While the mathematicians were still looking askance at the Greek gift of the irrational number, the Hindus of India were preparing another brain-teaser, the negative number, which they introduced about A. D. 700. The Hindus saw that when the usual, positive numbers were used to represent assets, it was helpful to have other number represent debts.
Morris KlineRelated topics
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There used to be a thing or a commodity we put great store by. It was called the People. Find out where the People have gone. I don't mean the square-eyed toothpaste-and-hair-dye people or the new-car-or-bust people, or the success-and-coronary people. Maybe they never existed, but if there ever were the People, that's the commodity the Declaration was talking about, and Mr. Lincoln.
John Steinbeck
Because most people are not sufficiently employed in themselves, they run about loose, hungering for employment, and satisfy themselves in various supererogatory occupations. The easiest of these occupations, which have all to do with making things already made, is the making of people: it is called the art of friendship.
Laura Riding
It is not possible to put the Gospel and secular logic together. In the Gospel there is love, while in secular logic there is self-interest. The Gospel says, And if any one forces you to go one mile, go with him two. (Mt. 5:41) What is logical about this saying? This is surely madness! This is why those who try to reconcile the Gospel with secular logic find themselves in utter confusion.
Paisios of Mount Athos
When an equation...clearly leads to two negative or imaginary roots, [Diophantus] retraces his steps and shows by how by altering the equation, he can get a new one that has rational roots. ...Diophantus is a pure algebraist; and since algebra in his time did not recognize irrational, negative, and complex numbers, he rejected equations with such solutions.
Morris Kline
The way in which the irrational numbers are usually introduced is based directly upon the conception of extensive magnitudes-which itself is nowhere carefully defined-and explains number as the result of measuring such a magnitude by another of the same kind. Instead of this I demand that arithmetic shall be developed out of itself.
Richard Dedekind