The mathematical sciences particularly exhibit order symmetry and limitations; and these are the greatest forms of the beautiful.
All exact science is dominated by the idea of approximation.
I had a feeling once about mathematics - that I saw it all... but it was after dinner and I let it go.
To understand this for sense it is not required that a man should be a geometrician or a logician, but that he should be mad.
If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
Obvious is the most dangerous word in mathematics.
Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.
What seems certain is that Pythagoras developed the idea of mathematical logic. He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths which were independent of opinion of prejudice and which were more absolute than any previous knowledge.
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.
Much of what I make is geometric, and has a kind of almost mathematical logic to the form.
I think part of the appeal of mathematical logic is that the formulas look mysterious - you write backward Es!
Here at Wisconsin we didn't get an undergraduate course in mathematical logic until the '60s.
It is all about numbers. It is all about sequence. It's the mathematical logic of being alive. If everything kept to its normal progression, we would live with the sadness-cry and then walk-but what really breaks us cleanest are the losses that happen out of order.
I am allowed to use plain English because everybody knows that I could use mathematical logic if I chose.
Russell's books should be bound in two colours, those dealing with mathematical logic in red - and all students of philosophy should read them; those dealing with ethics and politics in blue - and no one should be allowed to read them.
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