MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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The Five Hysterical Girls Theorem (2000)
Rinne Groff
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I think this play about a number theory conference at the British seaside at the turn of the 20th century may be misunderstood. The plot revolves around the neuroses of the senior researcher, Moses Vazsonyi, who fears that he is losing his skills and the young Frenchman, Pierre Louis Le Blanc de Fontanelle, who has apparently proved the theorem that Vazsonyi has been struggling with. The theorem, which it is hinted will be related to the Riemann Hypothesis, concerns the existence of prime numbers made up of strings of the digit '3' linked by individual '4's. The cutesy name for the theorem comes from the fact that (when written in the right font) these numbers look like "eeheeheee" when viewed upside-down. (An entry in the encyclopedia of integer sequences mentioning these numbers can be found here.)

The author certainly has done a lot of research about mathematics and the history of mathematics in order to write it, and I suspect that an audience member who is not similarly an expert in both will miss many of the plot twists and cultural references. Consider the following review in the New York Times:

Contributed by Bruce, Weber, New York Times

In this challenging, willfully baffling and finally irritating play, staged as an absurdist comedy by the Target Margin Theater and the director David Herskovits, the uncertainty is the point, I think -- that for all their beauty, numbers don't explain much. It's a reasonable enough premise, and that mathematicians are prone to pomposity as they seek to explain the world anyway is an apt focus of satire. Indeed, there is estimable ambition here, in the playwright's themes -- a lot of love and death and betrayal -- and stylized language. But for all the playwright's obvious research I'm not sure she understands the math, and I'm not sure she cares, and largely as a result her play's expostulations on the power and impotence of numbers are too oblique and disjointed to resonate with coherence. A little knowledge is, in fact, a dangerous thing.

Having now read the play myself (although I have never seen it), I must say that I disagree. It seems to me that the author most certainly understands the math. For instance, from the beginning of the play, Vazsonyi's daughter Hypatia is playing with the number 267-1. First she computes it by raising two to this large power and subtracting one. Then she also computes it as a product: 193,707,721 x 761,838,257,287. To most audience members, these scribbles that she writes without comment probably just look like "some math". But, it becomes quite important to the plot when one of the mathematicians at this conference is presenting his talk in which he will demonstrate the existence of an odd perfect number. This is a dramatic moment for the speaker and the audience because they consider this to be quite a significant discovery. The proof depends on the primality of the number 267-1, from the sequence of prime numbers discovered by Mersenne. However, Moses notices Hypatia's factorization of this number written on the wall, thus destroying the speaker's proof and leading to his suicide! In fact, Mersenne did mistakenly claim that 267-1 (abbreviated as M67) was prime, and this is connected to the theory of perfect numbers. Quoting Wikipedia:

Contributed by Wikipedia

Mersenne primes were considered already by Euclid, who found a connection with the perfect numbers. They are named after 17th century French scholar Marin Mersenne, who compiled a list of Mersenne primes with exponents up to 257. His list was only partially correct, as Mersenne mistakenly included M67 and M257 (which are composite), and omitted M61, M89, and M107 (which are prime). Mersenne gave no indication how he came up with his list, and its rigorous verification was completed more than two centuries later.

Another source of tension in the play is the growing concern about paradoxes and the possibility of undecidable propositions in mathematics, foreshadowing the discoveries of Kurt Gödel that the educated audience member realizes are only 20 years away (since the play takes place in 1911). Other points that may be lost on most viewers are the inside-jokes hidden in the names of some of the characters: Moses' daughters (Sophie and Hypatia) and especially the name of the hotel proprietress (Hilbert).

So, I think the play must be thought of as being more meaningful than NYT Reviewer Weber gives it credit for. Still, I must admit, I am not exactly sure what it is trying to say either. It does not seem to me that it is ridiculing the mathematicians as being pompous or criticizing them for thinking that math is valuable. Certainly, the limits of the powers of math are a factor in the play, but not so much that it overshadows the value and beauty of the math. Consider, for example, this soliloquy from Hypatia towards the end of the play:

(quoted from The Five Hysterical Girls Theorem)

Even if I was born physically deformed, and I had a hundred ninety-one fingers instead of ten, and my whole counting system was different than the base ten system that the rest of the world uses; even in base hundred nintey-one, the Prime Numbers would still be there, and they would be exactly the same Prime Numbers that we've always known. No matter how many digits God gave to us, and how we managed to count and organize numbers, the same Primes, with the same Properties, would exist. They are the building stones of our Universe, each one indivisible, altogether Infinite.

So, then, what is the play about? It seems much more about the emotions and human interactions at this beachside conference. The romances (illicit and otherwise), the marital difficulties, the egotism, the temptation to plagiarize. Perhaps the height of the dramatic tension occurs in the scene where people are arguing over the ownership of the notebooks in which the Five Hysterical Girls theorem is proved. My biggest complaint is that this seems too derivative of Auburn's Proof. I am not aware of any such argument occurring in the actual history of mathematics but, just like the math conference pill popping which occurs here and in Proof, it is becoming a standard part of mathematical fiction.

I would love to see this play performed sometime. Perhaps then I would even feel that I understand the point. Until then, I can only say that Groff has really included some interesting mathematics in a play reminiscent of Proof and Arcadia...and that's not bad company to be in at all!

Another review of the play can be found at http://www.curtainup.com/hystericalgirls.html

More information about this work can be found at www.playscripts.com.
(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to The Five Hysterical Girls Theorem
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Arcadia by Tom Stoppard
  2. Goldman's Theorem by R.J. Stern
  3. The Penultimate Conjecture by Leonard Michaels
  4. Continuums by Robert Carr
  5. Proof by David Auburn (playwright)
  6. A Beautiful Mind by Sylvia Nasar / Akiva Goldsman
  7. The Ishango Bone by Paul Hastings Wilson
  8. Sophie's Diary by Dora Musielak
  9. Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis
  10. Pythagorean Crimes by Tefcros Michaelides
Ratings for The Five Hysterical Girls Theorem:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
5/5 (1 votes)
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Literary Quality:
4/5 (1 votes)
..

Categories:
GenreHistorical Fiction,
MotifAnti-social Mathematicians, Academia, Proving Theorems, Female Mathematicians, Romance,
TopicAlgebra/Arithmetic/Number Theory, Real Mathematics, Logic/Set Theory,
MediumPlays,

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(Maintained by Alex Kasman, College of Charleston)