Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.
A bird is an instrument working according to mathematical law, which instrument it is within the capacity of man to reproduce with all its movements.
Wave particle duality is a core feature of our world. Or rather, we should say, it is a core feature of our mathematical descriptions of our world. But what is critical to note here is that, however ambiguous our images, the universe itself remains whole and is manifestly not fracturing into schizophrenic shards. It is this tantalizing wholeness and the thing itself that drives physicists onward like an eternally beckoning light that seems so teasingly near. It is always out of reach.
How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.
The orthodox believers in God are divided into two camps, one of which maintains that the existence of God is as demonstrable as any mathematical proposition, while the other asserts that his existence is not demonstrable to the intellect.
Mathematical high culture collides with pop culture and all hell breaks loose! Harris takes us on a wild ride--never a dull moment!
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.
If there was some sort of mathematical equation for beauty, I don't know if I would be the algorithm. I've always been OK with that. I'm not a supermodel. That's not what I do. What I do is music. I want my fans to feel the way I do, to know what they have to offer is just as important, more important, than what's happening on the outside.
The Handmaiden of the Sciences.
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.
If all art aspires to the condition of music, all the sciences aspire to the condition of mathematics.
Many persons entertain a prejudice against mathematical language, arising out of a confusion between the ideas of a mathematical science and an exact science. . . . in reality, there is no such thing as an exact science.
It is almost possible to say that there is a mathematical relationship between the beauty of his surroundings and the activity of the child; he will make discoveries rather more voluntarily in a gracious setting than in an ugly one.
Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it.
A physical law must possess mathematical beauty.
The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom to admit to the priesthood.
It is clear that economics, if it is to be a science at all, must be a mathematical science.
Poverty is a mathematical proof of the fact that mankind is a big failure!
Homeopathy seemed. . . both mathematical and poetic.
The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our age has to boast.