A mathematical proof is beautiful, but when you're finished, it's really only about one thing. A story can be about many things.
The extraction tax is based in part on production times the market value at the wellhead, so any downturn in the market price is going to be a mathematical impact on the shale tax. But beyond that, it also concerns me because it also impacts the health of the industry.
I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.
Love was even more mathematical than poetry. It was the pure mathematics of the spirit.
Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
Our external physical reality is a mathematical structure.
Criticized for using formal mathematical manipulations, without understanding how they worked: Should I refuse a good dinner simply because I do not understand the process of digestion?
Music is a science, in many ways it's mathematical.
One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers.
The best material model of a cat is another, or preferably the same, cat.
Mathematical Analysis is. . . the true rational basis of the whole system of our positive knowledge.
It is a safe rule to apply that, when a mathematical or philosophical author writes with a misty profundity, he is talking nonsense.
At the earliest drawings of the fractal curve, few clues to the underlying mathematical structure will be seen.
We have failed to protect science against speculative extensions of nature, continuing to assign physical and mathematical properties to hypothetical entities beyond what is observable in nature.
After two years of undergraduate study, it was clear that I was bored by the regime of problem-solving required by the Cambridge mathematical tripos. A very sensitive mathematics don recommended that I talk to the historian of astronomy, Michael Hoskin, and the conversation led me to enroll in the History and Philosophy of Science for my final undergraduate year.
It's the vision of the composer that we have to determine, and not the absolute mathematical adherence of the score. In my experience, there have been occasions where I feel that a composer has not notated something as they meant to have it represented.
Mathematical Analysis is as extensive as nature herself.
We feel certain that the extraterrestrial message is a mathematical code of some kind. Probably a number code. Mathematics is the one language we might conceivably have in common with other forms of intelligent life in the universe. As I understand it, there is no reality more independent of our perception and more true to itself than mathematical reality.
I would have private conversations with [Buckminster Fuller]. I once had an argument, for four hours, about the existence of the Mobius strip. Because he believed in the Klein Bottle, you see. And I said, "How in hell can you claim to believe in the Klein Bottle and think that the Mobius strip is dubious?" He said, "Well, it's a torus. " I don't know what he had in his mind as a mathematical background, because I don't think he got topology. Because, in other words, the Mobius strip didn't have angles in it.
Here is a quilted book about mathematical practice, each patch wonderfully prepared. Part invitation to number theory, part autobiography, part sociology of mathematical training, Mathematics without Apologies brings us into contemporary mathematics as a living, active inquiry by real people. Anyone wanting a varied, cultured, and penetrating view of today's mathematics could find no better place to engage.