## Full Biography

Victor Hill was born in Pittsburgh and received his musical training there from his first piano lessons at age four through his graduation from Carnegie Mellon University, where he majored in mathematics, but also completed a four-year program of music theory and composition under Nikolai Lopatnikoff and Roland Leich, and in Dalcroze Eurythmics with Marta Sanchez. During his senior year he had the unusual distinction of holding a part-time Faculty appointment in music theory while still an undergraduate in mathematics.

He went on to do graduate work at the University of Wisconsin on Woodrow Wilson and Danforth Graduate Fellowships, and on National Science Foundation Research Grants. While in graduate school he continued his organ and harpsichord studies and played many recitals, including the first performance ever given at the University of Wisconsin of the complete Art of Fugue by J. S. Bach. In 1966 he received his Ph.D. in mathematics from the University of Oregon (as a student of Charles W. Curtis) and was also awarded the first Performer’s Certificate in Harpsichord to be granted by the University’s School of Music. His organ teachers included Vernon de Tar (New York) and James Evans (Pittsburgh). His harpsichord study was with Alice Ehlers, James Tallis, John Hamilton, and (in Amsterdam) Gustav Leonhardt.

Dr. Hill is the Thomas T. Read Professor of Mathematics, Emeritus, at Williams College (Massachusetts), where he was also Harpsichordist-Organist in his own college-sponsored concert series. Since his retirement from Williams in 2006, he has continued in his concert career. From 1972 to 1996 he was Organist-Choirmaster of St. John’s Episcopal Church in Williamstown. From 1982 to 2011 he served as Archivist of the Association of Anglican Musicians, an international organization of professionals in the Episcopal Church, the Anglican Church of Canada, and the Church of England. Since 1996 he has been a member of the Editorial Board of the Journal of the Association of Anglican Musicians, and from 1998 to 2010 was the Association’s Reviewer of Recordings. He has played more than 900 concerts throughout the United States and in Europe.

His principal mathematical interests are in group representation theory and in history of mathematics; he also taught courses in mathematical logic, mathematics of finance, and in English literature with particular emphasis on the fiction of C.S. Lewis and Charles Williams. He is the author of Groups, Representations, and Characters (Hafner/Macmillan 1975) and Groups and Characters (Chapman & Hall, 2000); he has published scholarly articles in both mathematics and music. His multi-media lecture-recital “Mathematical Aspects of the Music of Bach” has been given more than 50 times throughout the country, including at national meetings. In 1988 he was Visiting Professor of Mathematics and Artist-in-Residence at the Georgia Institute of Technology in Atlanta; he returned to Georgia Tech for 1991-92 as Visiting Professor of Mathematics. He has also held visiting appointments at Carnegie Mellon, SUNY-Albany, North Adams State College (Mass.), and the University of Oregon.

Dr. Hill has two children, Victoria Hill Resnick (Kenyon College ’93) and Christopher Hill (Georgia Tech ’98), and two granddaughters. As an Eagle Scout (1955), he particularly enjoys swimming and canoeing at his summer home on a lake in Sturbridge, Mass.

## Mathematics and Music

### “Mathematical Aspects of the Music of Bach”

- Many people think that mathematics and music have some vague sort of affinity, but most often the supposed relationship between the two fields turns out to be in details that are not central to either. In contrast, VICTOR HILL explores in this multi-media lecture-recital his own experience, as a professional in both fields, of how the concept of a four-dimensional cube relates to the structure of Bach’s fugues. These ideas lead him to a characterization of “elegance” in mathematical proofs and in Bach’s music. The presentation includes a computer-generated film, a painting by Salvador Dali, and musical examples. No technical background in either mathematics or music is presumed.
- Victor Hill has given this presentation more than 50 times throughout the United States.
- This presentation has specific requirements for audio-visual support, physical arrangements on the stage, and honorarium/expenses. Further information is available from Victor Hill by e-mail, phone, FAX, or U.S. mail, as listed on the home page.

### “Comprehending Beauty in Mathematics and in Music”

- Edward Rothstein’s recent book, “Emblems of Mind: the Inner Life of Music and Mathematics,” investigates not only what music and mathematics have in common, but the reasons why the two fields are so intimately related as they seem to be. What is beautiful about creative work in the two fields? Can one find parallels in the concepts of beauty? What is the role of comprehension?
- Victor Hill discusses some aspects of Rothstein’s work and enlarges upon them with ideas of his own, using selected recorded examples.
- Further information is available from Dr. Hill by e-mail, phone, FAX, or U.S. mail, as listed on the home page.

