Biographical Sketch of Henry W. Gould

Henry W. Gould, Professor Emeritus of Mathematics, West Virginia University, was born in Portsmouth, Va. (26 August 1928). He graduated from Woodrow Wilson High School in Portsmouth in Jan. 1946. He studied at the Norfolk Divison of the College of William and Mary (now Old Dominion University) (1946-48), at the University of Virginia where he received his B.A. (1954) and M.A. (1956) in Mathematics, and at the University of North Carolina at Chapel Hill (1957-58), where he was a Research Assistant to Professor Alfred T. Brauer in his work on the location of characteristic roots of matrices using ovals of Cassini. He is also a graduate of the National Radio Institute, Washington, D.C. (1947), and studied communications theory at The Southeastern Signal School (TSESS), U. S. Army, Fort Gordon, Ga. (1951-52). In the late 1980's Gould studied Chinese, linguistics, and took graduate work in behavioral psychology (Behaviorology a la B. F. Skinner) at West Virginia University. Beginning in 1952, and until his death in 1999, Gould's mentor in mathematical research was Professor Leonard Carlitz at Duke University.

In 1957, at the University of Virginia, he was elected a full member of the Sigma Xi Research Society for his distinction in mathematics.

Early in his career (1963) he was elected a Fellow of the American Association for the Advancement of Science. 

Gould was elected to the Beta Chapter of the national mathematics honorary Pi Mu Epsilon at the University of North Carolina (Chapel Hill) in 1957, and was one of the charter members of the Alpha Chapter at West Virginia University in 1967.

He joined the faculty of West Virginia University as an instructor in 1958, and received the rank of Professor in 1969, becoming Professor Emeritus, Spring 2007, after 49 years of service at WVU. He continues his research, writing and working with faculty and students at West Virginia University even as he is past the age of 83 years.

He has been a consultant with the National Security Agency, Principal Investigator at WVU with several College of Arts and Sciences grants, and grants from the National Science Foundation on the topic of Combinatorial Identities, and has served as a reviewer for the Mathematical Reviews and the Zentralblatt für Mathematik. At West Virginia University he directed a Research Program under auspices of the Office of the Provost in 1976-77 concerned with mathematical computations for coal mine valuation, using Bondurant's variation of the Hoskold actuarial formula.

He received the J. Shelton Horsley Research Award from the Virginia Academy of Science in 1977. 

In 1976 he was invited to organize a Special Session on Combinatorial Identities for the American Mathematical Society at its Summer Meeting in Toronto, Canada. He was an invited lecturer at the NSF CBMS Regional Conference on Special Functions at V.P.I. in 1974. He was a Visiting Lecturer for the Mathematical Association of America (1967-70) and for the Society for Industrial and Applied Mathematics (1974-76). He was an invited participant to the first Annual Symposium on the History of Mathematics held at the National Museum of Science and Technology, Smithsonian Institution, Washington, D.C., in 1976, concerned with Cauchy's contributions to analysis. Gould has published  extensive bibliographies on combinatorial topics and on Cauchy's integral theorem. 

Professor Gould was elected a Foundation Fellow of the Institute of Combinatorics and its Applications (1990).

Gould was elected an Honorary Fellow of the Institute of Combinatorics and its Applications at the 19th Annual General Meeting of the Institute, 10 March 2010 at Florida Atlantic Univesity.

Gould's continuing research and long-time service to West Virginia were recognized by his receiving the prestigious Benedum Distinguished Scholar Award for Physical Sciences and Technology in ceremonies in March 1988.

On the occasion of his 70-th birthday in 1998, a Colloquium was held at West Virginia University in honor of Henry and his wife Jean, with invited talks by mathematicians from the U.S., Canada, Zimbabwe, and Denmark. A special framed letter of commendation was presented to him from U. S. Senator Robert C. Byrd, acknowledging and praising Gould's long-time service to WVU. Gould jokingly called the event his "mid-career celebration". 

Volume 204(1999) of the journal Discrete Mathematics was dedicated in honor of Gould and his work and contained numerous invited papers in his honor. The volume was edited by Ira M. Gessel, Louis W. Shapiro and Douglas Rogers. It contained an amusing biographical preface by the editors.

