Diophantus and Arabic Algebra

 

On Monday, February 3 at 4pm in Olin 201 Dr. Matt Petersen will talk about how in 1842 the Orientalist G.H.F. Nesselmann identified three stages in the progressive development of algebra: 1) Rhetorical algebra, in which problems are stated and solved in words. 2) Syncopated algebra, in which abbreviations are used in the place of words. Finally, 3) at the highest level, a fully symbolic algebra, in which words are entirely replaced with symbols and general numeric claims can be formed. There are numerous problems with this eurocentric history of mathematics (though it remains popular) but one of the most critical is that it treats algebra itself as an unproblematic object, and thus blinds us to deep differences in the discipline called algebra, whether the algebra is written in words (as was standard in Islamic mathematical texts), in abbreviations (as in Diophantus,or Tartaglia), or in a fully syncopated algebra, as was used for calculations by Islamic mathematicians from the Maghreb and al-Andalus from the eleventh through the fifteenth centuries, and which modern historians of mathematics have said is a perfect fit for algebra as practiced by algebraists as diverse as Diophantus, al-Kwarizmi and Tartaglia (none of whom actually used it). This presentation will discuss the changing nature of algebra itself through history, the Maghrebi symbolic algebra and the use of an adapted form of it in translating Diophantus, and finally, the pedagogical questions these differences raise for teaching a non-Eurocentric history of mathematics in the mathematics curriculum.

BIO: Dr. Matthew Petersen is currently working on a series of school mathematics textbooks for Zaytuna College. The goal of these books is to give school mathematics the place it had in the works of the great Muslim philosophers like al-Farabi, ibn Tufayl, and ibn Sina, as a liberal art and integral part of wisdom--see also Metaphysics XI.4 (1061b33)--while linking that mathematics up with modern school mathematics. He earned his PhD in mathematics education from Portland State University in 2020 (defending his dissertation the day before the NBA suspended their season and everything closed). His doctoral work, an ethnomathematical investigation of the bodily practices of mathematicians and mathematics majors, was deeply indebted to the work of Saba Mahmood and Talal Asad exploring the place of the body in the practice of Muslims in the piety movement. He has taught mathematics at the University of Idaho, Portland State University, the University of Oregon, and Whitman College.