Number Theory

This essay by dramaturg Drew Lichtenberg was originally published in the program for The Huntington's production of Leopoldstadt in September 2024. 

Prime numbers are mysterious. They are indivisible. Each is unique. And they are infinite in number. But otherwise they have proven resistant to totalizing theories. No one knows why they behave the way they do. They appear to be distributed according to the laws of complete randomness. 

“Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers.” Leonard Euler wrote that in the 18th century. “It is a mystery into which the human mind may never penetrate.” 

Prime numbers are one of the prime metaphors in Tom Stoppard’s Leopoldstadt. Early in the play, Ludwig Jacobowitz, a mathematician, recounts a recurring dream. He has solved the riddle of prime numbers. He has proven the hypothesis of Bernhard Riemann, first postulated in 1859. 

Of course, Ludwig is wrong. Riemann’s Hypothesis remains unproven to this day.

The scenes in Tom Stoppard’s Leopoldstadt at first move through time in a linear sequence. It starts firmly as a play set in 1899. Before intermission, it leaps forward to 1924, initiating a sudden series of rapid shifts. After the interval, we are off, hurtling through time and space. With each of these shifts, the world of the characters changes in unthinkable ways. History, it seems, is like a prime number, too. It defies rational explanation. 

“If we think of the world’s future, we always mean where it will be if it keeps going as we see it going now,” Ludwig Wittgenstein wrote in 1929. “It doesn’t occur to us that it is not going in a straight line but in a curve, constantly changing direction.” 

Tom Stoppard has performed metafictional gambits like these throughout his remarkable career. Rosencrantz and Guildenstern are Dead (1966) mashes up Hamlet with the dramaturgy of Beckett’s tramps. Travesties (1974) combines Oscar Wilde with Dadaism, Joyce’s Ulysses, and the Russian Revolution. But Arcadia (1993) is Leopoldstadt’s most clear forebear. Using chaos theory as a governing principle, it toggles between the Romantic epoch of 1809 and pre-millennial Britain. 

Through techniques like these, Stoppard makes thought itself—often dull in the theatre—come alive. His plays are intellectual farces, intellectual romances, intellectual tragedies. Philosophical, mathematical, and scientific paradoxes lie at their heart. But these abstract ideas obtain the limpid quality we associate with deep emotion. 

If Arcadia connects past to present, Leopoldstadt recreates a world lost to the abyss of time. It is Stoppard’s most autobiographical play. He refused to write it while his mother was alive. He has sometimes claimed it will be his last. He has been waiting his whole life to write it, though it was inspired by a late self-discovery. 

In 1993, Tom Stoppard was visiting Prague on literary business. He was 57. A young man was waiting in his hotel lobby, holding photographs of Stoppard as a baby and his mother in jazz-age outfits. “The fact that my mother was beautiful had escaped me,” Stoppard recalls. “The realization was shocking.” 

Stoppard was born Tomáš Sträussler in 1937 in Zlin, Czechoslovakia. Raised in England, he never knew the full truth of his identity: he was Jewish. His family fled the Nazis after the annexation of the Sudetenland. His father died when he was four, and his mother remarried a British army major, Kenneth Stoppard. But the bulk of this relatives remained behind; they died in the Holocaust. 

The young man was Alexandr, Stoppard’s Czech cousin. Alexandr took him to the Pinkas Synagogue. The names of his relatives were on the wall, along with nearly 80,000 others. 

Leopoldstadt is the name of the Jewish ghetto in Vienna. It was the quarter where thousands of Jews emigrated from Eastern European shtetls. Many arrives bearded and in kaftans. Their grandchildren would wear top hats, monocles, fancy dresses. And regard themselves as completely Viennese. 

At the turn of the century, Vienna was the cosmopolitan capital of an enormous, wealthy empire. It had the largest number of converted Jews in the world. As Stoppard’s play reminds us, Jewish genius was everywhere. Arthur Schnitzler introducing the stream-of-consciousness to literature. Sigmund Freud inventing psychoanalysis. Gustav Mahler reimagining modern music. Hugo von Hoffmansthal writing the greatest German verse since Goethe. And Wittgenstein the most profound philosophical texts of the 20^th century. 

To many assimilated Jews in Vienna, culture was a secular religion. Through merit, they thought they would earn the respect of their fellow Austrians. 

They were wrong. Historian George Berkeley calls the Jewish love for Vienna “the most unrequited love affair in urban history.” During the Anschluss—March 13, 1938—Nazi troops crossed the border into Austria. Much to their surprise, cheering crowds greeted them. The majority of Austrians were in favor of German unification, even if it meant adopting antisemitic policies. 

Leopoldstadt shows us how fragile society is—how quickly the world can change. Stoppard may well intend it as a warning about the future. The sophisticated culture of fin-de-siècle Vienna also attracted a young Austrian named Adolph Hitler. He applied to the Academy of Fine Arts to be a painter. After his rejection, he became a murderous madman. The beautiful world of Vienna helped give rise to Nazism. It is a tragic historical irony, one very much in line with Stoppard’s metaphor of the terrifying randomness of the distribution of primes. 

But Stoppard also seems to be saying something more personal, about the paradox of human identity. We are like prime numbers. Each of us is indivisible, unique. We behave in mysterious ways. And yet we are part of something much larger, a sequence that appears random but that follows its own inexplicable logic. 

Riemann’s Hypothesis sets out to prove the distribution of prime numbers—to predict the future, in other words. It is a complex equation that posits that one needs to count backwards as well as forward, upward to infinity but also backward toward infinity. When laid out graphically in three dimensions, it produces a beautiful landscape. Atomic physicist Freeman Dyson likens it to the behavior of energy patterns in large atoms such as uranium. If true—and evidence suggests it is—prime numbers may well be the pattern of our natural world, expressed in numbers. They are the mathematical face of God, beautiful and terrible in their apparent randomness. 

The Riemann Hypothesis is also a family tree. We all may be prime numbers. But we can only be understood, in all of our uniqueness, by looking at the past where we come from.