July 5, 2006
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Solemn Dance
Virgil on the Elysian Fields:Some wrestle on the sands, and some in play
And games heroic pass the hours away.
Those raise the song divine, and these advance
In measur'd steps to form the solemn dance.(See also the previous two entries.)
“The cover of this issue of the Bulletin is the frontispiece to a
volume of Samuel de Fermat’s 1670 edition of Bachet’s Latin translation
of Diophantus’s Arithmetica. This edition includes the marginalia of
the editor’s father, Pierre de Fermat. Among these notes one
finds the elder Fermat’s extraordinary comment [c. 1637] in connection
with the Pythagorean equationx2 + y2 = z2 , the marginal comment that
hints at the existence of a proof (a demonstratio sane mirabilis) of
what has come to be known as Fermat’s Last Theorem.”– Barry Mazur, Gade University Professor at Harvard
Mazur’s concluding remarks are as follows:
“But however you classify the branch of mathematics it is concerned
with, Diophantus’s Arithmetica can claim the title of founding
document, and inspiring muse, to modern number theory. This brings us
back to the goddess with her lyre in the frontispiece, which is the
cover of this issue. As is only fitting, given the passion of the
subject, this goddess is surely Erato, muse of erotic poetry.”Mazur has admitted, at his website, that this conclusion was an error:
“I
erroneously identified the figure on the cover as Erato, muse of erotic
poetry, but it seems, rather, to be Orpheus.”“Seems”?
The inscription on the frontispiece, “Obloquitur
numeris septem discrimina vocum,” is from a description of the Elysian Fields in Virgil’s Aeneid, Book VI:
His demum exactis, perfecto munere divae,
Devenere locos laetos, & amoena vireta
Fortunatorum nemorum, sedesque beatas.
Largior hic campos aether & lumine vestit
Purpureo; solemque suum, sua sidera norunt.
Pars in gramineis exercent membra palaestris,
Contendunt ludo, & fulva luctanter arena:
Pars pedibus plaudunt choreas, & carmina dicunt.
Necnon Threicius longa cum veste sacerdos
Obloquitur numeris septem discrimina vocum:
Jamque eadem digitis, jam pectine pulsat eburno.PITT:
These rites compleat, they reach the flow'ry plains,
The verdant groves, where endless pleasure reigns.
Here glowing AEther shoots a purple ray,
And o'er the region pours a double day.
From sky to sky th'unwearied splendour runs,
And nobler planets roll round brighter suns.
Some wrestle on the sands, and some in play
And games heroic pass the hours away.
Those raise the song divine, and these advance
In measur'd steps to form the solemn dance.
There Orpheus graceful in his long attire,
In seven divisions strikes the sounding lyre;
Across the chords the quivering quill he flings,
Or with his flying fingers sweeps the strings.
DRYDEN:
These holy rites perform'd, they took their way,
Where long extended plains of pleasure lay.
The verdant fields with those of heav'n may vie;
With AEther veiled, and a purple sky:
The blissful seats of happy souls below;
Stars of their own, and their own suns they know.
Their airy limbs in sports they exercise,
And on the green contend the wrestlers prize.
Some in heroic verse divinely sing,
Others in artful measures lead the ring.
The Thracian bard surrounded by the rest,
There stands conspicuous in his flowing vest.
His flying fingers, and harmonious quill,
Strike seven distinguish'd notes, and seven at once they fill.It is perhaps not irrelevant that the late Lorraine Hunt Lieberson‘s next role would have been that of Orfeo in Gluck’s “Orfeo ed Euridice.” See today’s earlier entries.
The poets among us may like to think of Mazur’s own role as that of the lyre:
