Title: What We Don't Know We Don't Know
Being aware that we don't know something is one thing. For instance, we can be aware that we don't know how to solve a cubic equation; it is clear to us that we do not know who will win the World Series this year; and we are perfectly comfortable with the fact that we don't know the Inuit word for porcupine.
But when we aren't even aware of our ignorance about something, its discovery can have serious and unexpected consequences. Some of them can be scary, and others innovating and exciting. For example, when Pythagoras discovered that there are numbers that are not simple fractions, it frightened many of his compatriots who feared that the comforting notion of the "harmony of the spheres" was threatened by the very existence of these so-called "irrational" numbers. However, Pythagoras' discovery led to the development of one of mathematics' most beautiful areas of research - Number Theory.
In this lecture, I will present another remarkable discovery of something we didn't know we didn't know|this time about the notion of area and discuss how it spawned and reformulated many important areas of mathematics, including Analysis, Probability, and Set Theory.
Knobloch Campus Center Alvarez- Smith 900 Room
Victor, Vanessa M