This discussion will explore the thesis that learning, research, and thinking in mathematics is suffused with ambiguity, the contradictory, and paradox. The thesis is presented in the 2007 book by William Byers "How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics" (Princeton University Press's web page for Byers' book "How Mathematicians Think").
"If the modern world stands on a mathematical foundation, it behooves every thoughtful, educated person to attempt to gain some familiarity with the world of mathematics. Not only with some particular subject, but with the culture of mathematics, with the manner in which mathematicians think and the manner in which they see this world of their own creation."
--- William Byers
I led a discussion on this topic for the Greater Philadelphia Thinking Society last November (http://www.meetup.com/thinkingsociety/events/80974562/). I found the thesis so interesting, I wanted to discuss it again with a more mathematical audience. No mathematical background nor familiarity with Byers' book is required. But it would be nice if you could at least read the introduction that the publisher provides on-line for free (see my comments below).