The Hindus saw clearly that if the arithmetic operations... were properly defined for negative numbers, these numbers could be employed to as good advantage as people had previously derived from positive numbers. ...To people to whom the word number had always meant positive whole numbers and positive fractions, the very idea that there could be other numbers came hard. For many centuries negative numbers were either rejected or treated as second-class citizens. What was especially difficult for mathematicians to swallow was that negative numbers could be acceptable roots of equations.
Morris KlineRelated topics
advantage arithmetic came good hard idea mean number saw swallow word roots operationsRelated quotes
If you wish to alter or annihilate a pyramid of numbers in a serial relation, you alter or remove the bottom number. If we wish to annihilate the junk pyramid, we must start with the bottom of the pyramid: the Addict in the Street, and stop tilting quixotically for the "higher ups" so called, all of whom are immediately replaceable. The addict in the street who must have junk to live is the one irreplaceable factor in the junk equation. When there are no more addicts to buy junk there will be no junk traffic. As long as junk need exists, someone will service it.
William S. Burroughs
Let's begin with capitalism, a word that has gone largely out of fashion. The approved reference now is to the market system. This shift minimizes - indeed, deletes - the role of wealth in the economic and social system. And it sheds the adverse connotation going back to Marx. Instead of the owners of capital or their attendants in control, we have the admirably impersonal role of market forces. It would be hard to think of a change in terminology more in the interest of those to whom money accords power. They have now a functional anonymity.
John Kenneth Galbraith
Fresh beauty opens one's eyes wherever it is really seen, but the very abundance and completeness of the common beauty that besets our steps prevents its being absorbed and appreciated. It is a good thing, therefore, to make short excursions now and then to the bottom of the sea among dulse and coral, or up among the clouds on mountain-tops, or in balloons, or even to creep like worms into dark holes and caverns underground, not only to learn something of what is going on in those out-of-the-way places, but to see better what the sun sees on our return to common every-day beauty.
John Muir
If someone offends you, don't tell anyone about it except your elder, and you will be peaceful. Bow to everyone, paying no attention whether they respond to your bow or not. You must humble yourself before everyone and consider yourself the worst of all. If we have not committed the sins that others have, perhaps this is because we did not have the opportunity - the situation and circumstances were different. In each person there is something good and something bad; we usually see only the vices in people and we see nothing that is good.
Ambrose
I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe.
Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.
Marcus du Sautoy