## Memberships

Association of Anglican Musicians, 1979-

- Archivist, 1982-2011
- Editorial Board of the Journal of AAM, 1996-
- Recordings Reviewer for the Journal of AAM, 1998-2010

American Guild of Organists, 1953-2007

- Dean, Berkshire Chapter, 1982-84
- Executive Board, Berkshire Chapter, 1996-1999

Recording for the Blind and Dyslexic, Inc., 1971-2013 (now LearningAlly)

- Reader, 1971-2013
- Board of Directors, Berkshire Unit, 1996-1999

Charles Williams Society, 2001-

- Lecturer, 2009

Associate of the Society of St Margaret, 2002–

Association of Christians in the Mathematical Sciences, 1994–

National Association of Scholars, 1999–

C. S. Lewis Society, 1987–

Richard III Society, 2001–

Mathematical Association of America, 1961–2005

Society for Literature and Science, 1991–2008

Associate of the Society of St. Margaret, 2002-

Association of Christians in the Mathematical Sciences, 1994-

National Association of Scholars, 1999-

C. S. Lewis Society, 1987-

Richard III Society, 2001-

Mathematical Association of America, 1961- 2005

Society for Literature and Science, 1992-1998

## Sample Colloquium Topics

**“Mathematical Aspects of the Music of Bach”**

**“Comprehending Beauty in Mathematics and in Music”**

**“The Burnside Counting Theorem and Group Characters”**

In 1911, W. F. Burnside published (in a form that is only scarcely recognizable when compared to modern notation) a remarkable theorem relating two abstract algebraic concepts that were then still in their youth: what we now refer to as orbits and group characters. Polya in 1957 and Liu in 1968, among others, showed how these concepts can be applied to more recent problems in mathematics. In this talk, Dr. Hill shows how the Burnside Counting Theorem can begin with a simple problem relating to the planning of a set of children’s blocks and can extend to basic questions in group character theory, with applications to spectroscopy in chemistry. This talk assumes a basic background in linear algebra, but does not require a background in group theory; it is accessible to undergraduates in mathematics and the physical sciences.

**“Nearly So and Nearly Not”**

The supposition that “true” and “false” do not exhaust the possible truth values that can be assigned to statements gives rise to many-valued logics. This talk explores some systems of logics with more than two truth values. No technical background is assumed, but some mathematical frame of mind is helpful.

**“Rigor and Pitfall in the Work of Regiomontanus”**

Johannes Mueller of Koenigsberg (1436-1476), who adopted the pen name of Regiomontanus, was probably the most significant and influential mathematician of the 15th century. The printing press and observatory that he set up at Nuremberg were intended to advance the interest of both science and literature. His major work, “De triangulis omnimodis” (1464, pub. 1533), may be regarded as the first mathematical treatise in Western Europe to rise above the elementary and imprecise writings of the preceding centuries. Still, this book curiously combines Greek deductive reasoning with arguments that are often at best not rigorous and at worst simply incorrect. This talk compares those elements in selected proofs from the work of Regiomontanus.

**“Story Problems: their History, Purposes, and Solutions”**

“Story problems” (or “word problems”) have often been feared or hated by generations of students. Yet these problems have a fascinating history, sometimes progressing over centuries from the practical to the absurd, and often presenting additional problems of interpretation, assumptions, or cultural context. In this talk (which assumes only a bit of high school algebra as background), Dr. Hill categorizes these problems from PRACTICE to PREPOSTEROUS and surveys, in particular, the possibility that a given problem may, upon inspection, turn out to have many legitimate solutions.

**“Zero and the Null Set: a Mathematical Talk on Nothing”**

The concept of nothing, zero, came curiously late into the history of mathematics, and it gained intellectual acceptance against much resistance. Still, this idea turns out to be an intriguing thread through the long development of mathematical thought. The relationship between zero and the empty set leads to the remarkable construction in the 20th century of a full set theory out of the mathematical concept of nothing. In this talk, Dr. Hill traces the history of “nothing” in mathematics from prehistory to the present, with literary references from Homer to Hemingway.