Bar Ilan Mathematics Colloquium 
 
Date: April 10, 2011
 
Time: 12:00 ? 
(I am guessing that it is the usual time. I was not explicitly informed. M.C.)
 
Place: ? Presumably the usual place. M.C. 
 
Speaker: Prof. Misha Katz (Bar-Ilan University)
 
Title: Ten misconceptions from the history of analysis and their debunking
 
ABSTRACT: The founders of infinitesimal calculus were working in a
vacuum caused by an absence of a satisfactory number system.  The
incoherence of infinitesimals was effectively criticized by Berkeley
as so much hazy metaphysical mysticism.  D'Alembert's visionary
anticipation of the rigorisation of analysis was ahead of his time.
Cauchy took first steps toward rigor and epsilontics without
infinitesimals, in particular giving a modern definition of
continuity.  Cauchy's false 1821 version of his "sum theorem" was
corrected by Cauchy in 1853 by adding the hypothesis of uniform
convergence.  Weierstrass finally rigorized analysis and eliminated
infinitesimals from mathematics.  Dedekind discovered "the essence of
continuity," which is captured by his cuts.  One of the spectacular
successes of the rigorous analysis was the mathematical justification
of ``Dirac delta functions''.  Robinson develops a new theory of
infinitesimals in the 1960s, but his approach has little to do with
historical infinitesimals.  Lakatos pursued an ideological agenda of
Popperism and fallibilism, inapplicable to mathematics.  Each of the
above ten claims is in error.
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Colloquium no-reply   <colloquium@macs.biu.ac.il>