The mathematics of quantum mechanics very accurately describes how our universe works. And it tells us our reality is continually branching into different possibilities, just like a coral.
The power of mathematics is often to change one thing into another, to change geometry into language.
Except in pure mathematics, nothing is known for certain (although much is certainly false).
The fact that mathematics does such a good job of describing the Universe is a mystery that we don't understand. And a debt that we will probably never be able to repay.
When we talk about the impact inside mathematics, and applications in the sciences, [Mandelbrot] is one of the most important figures of the last 50 years.
Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functions together, each valid in another interval or bracket of income. An archeologist who, five thousand years from now, shall unearth some of our income tax returns together with relics of engineering works and mathematical books, will probably date them a couple of centuries earlier, certainly before Galileo and Vieta.
I think, therefore I laugh.
A good calculator does not need artificial aids.
The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. "Perfect numbers" certainly never did any good, but then they never did any particular harm.
For a good notation has a subtlety and suggestiveness which at times make it seem almost like a live teacher.
Algebra and money are essentially levelers; the first intellectually, the second effectively.
In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished.
There is no nature at an instant.
I am not a teacher. I am an awakener.
Why do children dread mathematics? Because of the wrong approach. Because it is looked at as a subject.
Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.
The main application of Pure Mathematics is to make you happy.
These long chains of perfectly simple and easy reasonings by means of which geometers are accustomed to carry out their most difficult demonstrations had led me to fancy that everything that can fall under human knowledge forms a similar sequence; and that so long as we avoid accepting as true what is not so, and always preserve the right order of deduction of one thing from another, there can be nothing too remote to be reached in the end, or to well hidden to be discovered.
At the beginning of the new millennium, we still do not know why mathematics is true and whether it is certain. But we know what we do not know in an immeasurably richer way than we did. And learning this has been a remarkable achievement-among the greatest and least-known of the modern era.
We the undersigned, intend to establish an instruction and training institution which differs from the common elementary schools principally in that it will embrace, outside of (in addition to) the general and elementary curriculum, all branches of the classical high school, which are necessary for a true Christian and scientific education, such as: Religion, the Latin, Greek, Hebrew, German, French and English languages; History, Geography, Mathematics, Physics, natural history, Introduction to Philosophy, Music, and Drawing.
Football is not played on paper, it is played on a pitch. This game is not mathematics and in football, two plus two very rarely equals four - it's usually three or five.
Fourier is a mathematical poem.
War can protect; it cannot create.
One began to hear it said that World War I was the chemists' war, World War II was the physicists' war, World War III (may it never come) will be the mathematicians' war.
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.
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