## February 13, 2011

Sundays at 3 pm (doors open at 2:15)

Royal Canadian Institute

## Dror Bar-Natan, University of Toronto

*The Hardest Math I've Ever Really Used*

MacLeod Auditorium, Medical Sciences Building, University of Toronto

1 King’s College Circle (Nearest Subway is Queen’s Park
Station)

Co-sponsored by the Fields Institutue

What's the hardest math I've ever used in real life? Me, myself,
directly - not by using a cellphone or a GPS device that somebody
else designed? And in "real life" - not while studying
or teaching mathematics?

I use addition and subtraction daily, adding up bills or calculating
change. I use percentages often, though mostly it is just "add
15 percents". I seldom use multiplication and division: when
I buy in bulk, or when I need to know how many tiles I need to replace
my kitchen floor. I've used powers twice in my life, doing calculations
related to mortgages. I've used a tiny bit of geometry and algebra
for a tiny bit of non-math-related computer graphics I've played
with. And for a long time, that was all. In my talk I will tell
you how recently a math topic discovered only in the 1800s made
a brief and modest appearance in my non-mathematical life. There
are many books devoted to that topic and a lot of active research.
Yet for all I know, nobody ever needed the actual formulas for such
a simple reason before.

Hence we'll talk about the motion of movie cameras, and the fastest
way to go from A to B subject to driving speed limits that depend
on the locale, and the "happy segway principle" which
is a the heart of the least action principle which in itself is
at the heart of all of modern physics, and finally, about that funny
discovery of Janos Bolyai's and Nikolai Ivanovich Lobachevsky's,
that the famed axiom of parallels of the ancient Greeks need not
actually be true.

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