Music has a lot in common with mathematics. But in music, two and two need not make four: they add up to whatever you wish.
One would normally define a "religion" as a system of ideas that contain statements that cannot be logically or observationally demonstrated. . . Gödels theorem not only demonstrates that meathematics is a religion, but shows that mathematics is the only religion that proves itself to be one!
I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.
The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving. . . The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.
Yet things are knowable! They are knowable, because, being from one, things correspond. There is a scale: and the correspondence of heaven to earth, of matter to mind, of the part to the whole, is our guide. As there is a science of stars, called astronomy; and science of quantities, called mathematics; a science of qualities, called chemistry; so there is a science of sciences,--I call it Dialectic,--which is the Intellect discriminating the false and the true.
The public does not need to be convinced that there is something in mathematics.
Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.
Chess, like mathematics and music, is a nursery for child prodigies.
The Handmaiden of the Sciences.
Mathemata mathematicis scribuntur Mathematics is written for mathematicians De Revolutionibus
What is mathematics? Ask this question of person chosen at random, and you are likely to receive the answer "Mathematics is the study of number. " With a bit of prodding as to what kind of study they mean, you may be able to induce them to come up with the description "the science of numbers. " But that is about as far as you will get. And with that you will have obtained a description of mathematics that ceased to be accurate some two and a half thousand years ago!
James Brown is important because he decorates the clock correctly and he's good with lower mathematics. Don't get me wrong - he's good.
Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
It is perplexing to see the flexibility of the so-called 'exact sciences' which by cast-iron laws of logic and by the infallible help of mathematics can lead to conclusions which are diametrically opposite to one another.
I had drawings that were the first time that mathematics was put into visual form.
Mathematics is not a spectator sport!
Inspiration is constantly in the air. It's up to us to develop the sensitivity to pick up on it.
There are only two kinds of certain knowledge: Awareness of our own existence and the truths of mathematics.
If you don't donate to Obama and you're a major corporation like Big Oil, then they're gonna blame you for climate change, destroying the planet and they're gonna get everybody turned against you and hating your guts and so forth, and that's how they operate. That's not how Trump operates. That's not how Mike Pence operates. They understand the simple mathematics of economics.
The abstract analysis of the world by mathematics and physics rests on the concepts of space and time.