schrijfwijze voor differentiaalquotiënt en integraal. Een goed gekozen notatie weerpiegelt de werkelijkheid beter dan een onhandige. Daardoor lijkt het wel of een goede notatie een eigen leven leidt, de symbolen denken voor ons en zo komen nieuwe resultaten voor de dag.

 

Mario Livio (Astrofysicus, schrijver)

  • Mathematical symbols are much more than squiggles on paper.They serve as potent sources of insight into a wonderfully complex language.

 

Jean le Rond d’Alembert (Frans wiskundige)

  • Algebra is generous; she often gives more than is asked of her.

 

Albert Einstein

  • Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.

 

Hermann Hankel (Duits wiskundige)

  • In most sciences one generation tears down what another has built, and what one has established, another undoes. In mathematics alone, each generation adds a new story to the old structure.

 

Tobias Dantzig (Amerikaans wiskundige)

  • Wiskunde is de hoogste rechter; tegen haar beslissingen is geen hoger beroep mogelijk.

 

Alexander Grothendieck (Franse wiskundige)

  • The introduction of the digit 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps.

 

Jacques Hadamard (Frans wiskundige)

  • The shortest path between two truths in the real domain passes through the complex domain.

 

Philip Davis,  Reuben Hersh (Davis is wiskundige)

  • Mathematics consists of true facts about imaginary objects.

 

Bernhard Riemann

  • If only I had the theorems! Then I should find the proofs easily enough.

 

Donald Coxeter (Canadees meetkundige)

  • I believe that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered.

 

August Crelle (Duits wiskundige en ingenieur)

  • It is indeed wonderful that so simple a figure as the triangle is so inexhaustible in properties. How many as yet unknown properties of other figures may there not be?

 

John von Neumann (Hongaars/Amerikaan wiskundige)

  • In mathematics you don’t understand things. You just get used to them.
  • Truth is much too complicated to allow anything but approximations.

 

Stanley Gudder (Amerikaans wiskundige)

  • The essence of math is not to make simple things complicated, but to make complicated things simple.

 

Vladimir Arnold  (Russisch wiskundige)

  • Mathematics is the part of physics where experiments are cheap.

 

George Polya (wiskundige)

  • Mathematics consists of proving the most obvious thing in the least obvious way.

 

Israel Nathan Herstein (Amerikaans wiskundige)

  • Very often in mathematics the crucial problem is to recognize and discover what are the relevant concepts; once this is accomplished the job may be more than half done.

 

Ludwig Wittgenstein (Oostenrijks filosoof)

  • We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.

 

François Voltaire (Filosoof en schrijver)

  • There are no sects in geometry.

 

Stefan Banach (Pools wiskundige)

  • Good mathematicians see analogies. Great mathematicians see analogies between analogies.

 

Alfred North Whitehead (Brits wiskundige, filosoof)

  • Civilization advances by extending the number of important operations which we can perform without thinking of them.

 

David Hilbert (Duits wiskundige)

  • Mathematics is a game played according to certain rules with meaningless marks on paper.
  • The art of doing mathematics is finding that special case that contains all the germs of generality.
  • Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

 

Paul Halmos (Wiskundige)

  • I’m not a religious man, but it’s almost like being in touch with God when you’re thinking about mathematics. God is keeping secrets from us, and it’s fun to try to learn some of the secrets.

 

James Joseph Sylvester (Brits wiskundige)

  • It is the constant aim of the mathematician to reduce all his expressions to their lowest terms, to retrench every superfluous word and phrase, and to condense the Maximum of meaning into the Minimum of language.

 

Ian Stewart (Wiskundige, schrijver van o.a. Galois Theory)

  • Mathematics happens to require rather a lot of basic knowledge and technique.

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Kansrekening/statistiek

 

Anoniem

  • There are lies, damned lies, and statistics.

 

Ernest Rutherford (Experimenteel kernfysicus)

  • If your experiment needs a statistician, you need a better experiment.

 

Jules de Goncourt (Frans schrijver)

  • Statistics is the main of all inaccurate studies.

 

Martin Gardner (Amerikaans schrijver van  populaire wiskundeboeken)

  • In no other branch of mathematics is it so easy for experts to blunder as in probability theory.