Professor Gould has published over 200 papers, which have appeared in about 20 countries. He is the author of the widely used, major reference book Combinatorial Identities published in 1972. His research has been in combinatorial analysis, number theory, special functions of mathematical physics, and the history of mathematics and astronomy.

Some of his early work (1956) was used by Oakley and Wisner (1957) to enumerate hexaflexagons.

In 1962 Gould was one of the founding editors of the number theory journal Fibonacci Quarterly and for many years has been an associate editor of the Journal of Mathematical Research and Exposition founded by L. C. Hsu and published at Dalian, People's Republic of China. Professors Hsu and Gould began a research collaboration in 1965, seven years before Nixon's famous visit to China. Gould is also an associate editor of the on-line electronic Journal of Integer Sequences, and is a member of the editorial board of the journal Applicable Analysis and Discrete Mathematics published by the University of Belgrade, Serbia. 

From 1974 to 1979, Professor Gould was Editor-in-Chief of the Proceedings of the West Virginia Academy of Science.

Gould founded and circulated a mathematical serial Mathematica Monongaliae, of which 12 issues were published from 1961 to 1971. Several of these have been reprinted extensively, such as issue No. 12, a "Bibliography of Bell and Catalan Numbers". This annotated bibliography was cited in two separate articles by Martin Gardner in his mathematical column in the Scientific American magazine. Issue No. 10, a "Chronological Bibliography of the Cauchy Integral Theorem" listing 200 proofs of the famous theorem was coauthored with Herbert K. Fallin. The bibliography was cited in the journal  Historia Mathematica. With the aid of WVU graduate student Timothy Glatzer, the Bell and Catalan number bibliography is being revised and re-alphabetized with the intent of making it available online. 

At WVU he was in charge of the development of a Departmental Mathematics Research Library 1960-2007. The library had only some 89 journals in 1958, but was expanded to reach as many as 250 titles by 1978. Since then money has been tight at WVU and subscriptions have been lost. The WVU Departmental Library was discontinued in June 2008 and its holdings moved into Wise Library and older materials into a WVU Depository storage facility. The former library space is now used to house an undergraduate calculus tutorial center with more than a hundred computers.

Gould served as mathematics consultant to the 'Dear Abby' newspaper column. One interesting aspect of this work was writing an explanation of the three ancient Greek problems (trisecting an angle, squaring the circle, and duplicating the cube). A pamphlet on this material was sent to hundreds of readers (mostly secondary school students) in every state and overseas, who wanted to know more about these famous problems.

An article entitled "An Interview with H. W. Gould", by Prof. Scott H. Brown, appears in the College Mathematics Journal, Vol. 37, No. 5, November, 2006, pp. 370 - 379. This includes biographical notes and photos.

As Professor Emeritus of Mathematics, Gould continues his research and service at West Virginia University. On the occasion of his recent retirement another special framed letter of commendation was presented to him from U. S. Senator Robert C. Byrd, and a similar letter from U. S. Senator Jay Rockefeller, acknowledging and praising Gould's long service to WVU.

A Mathematics Colloquium was held in Gould's honor on 20 Sept. 2007, at which time George E. Andrews, Evan Pugh Professor in the Department of Mathematics at The Pennsylvania State University and President-Elect of the American Mathematical Society, presented a paper “Gould’s Function and Problems in Partitions,” as part of the WVU Distinguished Lecture Series in Mathematics in the Eberly College of Arts and Sciences. Andrews' paper was motivated by Gould's 1964 paper on compositions into relatively prime parts.

Also at this celebration Dot Underwood, Assistant to West Virginia Governor Joe Manchin, III, presented a special certificate to Gould, signed by the Governor, making Gould an "Honorary Mountaineer" in recognition of his 49 years of outstanding service to WVU and for his dedication to research and education in the field of mathematics.

Among his recent activities, Gould began a research collaboration with Dr. Jocelyn Quaintance, Visiting Research Assistant Professor of Mathematics at WVU in 2006-2010. They are working on a long-term revision of Gould's 1972 book "Combinatorial Identities", and Gould's manuscript notes covering 1945-1990. Since 2010 Dr. Quaintance has been supported as a consultant by a private foundation.

