Seminars & Colloquia Calendar
The Continuum Hypothesis: From Cantor to Cohen
Iian Smythe - Rutgers University
Location: Hill 425
Date & time: Monday, 19 November 2018 at 7:00PM - 8:00PM
Abstract: In 1874, the young German mathematician Georg Cantor discovered the startling fact that the set of real numbers was "bigger" than the set of natural numbers. But is there anything which lies between these two distinct infinities? Cantor conjectured "no", a statement which became known as the Continuum Hypothesis. Nearly 90 years after Cantor's original discovery, the American mathematician Paul Cohen proved that the Continuum Hypothesis was itself not provable from the usual axioms underlying mathematics. Why did Cantor make his conjecture? What came between Cantor's original work and Cohen's ultimate solution to the problem? What are some of the ingredients that went into Cohen's remarkable proof? And what are we to make of all this? We will survey these topics and more.