 

Thomas Sowell (Econoom)

  • One of the first things taught in introductory statistics textbooks is that correlation is not causation. It is also one of the first things forgotten.

 

Bruno De Finetti (Schrijver van het studieboek ‘Theory of Probability: A Critical Introductory Treatment’)

  • Probability does not exist outside the mind.

 

George Boole (Brits wiskundige)

  • Probability is expectation founded upon partial knowledge.

 

Pierre Simon Laplace

  • The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which ofttimes they are unable to account.

 

Henri Poincaré  (Frans wiskundige)

  • Een kleine oorzaak, die ons ontgaat, heeft een groot effect, wat we niet zien, en dan zeggen we dat dit effect het gevolg is van toeval.
  • Het is onmogelijk om een bevredigende definitie te geven van de wiskundige kans.
  • Er moet iets mysterieus zijn aan de normaalverdeling, omdat wiskundigen denken dat het een natuurwet is, terwijl natuurkundigen ervan overtuigd zijn dat het een wiskundige stelling is.

 

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Natuurkunde

 

Galileï Galileo

  • Mathematics is the language with which God wrote the universe.

 

Isaac Newton

  • If I have been able to see further, it was only because I stood on the shoulders of giants.

 

Henri Poincaré  (Frans wiskundige)

  • Omdat we geen algemene definitie van energie kunnen geven, betekent het principe van het behoud van energie eenvoudig dat er iets is dat constant blijft.
  • Tijd en ruimte. Het is niet de natuur die dit aan ons oplegt, wij zijn het die dit opleggen aan de natuur omdat wij dit gemakkelijk vinden.

 

Richard Feynman (Natuurkundige, nobelprijswinnaar)

  • It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong.
  • You’re unlikely to discover something new without a lot of practice on old stuff.
  • To not know math is a severe limitation to understanding the world.

 

Paul Dirac (Brits natuurkundige, nobelprijswinnaar)

  • As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which nature has chosen.
  • A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data.
  • In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite!

 

Ludwig Boltzmann (Oostenrijks natuurkundige)

Over de Maxwell vergelijkingen:

  • War es ein Gott, der diese Zeichen schrieb?

 

Eugene Wigner (Natuurkundige, nobelprijswinnaar)

  • The unreasonable efficiency of mathematics in science is a gift we neither understand nor deserve.
  • It is nice to know that the computer understands the problem. But I would like to understand it too.

 

Sander Bais (Natuurkundige)

  • The miracle is not the complexity of our world, but the simplicity of the equations describing that complexity.

 

Martin Gardner (Amerikaans schrijver van  populaire wiskundeboeken)

  • The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.
  • The universe is almost like a huge magic trick and scientists are trying to figure out how it does what it does.

 

Quantummechanica

 

Niels Bohr

  • If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet.

 

Erwin Schrödinger (Oostenrijks natuurkundige, nobelprijswinnaar)

Over de kansinterpretatie van de quantummechanica:

  • I don’t like it, and I’m sorry I ever had anything to do with it.

 

Brian Greene (Natuurkundige)

  • Quantum mechanics shatters our own personal, individual conception of reality.

 

Richard Feynman (Natuurkundige, nobelprijswinnaar)

  • If you think you understand quantum mechanics, you don’t understand quantum mechanics.
  • I think I can safely say that nobody understands Quantum Mechanics.
  • The electron is a theory we use; it is so useful in understanding the way nature works that we can almost call it real.

 

Martin Gardner (Amerikaans schrijver van  populaire wiskundeboeken)

  • The only thing you can say about the reality of an electron is to cite its mathematical properties. So there’s a sense in which matter has completely dissolved and what is left is just a mathematical structure.

 

Arthur Stanley Eddington (Brits sterrenkundige)

  • There was a time when we wanted to be told what an electron is. The question was never answered. No familiar conceptions can be woven around the electron; it belongs to the waiting list.
  • Something unknown is doing we don’t know what. That is what our theory amounts to.

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Richard Dawkins (Bioloog)

  • I am against religion because it teaches us to be satisfied with not understanding the world.
  • It is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics.

 

 

 

 

 

 

 

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