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Copyright © 2019 by John Urschel and Louisa Thomas
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ISBN 9780735224865 (hardcover)
ISBN 9780735224872 (ebook)
Version_1
For Joanna
Contents
Title Page
Copyright
Dedication
Preface
| Puzzles
ONE
| The Photograph
TWO
| Crashing Calculus Class
THREE
| Canisius
FOUR
| Rocket Science
FIVE
| Recruitment
SIX
| Arriving at Penn State
SEVEN
| Pushing until Failure
EIGHT
| Probability
NINE
| We Are
TEN
| Q.E.D.
ELEVEN
| Who’s Jerry Sandusky?
TWELVE
| Proof
THIRTEEN
| Sanctions
FOURTEEN
| Computers
FIFTEEN
| Who Needs Bowl Games?
SIXTEEN
| Graph Theory
SEVENTEEN
| Senior Season
EIGHTEEN
| Spectral Bisection
NINETEEN
| Combine
TWENTY
| John von Neumann
TWENTY-ONE
| Becoming a Raven
TWENTY-TWO
| Challenging Conventions
TWENTY-THREE
| Concussion
TWENTY-FOUR
| Uncertainty
TWENTY-FIVE
| MIT Football
TWENTY-SIX
| Passing a Test
TWENTY-SEVEN
| Moving On
TWENTY-EIGHT
Acknowledgments
About the Authors
Preface
I
am a mathematician, a PhD candidate at MIT.
I am also a former professional football player, a retired offensive
lineman for the Baltimore Ravens.
Many people see me as a walking contradiction. They think that the
pursuit of excellence in football makes the pursuit of excellence in
mathematics impossible. They think that a strong interest in one makes a
strong interest in the other improbable. People tend to think in binaries.
Right and wrong. Black and white. Mind and body. Math and football.
I don’t spend a lot of time wondering about the ways in which I’m an
anomaly. My life is the only one I know. It’s normal to me. We all have
multiple and sometimes diverging identities. In different ways, math and
football are both essential to me.
I’m sometimes asked about the connection between math and football.
People want to know what edge being good in a classroom gave me on the
field. I know what they want to hear, and I usually give it to them. I talk
about basic physics, intelligence, and problem solving. But the truth is,
football and math are disjoint in my experience. When the ball is snapped,
I’m not thinking about vectors and forces. I’m not really thinking about
much of anything. I’m simply moving.
Math gives me a way of making sense of the world. It helps me see past
the confusion of everyday life and glimpse the underlying structures of the
universe. It reveals the properties of shapes and the prevalence of patterns.
It describes the relationships between things. I’m drawn to the rigor and
clarity of mathematics, and to the elegance and simplicity of solutions to
even the most complex problems. I know no other feeling like the
satisfaction of discovery. I still feel the same sense of wonder and curiosity
when I try to prove a theorem that I felt when I did logic and math puzzles
as a kid.
Football put me in contact with something messier, something
elemental and deep within me. It strengthened not only my body, but also
my confidence and will. Football was a game, and I had a lot of fun playing
it. But it was always also a test for me. I look like a football player: I am 6-
foot-3, with shoulders that span a doorway, and massive hands and feet. But
I never had as much raw athletic talent as a lot of the guys I played with and
against. I relied on my intensity and competitiveness and desire.
—
THIS MEMOIR PROCEEDS on alternating parallel tracks. One is the story of my
life in mathematics. It begins when I was a toddler, the age that my mother
started buying me puzzle books and workbooks and started playing games
with me, encouraging my mathematical creativity and reasoning. If I am
truly an outlier, it is because of her—an African-American single mother
who loved math but was discouraged from it, who wanted me never to feel
that any door was closed to me. For me, math is the great intellectual
pursuit—though it calls upon my spirit too. It is a story of moving between
the ideal, abstract world and the reality we live in, a story of private
investigation and also collaboration—both with mentors such as Vadim
Kaloshin, who first introduced me to mathematical research, and Ludmil
Zikatanov, my collaborator and close friend, and with figures from the past:
Leonhard Euler, Henri Poincaré, John von Neumann, and others, whose
work my own has built on. It explores not only my experience of
encountering and learning mathematical concepts, from infinity to graph
theory to the uncertainty principle, but also learning how to think.
The other story is of my life in football, from the time I saw a picture of
my father in pads. It is the story of how I strengthened my body and my
will, how I learned to fail and learned from failing. It focuses on my
experiences on the field, but it is also the story of how I learned to make
friends and find my place in the social world. My football career began a
decade or so after I saw that picture, at Canisius High School in Buffalo,
New York, and continued at Penn State, during years when the team’s very
existence was threatened by scandal. Finally, I made my way to the
Baltimore Ravens, in the NFL, where I learned to navigate a different kind
of landscape, and faced a final difficult test: determining when to walk
away.
Those two stories, as different as they are, converge in me.
