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Our so-called "Arabic" notation owes its excellence to the application of the principle of local value and the use of a symbol for zero. It is now co… - Florian Cajori
" "Our so-called "Arabic" notation owes its excellence to the application of the principle of local value and the use of a symbol for zero. It is now conclusively established that the principle of local value was used by the ns much earlier than by the Hindus and that the Maya of Central America used the principle and symbols for zero in a well-developed numeral system of their own. The notation of Babylonia used the scale of 60, that of the Maya, the scale 20 (except in one step). It follows, therefore, that the present controversy on the origin of our numerals does not involve the question of the first use of local value and symbols for zero; it concerns itself only with the time and place of the first application of local value to the decimal scale and with the origin of the forms or shapes of our ten numerals. ... Hurt by the alleged arrogance of certain Greek scholars, Sebokht praises the science of the Hindus and speaks of "their valuable methods of computation. . . . I wish only to say that this computation is done by means of nine signs." Unfortunately, he leaves it to us to guess whether or not he used the zero. The passage, written about 662 A.D., is the earliest reference that has been found outside of India to our numerals. ...The form of the symbols with the zero, used in India, differed so widely from the old forms without the zero used there, that the former seem to have had an independent origin and to have been imported into India.
...The following are outstanding facts:
1. The earliest reliable record of the use of our numerals with zero is an inscription of 867 A.D. in India.
2. The validity of the testimony of early Arabic writers ascribing to India the numerals with zero is shaken, but not destroyed.
3. There is not a scintilla of evidence in the form of old manuscripts or numeral inscriptions to support the Greek origin of our numerals.
4. At present the hypothesis of the Hindu origin of our numerals stands without serious rival. But this hypothesis is by no means firmly established.
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About Florian Cajori
Florian Cajori (1859 – 1930) was a Swiss-American professor of mathematics and physics. He was one of the most celebrated historians of mathematics in his day. Cajori's A History of Mathematics (1894) was the first popular presentation of the history of mathematics in the United States and his 1928 –1929 History of Mathematical Notations has been described as "unsurpassed."
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Fermat died with the belief that he had found a long-sought-for law of prime numbers in the formula <math>2^{2^n} + 1 =</math> a prime, but he admitted that he was unable to prove it rigorously. The law is not true, as was pointed out by Euler in the example <math>2^{2^5} + 1 =</math> 4,294,967,297 = 6,700,417 times 641. The American lightning calculator Zerah Colburn, when a boy, readily found the factors but was unable to explain the method by which he made his marvellous mental computation.
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