Mathematics Vs Music
congrui t ies . The b ib l iog raphy does not quite m a t c h wi th the text. And what do we m a k e o f the fo l lowing “sequence of p r imes” w h i c h a p p e a r s on page 80: 2, 3, 5, 7, 9, 11, 12, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, . . . As an ac t of pen i t ence , Seuil should re- vise and r ep r in t the edi t ion.
R E F E R E N C E S
[1 ] Michael Atiyah, The Geometry and Physics of Knots, Cambridge: Cambridge University
Press, 1990.
[2] Jim Hoste, Morwen Thistlethwaite, Jeff
Weeks, The First 1 701 936 Knots, Math- ematical Intelligencer 20 (1998), no. 4, 33-48.
Fermat’s Last Tancjo, a Musical MUSIC BY JOSHUA ROSENBLUM, BOOK BY JOANNE
SYDNEY LESSNER, LYRICS BY LESSNER & ROSENBLUMr
A STAGE PRODUCTION FOR THE YORK THEATRE
COMPANY; VIDEOCASSEqTE AND DVD PRODUCED
BY THE CLAY MATHEMATICS INSTITUTE, CAMBRIDGE,
MA, 2001.
REVIEWED BY MICHELE EMMER
I n D e c e m b e r 1996 J o s h u a Rosenb lum read a r ev i ew of Ami r Acz6l ‘ s b o o k Fermat’s Las t Theorem [1] in The New York Times. He s h o w e d it to Joanne Sydney Lessner . “Is t he re a mus ica l in here?” L e s s n e r ‘ s a n s w e r was a def ini te yes. In sp i te of be ing math- phobic , she i m m e d i a t e l y s aw a com- pel l ing de t ec t ive s to ry inheren t in this t h r ee -hundred -yea r -o ld s ea r ch for a proof .
This was the b i r th of the idea of making a mus i ca l on A n d r e w Wiles ‘s adven tu re and the p r o o f of F e r m a t ‘ s theorem. In 1996, S imon Singh had made a f i lm on this proof , and a few months l a te r he p u b l i s h e d a b o o k by the s ame t i t le [2], [3].
Singh’s idea, fo l lowed by John Lynch, the BBC p r o d u c e r of the ser ies “Horizon” [4], [5], w a s tha t the s to ry of Wiles and his d e m o n s t r a t i o n could be- c o m e grea t c inema. It was an adven- ture in h u m a n emot ion , l o a d e d wi th un- e x p e c t e d o u t c o m e s , a rea l drama.
The s u c c e s s o f Singh ‘s f i lm and
b o o k was a n e c e s s a r y p r e c o n d i t i o n to making a mus ica l on the Wiles story. Many peop l e knew the f i lm and the book, so the mus ica l ‘ s a u d i e n c e could eas i ly fol low the story.
Joanne Lessne r is the wife of pi- anist , compose r , and o r c h e s t r a d i rec- tor Jo shua Rosenblum. She he r se l f had wr i t t en sc r ip t s and songs for o the r mu- sicals. What d id they wan t out of a mu- s ical cal led Fermat ‘s Last Tango? In the au thor ‘ s no t e s in the v ideo on the show ( f inanced by The Clay Mathe- mat ics Inst i tute, an ins t i tu te d e d i c a t e d to increas ing and d i s semina t ing math- emat ica l knowledge) , Lessner wri tes , “Our a im with Fermat’s Last Tango is, above all, to enter ta in . We th ink i t ‘s a moving, t ime less s tory tha t benef i t s f rom being to ld in a whimsical , some- t imes i r r everen t fashion. If, a f te r see- ing it, you ‘ re i n sp i r ed to t ake a c r a c k at t rying to f ind Fer ina t ‘ s s imple , ele- gant p r o o f yourself , go r ight ahead.”
If even b iog raphy and fi lm are nec- essar i ly f i c t i o n – – i n that the a u t h o r de- c ides wha t to include, emphas ize or ne- g l e c t – – a mus ica l need not be j u d g e d by its h is tor ica l t ru th fu lness nor by the ac- cu racy of its r e f e r ences to so-ca l led real life.
Never theless , unl ike mos t mus i ca l authors , the a u tho r s r e s e a r c h e d the i r subject . They had a head-s tar t . S ingh ‘s fi lm gives all the e l emen t s of the s tory, f rom the Sh inmra-Tan iyama conjec- ture to ell iptic curves .
Lessner and Rosenb lum m a k e the good choice o f br inging in o t h e r fa- mous ma thema t i c i ans to form wi th F e r m a t a kind o f chorus . As in G r e e k t ragedy, they c o m m e n t and in tervene . They are the gua rd ians of a ma the – mat ic ians ‘ p a r a d i s e which Keane (Wiles ‘s name in the mus ica l ) w o u l d l ike to reach. They are Carl F r i e d r i c h Gauss ( in t e rp re ted by Gilles Chiasson) , Py thagoras (Mitchel l Kantor) , Euc l id (Chr is t ianne Tisdale , a woman) , Sir I saac Newton ( a n o t h e r woman , the tal- en ted Carie Wilshusen) . The main char- ac te r s are obv ious ly Daniel Keane (Chris Thompson) and Pier re de Fer – mat (a very convinc ing J o n a t h a n Rabb). Anna Keane, the wife, is p l a y e d by Edwardyne Cowan.
The s tage set is s imple, the d e c o r
down to a bare minimum: chairs , big numbers , a few books .
