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 URL;TYPE=URI:/news/calendar/events/mathematical-science
 s-department-levi-l-conant-lecture-series-2023-andrej-bauer-university-lju
 bljana
Mathematical Sciences Department, Levi L. Conant Lecture Series 2023 - Andrej Bauer, University of Ljubljana Slovenia (UH 520)
\n\n\n      \n      \n\n\n\n\nMathematical Sciences Department\nLevi L. Conant Lecture Series 2023\nSpeaker:
  Andrej Bauer,University of Ljubljana, Slovenia\nFriday, February 10, 2023
 \n11:00 am\nUnity Hall 520\nTitle:Exploring strange new worlds of mathemat
 ics\nAbstract:In the 19th century Carl Friedrich Gauss, Nikolai Lobachevsk
 y, and J谩nos Bolyai discovered geometries that violated the parallel post
 ulate. Initially these were considered inferior to Euclid's geometry, whic
 h was generally recognized as the true geometry of physical space. Subsequ
 ently, the work of Bernhard Riemann, Albert Einstein, and others, liberate
 d geometry from the shackles of dogma, and allowed it to flourish beyond a
 nything that the inventors of non-euclidean geometry could imagine.\n\nA c
 entury later history repeated itself, this time with entire worlds of math
 ematics at stake. The ideal of one true mathematics was challenged by the 
 schism between intuitionstic and classical mathematics, as personified in 
 the story of rivalry between L.E.J. Brouwer and David Hilbert. Not long af
 terwards, Kurt G枚del's work in logic implied the inevitability of a multi
 tude of worlds of mathematics. These could hardly be dismissed as logical 
 sophistry, as they provided answers to fundamental questions about set the
 ory and foundations of mathematics. The second half of the 20th century br
 ought gave us many more worlds of mathematics: Cohen's set-theoretic forci
 ng, Alexander Grothnedieck's sheaves, F. William Lawvere's and Myles Tiern
 ey's elementary toposes, Martin Hyland's effective topos, and a plethora o
 f others.\n\nWe shall explore but a small corner of the vast multiverse of
  mathematics, observing in each the quintessential mathematical object, th
 e field of real numbers. There is a universe in which the reals contain Le
 ibniz's infinitesimals, in another they are all computable, there is one i
 n which they are cannot be separated into two disjoint subsets, and one in
  which all subsets are measurable. There is even a universe in which the r
 eals are countable. The spectrum of possibilities is bewildering, but also
  inspiring. It leads to the idea of synthetic mathematics: just like geome
 ters and physicists choose a geometry that is best for the situation at ha
 nd, mathematicians can choose to work in a mathematical universe made to o
 rder, or synthesized, that best captures the essence and nature of the top
 ic of interest.\nVideo archive of lecture\n
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