Robert Kantrowitz ’82, professor and chair of mathematics, was a speaker at the Joint Mathematics Meetings held Jan. 4-7, 2012, in Boston. 

In his talk, “When absolute convergence fails to imply convergence,” Kantrowitz provided several examples showing that a standard result about infinite sums breaks down in the absence of the completeness property of the real numbers.  The existence of such examples underlies the necessity of irrational numbers, such as the square root of 2 and pi, to ensure that the main theorems of calculus remain true.