[cmath] Fields Institute Keyfitz Lecture: Douglas Hofstadter (Indiana University) on The Ubiquity of Analogy in Mathematical Thought

[Andrea MacLeod]

The Nathan and Beatrice Keyfitz Lectures in Mathematics and the Social
Sciences:

The Ubiquity of Analogy in Mathematical Thought

Douglas Hofstadter (Indiana University)

March 21, 2013 at 6:00 p.m.
Room 610, Health Sciences Building, University of Toronto

Mathematicians generally like to present their work in the wraps of extreme
rigor and pure logic. This professional posture is in some ways very
admirable. However, where do their ideas really come from? Do they strictly
follow the straight-and-narrow pathways of pure, rigorous, logical axiomatic
deduction in order to reach their often astonishing conclusions?

No.

This talk will be about how deeply and universally mathematical thought, at
all levels of sophistication, is riddled with impure, nonrigorous, illogical
intuitions originating in analogies, often highly unconscious ones. Some of
these analogies are good and some of them are bad, but good or bad, it is
they that lurk behind the scenes of all mathematical thought.

What is curious, to my mind, is that so few mathematicians seem to take
pleasure in examining and exploring this crucial and wonderful aspect of
their minds, their thoughts, and their deep discoveries. Perhaps, however,
they can be stimulated to examine their own hidden thinking processes if the
ubiquity of analogies can be made sufficiently vivid as to grab their
interest. So in this talk, I will do my best to provoke mathematicians. At
the same time, I will try equally hard to convey to non-mathematicians the
sheer joy of mathematical thinking, of mathematical invention, of
mathematical discovery, of mathematical revelation.
 
To convey this intense type of joy, I will conclude the talk with some
highly personal tales of analogical invention/discovery in mathematics,
because I still recall the profound and heady exhilaration they gave me over
50 years ago so vividly that it all might as well have happened just
yesterday.

For more information, visit:
http://www.fields.utoronto.ca/programs/scientific/keyfitz_lectures/hofstadte
r.html