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Antoni Malet

Universitat Pompeu Fabra
Towards a history of mathematical consistency: tacit knowledge and conceptual change in early modern mathematics
01 October 2017 -
30 June 2018
History, philosophy and sociology of science

Antoni Malet is Professor of History of Science at the Universitat Pompeu Fabra (Barcelona). He majored in Mathematics (Universitat de Barcelona) and got a doctorate in History at Princeton University. He has been research fellow or visiting professor at the universities of Princeton, California (San Diego), Toronto, and París VII, and Marie Curie senior Fellow at the Max Planck Institut for the History of Science, Berlin (2013-2015). Editorial Board member of Annals of Science and Historia Mathematica, where he served as Book Review Editor (2006-2011), he is Fellow of the Académie Internationale d'Histoire des Sciences, and currently the President of the European Society for the History of Science (2016-2018). He is working on the sociological understanding of conceptual change in early modern mathematics.

Research Interests

His research focuses mainly on 16th- and 17th-century mathematics and optics, optical and mathematical instruments, and the early modern philosophy of mathematics. He has also worked on the politics and institutions of science in Francoist Spain and their legacy.

Towards a history of mathematical consistency: tacit knowledge and conceptual change in early modern mathematics

In the crucial early modern period, fundamental notions like number, geometrical magnitude, and ratio, essentially defined à la Euclid in 1500, had been abandoned by 1700. By then infinitesimals, a notion inconsistent with traditional mathematics, were widely used in mathematics and rational mechanics. No satisfactory account exists for such a revolution, although traditional histories of mathematics stressed the "lack of rigour" of early modern mathematicians. In fact, the new notions of number and magnitude and the legitimation of infinitesimal thinking provide striking evidence that in critical episodes the evolution of mathematics is not guided by deductive rules nor by mathematical consistency. Motivations and rationale must be social in nature.

This project studies the emergence of implicit novel mathematical notions in mathematical practice, as opposed to mathematical texts. In particular, we focus on practical geometry and the practitioners of the art of measuring as sources for tacitly introducing some form of arithmetical continuum. We want to reevaluate the criticism of "lack of rigour" in early modern calculus by situating the foundational discussions within the wider social context in which the sceptical crisis of the early enlightenment discredited traditional axiomatico-deductive structures of knowledge. In particular we think we will be able to show how fruitful turns out to be a Wittgensteinian account of 17th century philosophy of mathematics.

14 May 2018 09:00 -
14 May 2018 17:00,
Paris :
Some 16th-century attacks on Euclid's ideas of ratio and proportionality
10 Apr 2018 09:30 -
10 Apr 2018 12:30,
Paris :
Fortification and geometry in the 17th century – a Jesuit perspective
15 Jan 2018 09:30 -
15 Jan 2018 17:00,
Paris :
Contextes d’enseignement et démonstration mathématique
13 Jan 2018 09:30 -
13 Jan 2018 13:00,
Paris :
À propos du livre Reading Galileo, de Renée Raphael
17 Dec 2017 10:00 -
23 Dec 2017 18:00,
Oberwolfach :
Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950
30 Nov 2017 17:00 -
30 Nov 2017 19:00,
Paris :
Towards a social history of infinitesimals c. 1700 (or, 17th-century mathematical rigour revisited)

Modern period (1492-1789)
Western Europe