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 possesses not only truth, but also supreme beauty.
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself.
I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept,
Mathematics is the only science where one never knows what one is talking about nor whether what is said is true.
3. 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'.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture.
The doctrine, as I understand it, consists in maintaining that the language of daily life, with words used in their ordinary meanings, suffices for philosophy, which has no need of technical terms or of changes in the significance of common terms. I find myself totally unable to accept this view. I object to it 1. Because it is insincere 2. Because it is capable of excusing ignorance of mathematics, physics and neurology in those who have had only a classical education 3. Because it is advanced by some in a tone of unctuous rectitude, as if opposition to it were a sin against democracy 4. Because it makes philosophy trivial 5. Because it makes almost inevitable the perpetuation amongst philosophers of the muddle-headedness they have taken over from common sense.
At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.
The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
The desire for excitement is very deep-seated in human beings, eI was a solitary, shy, priggish youth. I had no experience of the social pleasures of boyhood and did not miss them. But I liked mathematics, and mathematics was suspect because it has n
Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
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