The method of "postulating" what we want has many advantages; they are the same as the advantages of theft over honest toil.
Introduction to Mathematical Philosophy, New York and London, 1919, p 71.
Loci: Convergence
Mathematical Quotations
Our library of quotations is organized alphabetically by surname of the author.
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Immanuel Kant (1724-1804)
All human knowledge thus begins with intuitions, proceeds thence to concepts, and ends with ideas.
Immanuel Kant (1724-1804)
The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.
Kaplan, Abraham
Mathematics is not yet capable of coping with the naivete of the mathematician himself.
Irving Kaplansky
We [he and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury.
Samuel Karlin (1924-2007)
The purpose of models is not to fit the data but to sharpen the questions.
Kasner and Newman
The testament of science is so continually in a flux that the heresy of yesterday is the gospel of today and the fundamentalism of tomorrow.
Kasner and Newman
Perhaps the greatest paradox of all is that there are paradoxes in mathematics.
Kasner and Newman
When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently it must first set its affairs in order at home.
Kasner and Newman
Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.
Kasner and Newman
Mathematics is the science which uses easy words for hard ideas.
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