Jeremy Case

Associate Professor of Mathematics

Taylor University

My intent is to examine the nature of proof—how it understood by mathematicians, by math educators, by theologians, and by culture. In particular, the main focus would be on the question of why playwrights are incorporating mathematics and the nature of proof in their plays. Does their work unintentionally point towards a creator or higher truth?

Carrying the theme of postmodernism and mathematics from the first ACMS book, I am interested in exploring the relationship of how a postmodern culture views mathematics. How do the recent theatrical productions such as Arcadia, Proof, and Copenhagen portray mathematics and mathematicians? How have reviewers and mathematicians responded to these plays? I believe many mathematicians have responded, but I think another Christian response is needed.

The playwrights spent some time researching mathematics and its culture and provide an outsider's perspective. Their perceptions of the assumptions and values of the mathematics community can be very informative. What are the stereotypes and caricatures of mathematicians? Furthermore, these perspectives are communicated not in academic jargon but in an accessible artistic form allowing multiple representations and perspectives.

The use of theatre has several additional advantages. Mathematicians seem to be always trying to communicate the nature of the discipline is to others. Perhaps plays and movies are a means towards this goal. However, serious plays tend to be better developed than Hollywood movies so they provide a deeper and richer context for discussion.

As mathematicians, we should represent our discipline to the general public in any way we can. As Christians, we should represent Christian ideals to our colleagues, and these plays may provide an opportunity.

Through an examination of these plays, we have another means of then asking, "What is truth?" If there is no absolute truth, what do we do with mathematics?

For some, in a postmodern culture where certainty and truth have been undermined, mathematics provides a counterexample. While not as widely held as it once was, the idea that mathematics is undisputedly certain still lingers. This theme of mathematical certainty is used in these plays to frame dramatic conflicts where the evidence points towards an inconceivable conclusion. The dramatic tension provides then an exploration of what the loss of certainty means on many fronts. For example, several characters accept reality only if it can be quantified or proven. Yet, the character's personal relationships are such that they cannot be quantified and thus unacceptable.

I hope to begin to explore in depth at least three plays Arcadia, Proof and Copenhagen. All have won prizes such as a Pulitzer Prize or a Tony award for best screenplay.

• Arcadia by Tom Stoppard explores the question of uncertainty, mathematical chaos, and time. A young female prodigy discovers a mathematical theory anticipating chaos theory and fractals. The mathematics provides background on a theme on the interaction of humans and science in a world of uncertainty.

• Proof by David Auburn presents a daughter of a mentally unstable mathematician who claims to have discovered a remarkable proof. How does one know for certain about life and about truth claims?
• Copenhagen by Michael Frayn is based on a meeting between theoretical physicists Bohr and Heisenberg in 1941. Heisenberg's uncertainty principle provides a metaphor for the examination of the two nuclear physicists and their role in the development of nuclear warfare.

These plays can raise interesting questions for Christians as well. What are the ethical dilemmas a mathematician might face? Should Christians participate in research that may cause incredible devastation? Should Christians put their personal relationships ahead of their professional goals? What values held by the mathematics community but not held by the general culture should be emulated?

It may be that the mathematical process might be analogous to the creative process. Therefore, the playwright might see in the mathematician someone who has something important to say but is misunderstood by peers and critics. The mathematician may be someone who sees the world from a different angle but cannot convince others. In this manner, the playwright can overtly avoid using the overplayed character of the tortured artist. This theme of being misunderstood occurs often in Christian genre. Are the analogies strong enough to make a meaningful, Christian connection?

For the classroom teacher, the nature of proof has changed. Many high school geometry courses are continuing to de-emphasize proof. Our experience at Taylor is that logical arguments regarding mathematical and theological issues have been less convincing for today's student than it was several decades ago. These plays may provide a context for students and instructors alike to reflect upon the process of convincing another something is true.

My hope is that the workshop can help me develop these ideas further. I have applied for a sabbatical for the spring of 2004 to continue work in this area.