News Highlights
Author:
Rima Cortbawi,
Office of Communications,
rgc01@aub.edu.lb
 CAMS website
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Origins of mathematics traced in two lectures
Mumford's powerpoint presentation |
Organized by the Center for Advanced Mathematical Sciences, the set of two lectures, given at College Hall's Auditorium B1 on October 20 and 23, gathered crowds of AUB community members, all eager to listen to valuable presentations by distinguished guest Professor David B. Mumford. The first lecture handled "the birth of mathematics in Babylon and the convoluted history of Pythagoras" theorem." Its antecedent tackled "four millennia of algebra- a useful or a useless art?" Mumford, who is of international renown, posed and helped answer that crucial question.
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 | Dallal giving an introductory speech
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Attended by President Peter Dorman, Provost Ahmad Dallal and a number of professors of mathematics and other disciplines, the first talk handled a history of geometry, particularly related to right angles, across cultures. After a brief introductory speech by Dallal, Mumford expressed that mathematics evolved into a "gigantic area of techniques of its own" throughout his celebrated career. But the story started long before that. As far as is known, mathematics was born, approximately 1800 BC in Babylon, only 520 miles east of Beirut. "We could probably get there in eight hours through a good system of highways," continued Mumford.
In ancient civilizations, much like the present times, geometry had to be embraced to calculate areas of fields/farms for taxation purposes. Perpendiculars were essential for rectangular and triangular spaces, like plots of land, streets, and buildings. And that was conducive to Pythagoras' theorem. In other words, "construction lead to putting right angles at the forefront of mathematical studies," according to Mumford. In Babylonian times they had "sophisticated math in use for construction purposes." However, the idea of Pythagoras' sums of squares permeates all areas of mathematics, as could be clearly shown from different cross-cultural perspectives. |
The second lecture's account also started from Babylonian times, where "the quadratic equation was solved geometrically," before moving on across centuries of mathematicians "playing" algebraic "games of numbers." Similar problems of practical algebra emerged in Middle Eastern, European, Chinese and Indian literature. But the convoluted story of how algebra came into its own is one "of cubic equations and complex numbers," according to Mumford. Complex numbers turned out to be "really real," as imaginary numbers were an unavoidable part of the work. "When some numerical relationship is puzzling, it can be really helpful to reify the unknown quantity so you can deal with it," said Mumford concluding that it is a "shame" to view algebra as though it were a "useless game;" practical "word" problems across the ages could more concisely be turned into algebraic equations.
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Audience and guests attending |
Mumford is Professor Emeritus at both Brown and Harvard Universities, where he taught for many years. His long career included extensive work in both pure and applied mathematics. In 1974 he was awarded the Fields Medal for his work in pure mathematics that found application in string theory. In the last decade, Mumford has been studying the history of mathematics and getting involved in issues related to teaching mathematics at high-school level. He has been a MacArthur Fellow and President of the International Mathematics Union. A member of US National Academy of Science, the Royal Society of London, the Norwegian Academy of Science and Letters, the Accademia Nazionale Dei Lincei and the Palestinian Academy for Science and Technology, he shared the Longuet-Higgins Prize from the IEEE (2005), the Shaw Prize in Mathematical Science (2006) and the Steele Prize from the American Mathematical Society (2007).
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