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. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Colloquium no-reply <colloquium@macs.biu.ac.il>