Wednesday, January 28, 2009
Way back in the late 1970's when I was in graduate school in mathematics at the University of North Carolina at Chapel Hill I had an algebra class with Dr Ladnor Geissinger. The very first day of class as we were all getting ready to leave he assigned the problem "Show that Zorn's Lemma and The Axiom of Choice are Equivalent". I recall thinking, "I know what The Axiom of Choice is, but what the heck is Zorn's Lemma!" I was totally at sea. It turns out that this result is apparently very well know. This did not keep me from searching endlessly first for Zorn's Lemma and then for something that showed it to be equivalent to The Axiom of Choice. I finally did find it in the Shaum's Outline of Set Theory this book is still in print and when you look at the index in the Amazon page you see Axiom of Choice and Zorn's Lemma are both still on page 220. I recall I still did not understand what was going on. I did read that proof over and over but I was a first year math grad student and had never had a formal course in Set Theory. Later that year someone (it may have been me) asked about the assignment and Dr Geissinger laughed and said it was not a real assignment. So imigine what I thought when I read this post by Terence Tao.