Konstantinos Nikolantonakis – Were there "Revolutions" in Mathematics? Examples from the History of Mathematics in light of T.S. Kuhn’s historical philosophy of science
The Montreal Inter-University Workshop on the History and Philosophy of Mathematics presents:
Konstantinos Nikolantonakis (U Western Macedonia, Greece):
Were there "Revolutions" in Mathematics? Examples from the History of Mathematics in light of T.S. Kuhn’s historical philosophy of science
Friday, November 9, 2012
McGill University, Leacock Building, Room 927. 3:30-5:00pm
Abstract: The second half of the 20th century witnessed a kind of revolution in the history and philosophy of science with the edition of T.S. Kuhn’s book Structure of Scientific Revolutions, published in 1962, presenting a view of science that is generally labeled as "historical philosophy of science". In this article I will discuss whether or not elements of the "historical philosophy of science" can be applied to the field of mathematics. My addressing the issue of whether or not Kuhn’s view of scientific revolutions is applicable to mathematics has been inspired by my study on the formation of our ten numerals and the methods for the operation of multiplication during the Middle Ages in Europe. After presenting notions (object level and
meta-level) from a very well known example from the bibliography concerning Non-Euclidean Geometry and using the analyses of Zheng and Dunmore we shall apply these notions to the field of arithmetic during the Middle Ages in Europe. Our argument focusses especially on the way we have passed from the arithmetic of pebbles, via Fibonacci and Pacioli, helped by the translation in Latin of Al-Khwarizmi’s treatise, to the foundation of modern arithmetic.
For more information, please contact:Gregory Lavers (Concordia), Mathieu Marion (UQÀM), Jean-Pierre Marquis (UdM), Dirk Schlimm (McGill).