“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 Kline

Source: Mathematics and the Physical World (1959), pp. 49-50.

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "While the mathematicians were still looking askance at the Greek gift of the irrational number, the Hindus of India wer…" by Morris Kline?
Morris Kline photo
Morris Kline42
American mathematician 1908–1992

Related quotes

“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 Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 51.

“The Hindus introduced negative numbers… The first known use is Brahmagupta about 628; he also states the rules for the four operations with negative numbers. Bhāskara points out that the square root of a positive number is twofold, positive and negative. He brings up the matter of the square root of a negative number but says that there is no square root because a negative number is not a square. No definitions, axioms, or theorems are given.
The Hindus did not unreservedly accept negative numbers. Even Bhāskara, while giving 50 and -5 as two solutions of a problem, says, "The second value is in this case not to be taken, for it is inadequate; people do not approve of negative solutions."”

Morris Kline (1908–1992) American mathematician

However, negative numbers gained acceptance slowly.
Source: Mathematical Thought from Ancient to Modern Times (1972), p. 185.

“In arithmetic the Arabs took one step backward. Though they were familiar with negative numbers and the rules for operating with them through the work of the Hindus, they rejected negative numbers.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 192.

“One of the first algebraists to accept negative numbers was… placed negative numbers on a par with positive numbers and gave both roots of a quadratic equation, even when both were negative. Both Girard and Harriot used the minus sign for the operation of subtraction and for negative numbers.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), pp. 252-253.

Henry Burchard Fine photo

“Judged by the only standards which are admissible in a pure doctrine of numbers i is imaginary in the same sense as the negative, the fraction, and the irrational, but in no other sense; all are alike mere symbols devised for the sake of representing the results of operations even when these results are not numbers (positive integers).”

Henry Burchard Fine (1858–1928) American academic

Source: The Number-System of Algebra, (1890), p. 86; Reported in Moritz (1914, 282)

Koenraad Elst photo

“While the minority separatists have the guns, the enraged Hindus will have the numbers.”

Koenraad Elst book Ayodhya and After

Source: 1990s, Ayodhya and After: Issues Before Hindu Society (1991)

Koenraad Elst photo

“The pogroms in Pakistan and Bangladesh after the demolition of the Babri Masjid left 50,000 Hindus homeless in Bangladesh and triggered another wave of refugees from both countries towards India. In Pakistan, 245 Hindu temples were demolished, in Bangladesh a similar number was attacked, and even in England some temples were set on fire by Muslim mobs.”

Koenraad Elst (1959) orientalist, writer

1990s, Negationism in India, (1992)

Swami Shraddhanand photo

“While Muhammadans multiply like anything, the numbers of the Hindus are dwindling periodical­l­y.”

Swami Shraddhanand (1856–1926) Indian monk and philosopher

Hindu Sangathan, Saviour of the Dying Race (Delhi 1926)

Richard Dedekind photo

“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 (1831–1916) German mathematician

Footnote: The apparent advantage of the generality of this definition of number disappears as soon as we consider complex numbers. According to my view, on the other hand, the notion of the ratio between two numbers of the same kind can be clearly developed only after the introduction of irrational numbers.
Stetigkeit und irrationale Zahlen (1872)

Richard Dedekind photo

“Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with these numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of the rational numbers alone. The question only remains how to do this.”

Richard Dedekind (1831–1916) German mathematician

p, 125
Stetigkeit und irrationale Zahlen (1872)

Related topics