The mus ica l s ta r t s wi th an intro- duc t ion to the p rob lem, as if it were a scient i f ic foreword . Jou rna l i s t s a re m o b b i n g Keane. It is the ev ident ly muc h -a w a i t e d m o m e n t of glory. They canno t help but comment , “He m u s t be c r a z y ” – – a r ecu r r en t i dea in f i lms and b o o k s abou t ma themat i c i ans . A m o n g o t h e r things, the j ou rna l i s t s inquire a b o u t the mean ing of the theo rem. In Singh ‘s fi lm the s tuden t s r e p e a t a lim- e r i ck on Py thagoras ‘ s theorem. In the musica l , natural ly, they sing it.
In the song “The Beauty of Num- bers ,” Keane regre t s having f in ished the p r o o f – – a s in the fihn a P r ince ton m a t h e m a t i c i a n a sks who will ever pro- v ide a c o m p a r a b l e p rob lem. It is fine thea t re . Some of the l ines a re good, even f rom a ma the ma t i c a l s t andpoin t : “Per fec t ion l ike pi and the go lden sec- t ion.”
In an amusing song, F e r m a t m a k e s fun of the c omple x i t y of Wiles ‘ s proof . Keane-Wiles come back wi th “Show me you r mmazelous proof .” F e r m a t refuses: “My lips a re sealed.” Keane: “The wor ld dese rves to see.” Fe rmat : “But if the mys te ry we re re- vea l ed I wou ld lose m y immorta l i ty ; I t ake the a n s w e r to my death.” Keane has the last word: “You a re al- r e a d y dead.”
Along with some of the quar te t s sung by the f amous ma themat i c i ans , the K e a n e – F e n n a t due t s are a m o n g the be s t pa r t s of the musical . Keane ‘ s en- c o u n t e r wi th the famous four is a lso enter ta in ing. Each of the four pro- c la ims his own super ior i ty . Keane rec- ognizes a h a p p y and grateful Gauss who excla ims: “Finally!” Then E u c l i d – – yes, the E u c l i d – – i s i n t roduced to him. T o w a r d the end, when Keane th inks he has s e c u r e d a p lace among the f amous ma thema t i c i ans , Fermat , who is stil l keen on def la t ing him, te l ls him tha t in his p r o o f the re is a “big fat hole.” Fer – m a t is bri l l iant , ironic. The ma thema t i – c ians b u r s t out laughing. F e r m a t sings, “No one will share my fame. It is the on ly th ing I have.” In the mos t amus ing scene of the musical , Keane is then s c o r n e d because , at a lmos t 40, he is t oo o l d – – t o o old to be c ons id e r ed for the
VOLUME 25, NUMBER 1, 2003 77
F i e l d s m eda l . T h e c h o r u s s ings , “Math-
e m a t i c s is a y o u n g m a n ‘ s g a m e . ”
K e a n e is d e s p e r a t e . Like t h e rea l – l i fe
Wiles , h e t a k e s r e f u g e in h i s f ami ly un-
til t h e e n l i g h t e n m e n t f ina l ly a r r ives .
D r a m a t i c as in S ingh ‘ s f i lm, w h e r e t h e
t r u e Wiles is s h o w n w e e p i n g w i t h e m o –
t i o n e v e n s ix m o n t h s la ter .
“You wil l a l w a y s b e t h e r e / I t h i n k I
wi l l be a b e t t e r h u s b a n d / It is o f t e n
sa id , w i t h i n y o u r fa i lu re lie t h e s e e d s
o f y o u r s u c c e s s . ” Th is l a s t p h r a s e , by
K e a n e ‘ s wi fe , c u e s an a s s o c i a t i o n al-
l o w i n g h i m to c o m p l e t e t h e p r o o f . N o t
a v e r y c o n v i n c i n g p l o t g i m m i c k . T h e
p r e s s c o n f e r e n c e e n d i n g is a l s o p r e –
d i c t ab le . K e a n e c o m e s to F e r m a t ‘ s de- [4]
f en se , s ay i n g h e w a s a g r e a t m a t h e –
m a t i c i a n a n d s u r e l y h a d a p ro o f . T h a t ‘ s
n o t w h a t t h e r e a l Wiles s a y s in S ingh ‘ s
film. On b a l a n c e , t h o u g h , t h e g a m b l e o f [5]
t ry ing to p r o d u c e an e n t e r t a i n i n g a n d
m a t h e m a t i c a l l y c o r r e c t m u s i c a l t u r n e d
o u t a s u c c e s s .
REFERENCES
[1] Amir Aczel, Fermat’s Last Theorem, Four
Walls Eight Windows. New York, 1996.
[2] Simon Singh, Fermat’s Last Theorem,
1997.
[3] – – & John Lynch, Fermat’s Last Theo-
rem, Video, BBC (1996).
Simon Singh, L’ult imo teorema di Fermat: il
racconto di scienza del decennio, in M. Em-
mer, ed., Matematica e Cultura 2, Springer- Verlag Italia, Milano (1999), p. 40-43.
John Lynch, Alcune riflessioni sulla con-
struzione del film, in M. Emmer and M. Man-
aresi, eds., Matematica, arte, tecnologia,
cinema, Springer-Verlag Italia, Milano
(2002), p. 266-267; English edition to ap-
pear.
Dipartimento di Matematica
Universita Ca’ Foscari
Dorsoduro 3825/E, Ca’ Dolfin
30123 Venice, Italy
e-mail: emmermve@unive.it
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78 THE MATHEMATICAL INTELLIGENCER