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Mathematics on Stage

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Title: Mathematics on Stage


1
Mathematics on Stage
  • Jeremy Case
  • Taylor University, jrcase_at_tayloru.edu
  • 2005 Biennial Conference of the ACMS
  • Huntington College
  • June 3, 2005

2
  • Proof by David Auburn
  • 2001 Tony Award for Best Play
  • Best Director-Play, Best Actress-Play
  • 2001 Pulitzer Prize for Drama
  • Copenhagen
  • by Michael Frayn
  • 2000 Tony Award for Best
    Play

  • Best director-play, best actress-play
  • Arcadia by Tom Stoppard
  • 1994 Olivier Award
  • 1995 New York Drama Critics' Circle Award for
    Best Play

Picture http//www.holtzbrinckpublishers.com/acade
mic/Book/BookDisplay.asp?BookKey402792
Picture http//www.pbs.org/hollywoodpresents/cope
nhagen/index.html http//www.maa.org/mathhorizon
s/volume/volume7.html
PBS
Picture http//www.maa.org/mathhorizons/volume/v
olume7.html
3
My questions at the start of this project
  • Why mathematical themes in plays?
  • Why now?
  • What do intelligent outsiders say about
    mathematics and mathematicians?
  • Do these plays provide a window into the
    mathematical endeavor?
  • In a postmodern world, what is said about the
    unreasonable effectiveness of mathematics?
    Morality? God?

4
  • Outline of Talk
  • Background
  • Theme 1 Knowledge
  • Theme 2 Permanence
  • Other themes
  • The use of literature in disseminating
    mathematical ideas.

Picture http//www.maa.org/mathhorizons/volume/v
olume7.html
Math Horizons May 1999 Photo by Christian Dohn
5
Arcadia
  • A young girl discovers chaos theory
  • in the early 1800s.
  • Lord Byron mystery
  • The play switches back and forth from the 1800s
    to present.
  • Chaos theory
  • Truth vs. history
  • Free will vs. determinism
  • Classical vs. Romantic thought
  • The attraction Newton left out
  • Mathematicians as romantics

Picture http//www.maa.org/mathhorizons/volume/v
olume7.html
6
Tom Stoppard
  • Rosencrantz and Guildenstern are Dead (1966)
  • Jumpers (1972)
  • A play about philosophers as acrobats I wanted
    to write a theist play, to combat the arrogant
    view that anyone who believes in God is some kind
    of cripple, using God as a crutch. The New
    British Dramatist, 1977.
  • Shakespeare in Love (1998 screenplay)
  • Star Wars III

Picture of Tom Stoppard
http//www.hrc.utexas.edu/research/fa/enlarged/sto
ppard_photograph.html Harry Ransom Humanities
Research Center at the University of Texas at
Austin
7
Tom Stoppard
  • Has incorporated mathematical/science ideas
  • Fascinated and suspicious of systems of logic
  • Belief in a moral order derived from Christian
    principles
  • (Not a Christian)
  • Supremacy of the individual over the determined
    and the enforced

Picture of Tom Stoppard
http//www.hrc.utexas.edu/research/fa/enlarged/sto
ppard_photograph.html Harry Ransom Humanities
Research Center at the University of Texas at
Austin
8
Chaos Theory
  • Thinking about Romanticism and Classicism
  • Then read James Gleicks book Chaos Making of a
    New Science
  • Chaos begins where classical science stops
  • Mountains are not pyramids and trees are not
    cones. God must love gunnery and architecture if
    Euclid is his only geometry. There is another
    geometry Thomasina, Scene 7, Arcadia
  • Who needed God when everything worked like
    billiard balls? Hapgood

Picture of Chaos by James Gleick
9
Copenhagen
  • In 1941, German Werner Heisenberg visited Niels
    Bohr (who was half-Jewish) in neutral Denmark.
  • Why did he go? What happened to cause their
    estrangement?

Picture of Heisenberg
Picture of Bohr
10
Picture of Michael Frayn
http//www.pbs.org/hollywoodpresents/copenhagen/id
/id_play_1.html (picture of Michael Frayn)
  • Read Moral Sciences (Philosophy) at university
  • Interested in quantum theory and Heisenbergs
    Uncertainty principle
  • Thomas Powers, Heisenbergs War.
  • How we know why people do what they do, and even
    how one knows what one does oneself?
  • It's a fundamental question... this is the heart
    of the play.

11
  • DAVID AUBURN It's the story of a young woman,
    Katherine, who has spent years caring for her
    father who is a brilliant mathematician, and her
    father began having various kinds of mental
    illness problems. She gave up her life to care
    for him. When the play begins the father died.
    She is sitting alone on the 25th birthday and
    wondering is this going to happen to me. How much
    of my father's mental illness have I inherited
    and have I inherited any of his talent as well?
    So the play is about a weekend in other life
    where she is trying to sort that out and she is
    trying to deal with her sister, who's flown in
    from New York and she has some plan's for
    Katherine's life. There is also a character who
    is a grad student who is a protégé of the
    father's who is upstairs in the house looking
    through the dad's papers hoping to find something
    he left behind. He also kind of has designs on
    Katherine.

