Weyl, Hermann (1885 - 1955)
We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context. UnterrichtsblŠtter fŸr Mathematik und Naturwissenschaften, 38, 177-188 (1932). Translation by Abe Shenitzer appeared in The American Mathematical Monthly, v. 102, no. 7 (August-September 1995), p. 646.
Lobatchevsky, Nikolai
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Newman, James R.
Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications. In J. R. Newman (ed.) The World of Mathematics, New Yorl: Simon and Schuster, 1956.
Russell, Bertrand (1872-1970)
"But," you might say, "none of this shakes my belief that 2 and 2 are 4." You are quite right, except in marginal cases -- and it is only in marginal cases that you are doubtful whether a certain animal is a dog or a certain length is less than a meter. Two must be two of something, and the proposition "2 and 2 are 4" is useless unless it can be applied. Two dogs and two dogs are certainly four dogs, but cases arise in which you are doubtful whether two of them are dogs. "Well, at any rate there are four animals," you may say. But there are microorganisms concerning which it is doubtful whether they are animals or plants. "Well, then living organisms," you say. But there are things of which it is doubtful whether they are living organisms or not. You will be driven into saying: "Two entities and two entities are four entities." When you have told me what you mean by "entity," we will resume the argument. In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Newman, James R.
The most painful thing about mathematics is how far away you are from being able to use it after you have learned it. In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Whitehead, Alfred North (1861 - 1947)
Through and through the world is infested with quantity: To talk sense is to talk quantities. It is not use saying the nation is large .. How large? It is no use saying the radium is scarce ... How scarce? You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves. In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Wittgenstein, Ludwig (1889-1951)
Mathematics is a logical method ... Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics. Tractatus Logico Philosophicus, New York, 1922, p. 169.
Adams, Douglas (1952 - )
Bistromathics itself is simply a revolutionary new way of understanding the behavior of numbers. Just as Einstein observed that space was not an absolute but depended on the observer's movement in space, and that time was not an absolute, but depended on the observer's movement in time, so it is now realized that numbers are not absolute, but depend on the observer's movement in restaurants. Life, the Universe and Everything. New York: Harmony Books, 1982.
Adams, Douglas (1952 - )
The first nonabsolute number is the number of people for whom the table is reserved. This will vary during the course of the first three telephone calls to the restaurant, and then bear no apparent relation to the number of people who actually turn up, or to the number of people who subsequently join them after the show/match/party/gig, or to the number of people who leave when they see who else has turned up. The second nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a recipriversexcluson, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive. Recipriversexclusons now play a vital part in many branches of math, including statistics and accountancy and also form the basic equations used to engineer the Somebody Else's Problem field. The third and most mysterious piece of nonabsoluteness of all lies in the relationship between the number of items on the bill, the cost of each item, the number of people at the table and what they are each prepared to pay for. (The number of people who have actually brought any money is only a subphenomenon of this field.) Life, the Universe and Everything. New York: Harmony Books, 1982.
Adams, Douglas (1952 - )
Numbers written on restaurant bills within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe. This single statement took the scientific world by storm. It completely revolutionized it. So many mathematical conferences got held in such good restaurants that many of the finest minds of a generation died of obesity and heart failure and the science of math was put back by years. Life, the Universe and Everything. New York: Harmony Books, 1982.
Kepler, Johannes (1571-1630)
Where there is matter, there is geometry. (Ubi materia, ibi geometria.) J. Koenderink Solid Shape, Cambridge Mass.: MIT Press, 1990
Aristotle
The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. Metaphysica, 3-1078b.
Kepler, Johannes (1571-1630)
The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.
Gardner, Martin
Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of? They're not made out of anything. 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. Gardner on Gardner: JPBM Communications Award Presentation. Focus-The Newsletter of the Mathematical Association of America v. 14, no. 6, December 1994.
Arbuthnot, John
The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning; and when they cannot it's a sign our knowledge of them is very small and confus'd; and when a Mathematical Reasoning can be had it's as great a folly to make use of any other, as to grope for a thing in the dark, when you have a Candle standing by you. Of the Laws of Chance. (1692)
Galileo Galilei
"É The universe, which stands continually open to our gazeÉ cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematicsÉ"
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