History of Mathematics in the Islamic World: The Present State of the Art

Abstract

In Recent Years, many discoveries in the history of Islamic mathematics have not been reported outside the specialist literature, even though they raise issues of interest to a larger audience. Thus, our aim in writing this survey is to provide to scholars of Islamic culture an account of the major themes and discoveries of the last decade of research on the history of mathematics in the Islamic world. However, the subject of mathematics comprised much more than what a modern mathematician might think of as belonging to mathematics, so our survey is an overview of what may best be called the “mathematical sciences” in Islam; that is, in addition to such topics as arithmetic, algebra, and geometry we will also be interested in mechanics, optics, and mathematical instruments.

Mathematics and Her Sisters in Medieval Islam: A Selective Review of Work Done from 1985 to 1995

“…ā riq, in order to calculate the brightness of the moon in terms of its position relative to the sun, 9 We capitalize the names of the trigonometric functions to remind the reader that the medieval trigonometric functions denoted the lengths of certain lines, not their ratios. 10 These are not the same as the zodiacal signs. In particular they depend on both the locality and the time for which they are calculated.…”

“…For that very reason special interest is given to Menso Folkerts's discovery [51] of a new manuscript-found in New York!-of 1 The author has made a serious search for all published papers from the period 1985-1995 not cited in his earlier survey [10] and has referenced such as he felt might appeal to a nonspecialist audience. As of this writing the year 1996 has not finished so a thorough survey of that year is impossible.…”

“…Much of the best of the medieval Arabic work, however, was not inspired by Euclid but by Archimedes, and in our previous survey [10] we called attention to the need for a study of the Archimedean tradition in the Islamic middle ages. Happily this gap in the literature has begun to be filled, and two studies of the Archimedean tradition in medieval Islam are (1) a philological study, by Richard Lorch [109], of Arabic, Hebrew, and Latin material germane to the problem of the direct transmission of the text of On the Sphere and Cylinder and (2) a study, also by Lorch [108], of the indirect transmission of the same work based on the theorems and proofs of a treatise on isoperimetry by the 10th-century astronomer Abū Ja c far al-Khā zin, who, according to Omar Khayyā m, used conics to solve the cubic equation to which al-Mā hā nī had reduced the problem Archimedes posed in On the Sphere and Cylinder, II, 4.…”

“…Ten years ago we surveyed recent work in the history of the mathematical sciences in medieval Islam [10], including mathematics itself and the sciences of astronomy, astrology, cartography, optics, and music, where mathematics played an essential role. Since that time much has been published in these areas, and it seems fitting once again to survey what has been learned about medieval Islamic achievements in the mathematical sciences during the past decade.…”

Perfect, Amicable and Numbers of Equal Weights (Historical Notes)

“…An important consideration here is whether Thabit was familiar with the methods of Archimedes. Al Karkhi 4 also singled out in his book ( Badi fil alhisab ), [9], chapter on the amicable numbers proving Ibn Qurra theorem and concludes the following: If D,E is a pair of amicable numbers,then it is nescerly that one of them is an abundant number and the other is a deficient number, E- [4,6], Ibn Qurra Theorem, and identify the two amicable numbers 17,296 and 18,416 in the case of n = 4,and Ibn Hidor Tadili (d. 1413 AD) identify the same lived and put the most important production in Baghdad at the end of the tenth and the begining of Eleventh century.He has spent apart of his life in the mountainous areas, where he worked in engineering, this work appeare in his book "About drilling of wells,.He "died in Baghdad in (421 AH = 1020 AD), considered by some as one of the greatest Mathematician who have had a real impact in the progress of Mathematical Sciences, he has several books, including: a book in the Indian account, which speaks for the extraction approximate polynomial roots, and a book in the induction , and Alkafi book which contains rules of the product signs and unknowns, sums of the Algebraic terms and the laws of the last term and the total sum in numerical sequence , and the square root of Algebraic amounts. while in his book Alfkhry in algebra he study many problems, he is the first Arab proved that .In his book "Ellal Algeber wa almukabla" and, in het set out rules to solve the equations of the second degree as well as multiplication and division and addition and subtraction rules formulas for two rational numbers and proved those rules algebraically.…”