Musical theater and mathematics

Summary: Mathematical concepts and mathematicians have become interesting subjects of musical theater.

After the popular and critical success of Tom Stoppard’sArcadia, first performed in London in 1993, playwrights began making regular use of mathematics as source material for new scripts. This interdisciplinary collaboration, however, has largely been confined to stage plays and in the early twenty-first century has not found its way into musical theater—with one glaring and quite remarkable exception. In 2000, the husband-and-wife team of Joanne Sydney Lessner and Joshua Rosenblum created Fermat’s Last Tango, a comic musical inspired by Princeton mathematician Andrew Wiles and his successful proof of Fermat’s Last Theorem.

Fermat’s Last Tango

Fermat’s Last Theorem (FLT) is arguably the most famous mathematical problem in history. When Pierre de Fermat left his tantalizing note in the margin of his copy of Diophantus’ Arithmetica in 1637, the result was a challenge that resisted the efforts of mathematicians for the next 350 years. By the twentieth century, FLT had acquired such a daunting reputation that when Princeton mathematician Andrew Wiles decided to take it on around 1986, he did not tell anyone what he was doing until seven years later, when he emerged from the office in his attic with what he thought was a proper proof of the Taniyama–Shimura conjecture. A proof of Taniyama–Shimura was known to imply FLT, and the unassuming Wiles was propelled to unprecedented stardom far beyond the mathematical community.

This event is the jumping-off point for Fermat’s Last Tango. Because of the fictional liberties they take with the story, Lessner and Rosenblum have changed the name of their protagonist from Andrew Wiles to Daniel Keane, and the first major piece of revisionism we experience is when Keane is visited by a devilish and vindictive Fermat and whisked off to “the Aftermath” to fraternize with Pythagorus of Samos, Euclid of Alexandria, Isaac Newton, and Carl Friedrich Gauss. The fantasy is enjoyable, but what is really striking is how few liberties are taken with the mathematics. That the authors have done their homework is clear early on when Fermat rhymes “Shimura–Taniyama” with “algebraic melodrama.” In the Aftermath, Fermat reveals that Keane has made some incorrect assumptions about the Galois representations he used in his argument—which is indeed a mistake Wiles had made—and Keane retreats to his attic to try to repair the “big fat hole” in his proof.

Wiles, like Keane, was deeply uncomfortable trying to fill the gap in his proof under the glare of public scrutiny. The writers also keep the touching anecdote that Wiles promised his wife a corrected proof by her birthday, although it is unlikely that the real Ms. Wiles tried to lure her husband away from his research by crooning “Check out my modular form.” Taken in the lighthearted spirit in which it was intended, Fermat’s Last Tango is roundly successful entertainment. Beyond this achievement, it also comes as close as any other piece of science theater to effectively staging the “moment of discovery,” creating a genuinely breathless moment when a defeated Keane finally realizes how to repair the hole in his proof using the Iwasawa theory approach he had abandoned several years earlier.

For those who do not have an opportunity to view a live production, a performance of Fermat’s Last Tango was recorded and is available through the Clay Mathematics Institute. Others have staged Fermat’s Last Tango specifically as a teaching experience. A 2007 article in PRIMUS, a publication dedicated to teaching undergraduate mathematics, describes a fully student-mounted production, along with suggestions for related educational activities. The play is cited as a good introduction to not only mathematics products but also the personalities of people and the processes involved in mathematics research.

The Natural Sciences

There does not seem to be any other piece of widely disseminated musical theater devoted to a mathematical topic, though certainly there are mentions of mathematics in various popular scores. For instance, in Pirates of Penzance, first performed in 1879, W. S. Gilbert and Arthur Sullivan include the following stanza in the famously tongue-twisting Major-General’s song:

I’m very well acquainted, too, with matters mathematicalI understand equations, both the simple and quadraticalAbout binomial theorem I’m teeming with a lot o’ newsWith many cheerful facts about the square of the hypotenuse

Broadening the net to include the mathematical sciences brings into play the work of American composer Philip Glass. In 1976, Glass scored and wrote Einstein on the Beach, which was viewed as groundbreaking in several ways—one being that it was nearly five hours long with no intermission. The implication here was that audience members were expected to come and go as they so desired. In a similar vein, it was not plot driven but did contain many references to Einstein, including a musical event meant to suggest a nuclear explosion.

In 2001, Glass wrote the music for the opera Galileo Galilei, which tells the life story of Galileo in reverse. The opera opens with Galileo blind and on his deathbed, follows him back through his trial and astronomical discoveries, and ends with Galileo as a child attending an opera written by his father. Glass returned to the natural sciences a third time in 2010 when he wrote the music for Kepler, an opera that features Johannes Kepler as the only named character, although there are six other soloists and a chorus.

Glass did study mathematics early in his education before devoting himself wholly to music, and he readily admits to seeing mathematics and music as being linked—not just technically but artistically. “The beauty of mathematics is something that mathematicians talk about all the time,” Glass said in a November 2009 feature for the Wall Street Journal. “And the elegance of a mathematical theorem is almost as good as its proof. Not only is it true, but it’s elegant. So you get into almost aesthetic questions.”

Kepler and Galileo are also the featured characters in a 2001 musical called Star Messengers, written by Paul Zimet with music composed by Ellen Maddow. A much more widely toured musical production was Dr. Atomic, written by John Adams with libretto by Peter Sellars. This opera tells the story of the Manhattan Project largely through the eyes of physicist J. Robert Oppenheimer, in part by borrowing text from government documents and interviews with scientists who worked on the bomb. First produced in San Francisco in 2005, Dr. Atomic has since been performed at multiple locations in Europe and the United States, including a live broadcast from the Metropolitan Opera in 2008.

Bibliography

Chin, Cynthia E. “Mathematical Heroes—No Longer Unsung.” PRIMUS 17, no. 1 (2007).

Shepherd-Barr, Kirsten. Science on Stage. Princeton, NJ: Princeton University Press, 2006.