I didn't do the engineering, and I didn't do the math, because I thought I understood what was going on and I thought I made a good rig. But I was wrong. I should have done it.
If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.
Medicine makes people ill, mathematics make them sad and theology makes them sinful.
With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.
There can never be surprises in logic.
There's a branch of math called the foundations of math. It's kind of like quantum mechanics. It's about how this very complex theory of math can be built up from very basic parts.
Algebra is generous; she often gives more than is asked of her.
We often hear that mathematics consists mainly of "proving theorems. " Is a writer's job mainly that of "writing sentences?"
Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things.
Many people keep deploring the low level of formal education in the United states (as defined by, say, math grades). Yet these fail to realize that the new comes from here and gets imitated elsewhere. And it is not thanks to universities, which obviously claim a lot more credit than their accomplishments warrant. Like Britain in the Industrial Revolution, America's asset is, simply, risk taking and the use of optionality, this remarkable ability to engage in rational forms fo trial and error, with no comparative shame in failing again, starting again, and repeating failure.
I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery.
. . . She knew only that if she did or said thus-and-so, men would unerringly respond with the complimentary thus-and-so. It was like a mathematical formula and no more difficult, for mathematics was the one subject that had come easy to Scarlett in her schooldays.
And you're a bad boy?" I asked. Ollie's grin was contagious. "Oh, I'm a bad, bad boy. " Cam shot his friend a look. "Yeah, as in bad at spelling, math, english, cleaning up after yourself, talking to people, and I could go on.
It is the peculiar beauty of this method, gentlemen, and one which endears it to the really scientific mind, that under no circumstance can it be of the smallest possible utility.
No employment can be managed without arithmetic, no mechanical invention without geometry.
Some people focus more on sonics. Some people focus more on story. I focus on both sonics and story, but music sometimes, just music itself, can turn into more of a maths problem. I guess everything in life is a math problem, but it can be more about an empirical route to getting the symmetry that you want, and this vibe, sonically.
Just go on. . and faith will soon return.
Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
The vast majority of us imagine ourselves as like literature people or math people. But the truth is that the massive processor known as the human brain is neither a literature organ or a math organ. It is both and more.
Our notion of symmetry is derived form the human face. Hence, we demand symmetry horizontally and in breadth only, not vertically nor in depth.