10 Bertrand Russell Quotes on Mathematics

Bertrand Russell quotes on mathematics

5. Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus 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. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

64. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of highest excellence, is to be found in mathematics as surely as in poetry.

65. The rules of logic are to mathematics what those of structure are to architecture.

66. Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

67. Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the world, but every possible world, must conform.

88. If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all.

171. The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic, because in arithmetic there is knowledge, but in theology there is only opinion.

208. To choose one sock from each of infinitely many pairs of socks requires the Axiom of choice, but for shoes the Axiom is not needed.

214. If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Godel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.

219. Its enduring value was simply a deeper understanding of the central concepts of mathematics and their basic laws and interrelationships. Their total translatability into just elementary logic and a simple familiar two-place predicate, membership, is of itself a philosophical sensation.