Gene Ward Smith: Difference between revisions

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Gene Ward Smith (born 1947) is an American mathematician and music theorist. In mathematics he has worked in the areas of [[Galois theory]] and [[Moonshine theory]]. In music theory, he is noted for a number of innovations in the theory of musical tuning, such as the introduction of [[multilinear algebra]] and for being the first to write music in a number of exotic intonation systems. A boyhood friend of [[Steven Spielberg]], a few of his biographical details appear incidentally in the biography of Spielberg by Joseph McBride.&lt;ref&gt;{{citation|first=Joseph|last=McBride|title=Steven Spielberg: A Biography|publisher=Da Capo Press|year=1999|isbn=0-306-80900-1}}.&lt;/ref&gt; While a graduate student at [[University of California, Berkeley|Berkeley]], he and fellow mathematician Matthew P. Wiener gained online notoriety for fierce debating and frequent participation in flame wars on [[Usenet]], causing them to be nicknamed the [[Brahms Gang]] (because ''brahms.berkeley.edu'' was the name of the server they posted from).

Smith introduced [[exterior algebra|wedge product]]s as a way of classifying [[regular temperament]]s, and of dealing with the problem of [[Torsion (abstract algebra)|torsion]]. In this system, a temperament is specified by means of a ''wedgie'', which technically may be identified as a point on a [[Grassmannian]].

Smith has long been drawing attention to the relationship between [[equal division of the octave|equal divisions of the octave]] and the [[Riemann zeta function]].&lt;ref&gt;[http://www.math.niu.edu/~rusin/uses-math/music/12 Why 12 tones per octave?], Dave Rusin. Sequence {{OEIS2C|A117536}} ''Increasingly large peaks of the Riemann zeta function on the critical line'' and {{OEIS2C|A117538}} ''Increasingly large integrals of the Z function between zeros'', [[On-Line Encyclopedia of Integer Sequences]].&lt;/ref&gt;

Smith was among the first to consider extending the [[Tonnetz]] of [[Hugo Riemann]] beyond the [[limit (music)|5-limit]] and hence into higher dimensional [[lattice (group)|lattices]]. In three dimensions, the [[hexagonal lattice]] of 5-limit harmony extends to a lattice of type A&lt;sub&gt;3&lt;/sub&gt; ~ D&lt;sub&gt;3&lt;/sub&gt;.

In mathematics, Smith's most notable achievement is the construction of what has been called the Smith [[generic polynomial|generic cyclic polynomial]].&lt;ref&gt;{{citation|first1=Christian U.|last1=Jensen|first2=Arne|last2=Ledet|first3=Noriko|last3=Yui|title=Generic Polynomials: Constructive Aspects of the Inverse Galois Problem|publisher=Cambridge University Press|location=Cambridge|year=2002|isbn=0-521-81998-9|url=http://www.msri.org/communications/books/Book45/files/book45.pdf}}.&lt;/ref&gt; For any integer ''n'' not divisible by eight, this constructs a polynomial which, upon specializing the values, gives all of the cyclic extensions of any given base field with [[characteristic (algebra)|characteristic]] prime to ''n''. This can then be extended to [[metacyclic]] extensions, such as [[dihedral group]]s.

Smith was also a member of the ''Amdahl Six'' group which held the largest prime record from 1989-1992.&lt;ref&gt;[http://www.isthe.com:/chongo/tech/math/prime/amdahl6.html The Amdahl Six].&lt;/ref&gt;

==References==

==External links==

*[http://lumma.org/tuning/gws/home.htm Smith's old website]

[[Category:American music theorists]]

[[Category:American mathematicians]]

[[Category:Usenet people]]

[[Category:1947 births]]