To expand search, see Number Systems. For material on related topics, see India and The Islamic World. Laterally related topics: The Quipu, TallySystems, Finger Numerals, Bhaskara, Mahaviracarya, Varahamihira, Brahmagupta, Pingala, Halayudha, The Harappan Civilization, The Tamil of South India, The Sulvasutras, Th\^abit ibn Qurra, Abu Abdullah Muhammed ibn Musa al Khwarizmi, Omar Khayyam (abu-l-Fath Omar ibn Ibrahim Khayyam), Nasir al-Din al-Tusi, and Abu Kamil (b. 850).
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Patel, D. M. Symbols for 1, 2, 3, 4, 5, 6, 7, 8, 9 & 0 in Sanskrit and English languages. Math. Ed. (Siwan) 15 (1981), no. 1, B1--B3. (Reviewer: Brij Mohan.) SC: 01A99 (01A32), MR: 82h:01080.
There have been many theories on the origins of the numerals 1 through 9. The numerals for 1, 2, and 3 are frequently thought to based on one two or three tally marks or fingers, drawn in the case of 2 and 3 so that the number is written in one stroke. There have been many theories for the origins of the other numerals. Patel suggests that the Hindu-Arabic numerals 4, 6, 7, 8, and 9 were derived from shapes made with the fingers (perhaps some kind of finger numerals?). It's likely that the last word has not yet been said. He also notes similarities between the Sanskrit and English words for the numbers one through nine; these similarities are however already very well known. Closely related topics: India and Finger Numerals.
Schaaf, William L. Mathematics as a Cultural Heritage. Arithmetic Teacher 8 (1961), 5--9.
Briefly discusses some of the key characteristics of the mathematics of the Babylonians, Egyptians, Greeks, and of Medieval Europe. Then discusses adoption of the Hindu-Arabic numerals, the development of computation, and more abstract mathematics. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: Ancient Egypt, Greece, and Medieval Europe.
Woodruff, Charles E. The Evolution of Modern Numerals from Ancient Tally Marks. American Mathematical Monthly 16 (1909), 125--33.
A theory that the Hindu-Arabic numerals actually started out in China. Gives a possible evolution of each of the digits 1--9. There are many other theories as well, so it would be valuable to find evidence of some of these "missing links". Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topic: China.