(Source: quoted by Jon Barwise)
(Source: Quoted by Jon Barwise)
Profession: mathematician, author.
Profession: mathematician, philosopher.
It can be shown that a mathematical web of some kind can be woven about any universe containing several objects. The fact that our universe lends itself to mathematical treatment is not a fact of any great philosophical significance.
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 paintings or music, yet sublimely pure and capable of a stern perfection such as only the greatest art can show.
Mathematics takes us still further from what is human into the region of absolute necessity, to which not only the actual world, but every possible world, must conform.
Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.
The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our age has to boast.
To create a good philosophy you should renounce metaphysics but be a good mathematician.
What is best in mathematics deserves not merely to be learned as a task but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.
Zeno was concerned with three problems . . . These are the problem of the infinitesimal, the infinite, and continuity ... From his to our own day, the finest intellects of each generation in turn attacked these problems, but achieved broadly speaking nothing ... Weierstrass, Dedekind, and Cantor, ... have completely solved them. Their ... solutions are so clear as to leave no longer the slightest doubt or difficulty. This achievement is probably the greatest of which our age can boast.
It is a pleasant surprise to [the mathematician] and an added problem if he finds that the arts can use his calculations, or that the senses can verify them, much as if a composer found that sailors could heave better when singing his songs.
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