The Commercial Tradition in the Development of Mathematics
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{'SignBlockName': 'Alicia Armstrong', 'PO_EMAI': 'aarmstro@nsf.gov', 'PO_PHON': '7032924743'}
Mathematics is widely accepted as the most "pure" of the sciences.              Its origins, of course, have long been related to the needs of                  surveying, etc. in ancient Egypt and Babylonia; but from that time              on, it has been assumed that mathematics has developed largely                  independantly from the "crass" world of everyday life.  "Imaginary              numbers" or "non-Euclidean geometries" would seem not likely to have            developed when they actually did from any practical application.                Astonishingly, however, Dr. Van Egmond has discovered the development           of very esoteric mathematics out of a commercial tradition.  His                discovery has radically shaken our long held understanding of the               history of mathematics and the nature of its growth.  With this                 grant, Dr. Van Egmond will prepare an edition and study of the                  remarkable text which he discovered in 1983.  The work which he will            edit is a 14th century algebra text attributed to Dardi da Pisa. This           work is the single most important text of Algebra written in Europe             in the Middle Ages to be discovered to date.  Not only does it                  provide the most comprehensive, advanced, and competent treatment of            algebra produced by a European writer before the 16th century, it               also contains the correct solution to equations of the third and                fourth degrees.  This anticipates by more than two centuries the                published solution of the cubic and quartic equations which had                 hitherto been taken to mark the beginning of algebraic studies in               Western Europe.  The discovery of this work thus shatters the                   prevailing view that European algebraists were incompetent                      mathematicians constrained to copying the work of the Arabs and                 incapable of doing original work of their own, and forces significant           revisions in our understanding of how mathematics developed in Europe           before modern times.  In his study of this work, Dr. Van Egmond will            put it in the tradition in which it developed--not that of the                  academic in the new universities in Europe but that of commercial               arithmetic written in the native Italian language.  This                        non-university tradition has remained almost entirely unknown in the            history of science.  This project thus will not only help us to                 appreciate the work of one of the most able of medieval                         mathematicians, but will also shed light on a previously unknown                tradition.  The study further helps us to understand the nature of              science and its growth.  Commercial needs clearly drove this work,              not the abstract work of the academics.  In our quest to understand             why science rose to its place of prominence in the West rather than             other, previously more scientifically sophisticated civilizations of            the East, the research of Dr. Van Egmond will surely play an                    important role.
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{'Code': '1353', 'Text': 'Hist & Philosophy of SET'}
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