Picture of Proof
http//www.pbs.org/newshour/bb/media/jan-june01/au
burn_04-20.html Newshour with Jim Lehrer April
20, 2001
12
  • Well, I didn't start with the idea about writing
    about math but I had this idea that the sisters
    who would start finding over something they found
    left behind after their dad's death. Since I also
    had this idea about someone who was worried that
    they would inheriting their parent's mental
    illness, I kind of went looking for the thing
    that the sisters would find, and it seemed to me
    that a scientific document or a mathematical
    document could be really interesting. I thought -
    you know -- its authorship could be called into
    question in some interesting ways and the
    historical fact that a number of famous
    mathematicians have suffered from mental illness
    kind of gave me the bridge to the other idea
    about someone worried about their own mental
    state. So it just seemed to fit the story that I
    wanted to tell.

Picture of David Auburn
David Auburn
http//www.pbs.org/newshour/bb/media/jan-june01/au
burn_04-20.html Newshour with Jim Lehrer April
20, 2001
13
  • DAVID AUBURN The real trick of writing the play
    was figuring out how much math to put in it. This
    ended up being constrained by the story. Since
    there is a mystery as to who wrote the
    mathematical proof, I sort of had to withdraw
    information when I could so that I didn't give
    away the solution to the mystery but I did try to
    get in as much kind of lore about the
    mathematical profession as I could. In that I was
    helped a lot by reading popular books and
    spending time with mathematicians. We even had
    some come in to meet and talk with the cast and
    talk to them, so that was really the fun part of
    doing the play, getting as much of the kind of
    world of mathematics into the play as possible
    and putting it up on stage.

Picture of David Auburn
David Auburn
http//www.pbs.org/newshour/bb/media/jan-june01/au
burn_04-20.html Newshour with Jim Lehrer April
20, 2001
14
Knowledge
  • How do we know what we know?
  • Who and what do we trust?
  • The wonder of knowledge
  • A creative human act
  • But incomplete
  • particularly in human relationships

15
  • Bohr You never cared what got destroyed on the
    way, though. As long as the mathematics worked
    out you were satisfied.
  • Heisenberg If something works it works.
  • Bohr But the question is always, What does the
    mathematics mean, in plain language? What are the
    philosophical implications?

Copenhagen, Michael Frayn
16
  • Heisenberg What something means is what it means
    in mathematics.
  • Bohr You think that so long as the mathematics
    works out, the sense doesn't matter.
  • Heisenberg Mathematics is sense! That's what
    sense is!

Copenhagen, Michael Frayn
17
  • Knowledge is what makes us human.
  • Its wanting to know that makes us matter.
    Otherwise we go out the way we came in. Arcadia

18
Permanence
  • One critic Why would we care about a proof?
  • The need to create something that lasts after we
    die
  • We are going to die enjoy our relationships and
    life now.

19
Other Themes
  • The worship/limitations of science
  • Mathematics as a human endeavor
  • Our place in the universe
  • Ethics-
  • Who are we responsible to? Family, friends,
    country, others, ourselves?
  • Moral relativism
  • Historical accuracy
  • Genius as madman
  • Math is a young mans game (Women in
    mathematics?)
  • Competition
  • Creativity
  • The values of mathematicians Intellect over
    style

20
Dissemination of Mathematics?
  • Where is the mathematics?
  • The artist revels in juxtaposition/paradox/ambigui
    ty
  • The mathematician tries to provide
    structure/clarify relationships
  • In art, the goal is not education
  • Hapgood example
  • Limited audience

21
Dissemination of Mathematics?
  • Must be a theme to capture an audience
  • Non-euclidean geometry example
  • The demands on the audience and the playwright
    are great
  • The playwright wants to get the math/science
    right
  • Difficult to capture the creative process in any
    field, let alone mathematics
  • A very difficult process
  • We must be willing to accept the metaphors
  • The mad genius stereotype is entrenched.

22
Math Dissemination
  • Reminds us of the human side of mathematics
  • Can communicate the joy of discovery
  • The importance of story
  • Leads us to consider mathematical ideas in a new
    light.
  • Raises questions
  • Reminds us to avoid special pleading
  • Provides interest motivation?
  • _________ cannot be about the mathematics itself
    but what the mathematics means.

23
Epilogue
  • Science writing
  • Mathematical fiction
  • Movies
  • Numb3rs

Proof, starring Gwyneth Paltrow (left), Anthony
Hopkins (not shown) Miramax films, opening
August 2005?
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