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SUMMARY:Mathematical fictions and mathematicians’ choices - Frédéric B
 rechenmacher (École Polytechnique)
DTSTART:20250123T113000Z
DTEND:20250123T123000Z
UID:TALK220546@talks.cam.ac.uk
DESCRIPTION:Articulating various scales of historical analysis is what I c
 onsider as the most significant open question in my areas of research. Inq
 uiries that defined their scope over a long time period and/or a large geo
 graphical range were common from the 17th to the 20th century. A typical e
 xample is the conception of the evolution of algebra in the long run\, fro
 m &nbsp\;procedures for solving equations to a discipline dealing with abs
 tract structures. Yet\, the more recent development of &nbsp\;archives-dir
 ected researches on short-term time-scales and local social spaces &nbsp\;
 has challenged the historical outcomes that large-scale history had &nbsp\
 ;undertook to account for\, e.g. &nbsp\;large structural characteristics\,
  processes\, and conditions.&nbsp\; To be sure\, such issues are not limit
 ed to the field of history of mathematics: the distinction between the lon
 gue dur&eacute\;e\, short term events and medium-term conjunctures had esp
 ecially been much discussed by the French Annales School in the 1930s\, wh
 ile the development of Microhistory in the 1970s has lead to an interest i
 n the interaction between micro and macro-levels of history.\n&laquo\; Mat
 hematical fictions &raquo\; provide an opportunity for playing with scales
  of historical analysis. In several epistemological approaches\, &laquo\; 
 fictions &raquo\; have been used as an analytical category to divide the h
 istory &nbsp\;of mathematics into several periods. This category has often
  encompassed various notions &nbsp\;and problems in the longue dur&eacute\
 ;e\, e.g. the infinite\, squaring the circle\, negative quantities\, imagi
 nary numbers\, infinitesimals\, non euclidean geometry\, or even mathemati
 cs as a whole. But &laquo\; mathematical fictions &raquo\; may also be inv
 estigated as an actor&rsquo\;s category\, which meanings may change in var
 ious times and social spaces. In this talk I will contrast the longue dur&
 eacute\;e historiography of mathematical fictions with investigations on t
 he short term of the 1880s and the medium-term of 1860-1960. While philoso
 phers have usually associated fictions with ontological issues raised by m
 athematics\, we will see that this terminology was rather used by practiti
 oners of mathematics to address the issue of the choice that one has to ma
 ke for mathematizing a situation. Mathematical fictions thus call for a hi
 story of mathematicians&rsquo\; choices.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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