Gene Ward Smith

Gene Ward Smith (born 1947) is an American mathematician, composer and music theorist. In mathematics he has worked in the areas of Galois theory and Moonshine theory. As a composer, he is noted for pioneering many different tuning systems Fact|date=April 2008. In music theory, he is noted Fact|date=April 2008 for a number of ideas and innovations in the theory of musical tuning, such as the introduction of multilinear algebra. A boyhood friend of Steven Spielberg, a few of his biographical details appear incidentally in the biography of Spielberg by Joseph McBride. [citation|first=Joseph|last=McBride|title=Steven Spielberg: A Biography|publisher=Da Capo Press|year=1999|isbn=0-306-80900-1.] While a graduate student at 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).

Music theory

Smith introduced wedge products as a way of classifying regular temperaments, and of dealing with the problem of 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 divisions of the octave and the Riemann zeta function. [ [http://www.math.niu.edu/~rusin/uses-math/music/12 Why 12 tones per octave?] , Dave Rusin. [http://www.research.att.com/~njas/sequences/A117536 Increasingly large peaks of the Riemann zeta function on the critical line] and [http://www.research.att.com/~njas/sequences/A117538 Increasingly large integrals of the Z function between zeros] , On-Line Encyclopedia of Integer Sequences.]

Smith was among the first to consider extending the Tonnetz of Hugo Riemann beyond the 5-limit and hence into higher dimensional lattices Fact|date=April 2008. In three dimensions, the hexagonal lattice of 5-limit harmony extends to a lattice of type A₃ ~ D₃.

Mathematics

In mathematics, Smith's most notable achievement is the construction of what has been called the Smith generic cyclic polynomial. [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.] 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 prime to "n". This can then be extended to metacyclic extensions, such as dihedral groups.

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

References

External links

* [http://66.98.148.43/~xenharmo/ Smith's music site]
* [http://66.98.148.43/~xenharmo/gene.html Smith's compositions]