Henry Gould and Jocelyn Quaintance have just signed a contract in July 2014 with World Scientific Publishing Co., Singapore, for one volume of  a three-volume text based on seven volumes (2000 handwritten pages) of formulas and identities which Gould put together from 1945 to 1990. This first book is titled "Combinatorial Identities for the Stirling numers", and may appear in 2015,

Other Biographical Details:

Among his hobbies are poetry, cryptography, philosophy, debating, hiking in the mountains, stamp collecting, genealogy, astronomy, carpentry and Dumpster Diving (he is the local "Oscar the Grouch", known for retrieving valuable papers, books and journals from WVU dumpsters and creating the "WVU Math Library in Exile"). He has had a long-time interest in drawing cartoons and caricatures, being influenced by his late distant cousin Chester Gould who invented and drew "Dick Tracy" for 50 years. Chester's grandfather was from West Virginia. One of Gould's principal hobbies is book collecting, and his personal library has holdings of some 60,000 general titles, but also several thousand mathematics titles and many journals and a large mathematics reprint file. Gould now contributes notes on Facebook.

In 1945 Gould learned glass blowing and designed and built a Geiger counter tube (with associated circuitry) that was used in efforts to locate lost radium at Norfolk General Hospital. In 1944-45 Gould designed and built several giant million-volt Tesla and Oudin coils, and designed a special, small, cigar-box Tesla coil for the late Hubert J. Davis, Director of the Norfolk County Teaching Aids Library, that was used in schools all over the South to encourage students to study science.

In 1944-45 he built and operated Civil Defense UHF radio station WJWB-12 in Portsmouth, Va, as part of the War Emergency Radio Service (WERS). Gould has been an amateur radio operator (ham) since 1955. His call letters are K4CQA (and also for a time WB8OSE), and he has contacted stations in over 100 countries using Morse code at up to 25 words per minute. He served as a Class I Official Observor for the American Radio Relay League, monitoring amateur radio operations, making precise frequency measurements, and sending warning notices. He received certified ARRL recognition of Morse code proficieny of 25 words per minute, 

In the mid-1950's he received a special Letter of Commendation from the Secretary of the Federal Communications Commission for helping to monitor and close down an illegal ham station operating on a secret NATO cruise in the English Channel. 

Gould was instrumental in establishing amateur radio clubs at the University of North Carolina (1957) and at West Virginia University (1958). He worked for some years as a radio engineer (holder of FCC First Class Radio Operator License since 1955 and a third class commercial licence from 1945) and announcer, especially at WUVA, the student radio station at the University of Virginia (1948-57), where he was specially recognized for his work in improving the broadcast transmitting equipment. As an announcer he ran programs of classical, popular and country music.

Starting 4 Oct. 1957, at Chapel Hill, NC, Gould monitored the first 300 orbits of the first Russian SPUTNIK, which broadcast beeping sounds on 20.005 MHz. He followed the news of the Sputnik in the Soviet newspaper PRAVDA.The orbits were traced out on a world globe and tracking data was sent by ham radio to Cape Canaveral. He monitored 200 orbits of the second Sputnik and 150 orbits of the third Sputnik, and developed a mathematical formula to determine the distance of closest approach of the Sputnik above the observer. This was based on measuring the Doppler effect by checking against a precise frequency standard. The formula and proof were published in the Proceedings of the West Virginia Academy of Science, Vol. 36(1964), pp. 169-174. 

He was one of the founders of the Morgantown Astronomy Club. From 1965 to 1980 Prof. Gould, together with Wilbur Bluhm (deceased), A. Dale Randolph (deceased), and others, founded and ran the Morgantown Astronomy Club. Gould was President and edited their newsletter for ten years. The club had 60 members and some 40 telescopes. Public viewing sessions were held.

Gould's wife Jean is a full-time student at West Virginia University, receiving a bachelor's degree in art history (specializing in fifteenth and sixteenth century Florentine sculpture and painting) in 2005, and  receiving her BFA degree in sculpture in May 2009, and she is now studying therapeutic horsemanship and working with autistic children.

For ten years (circa 1970-1980) Gould and his late first wife Josephine founded and ran the Morgantown Orchid Society and Gould edited their Newletter. Lectures and slide presentations were given, introducing many people to orchid culture. Bus trips were organized to take hundreds of people to orchid shows in Pittsburgh.

Gould has had a life-long interest in languages. Besides being fluent in German, he has taken courses in Greek, Hebrew, Arabic, and Chinese. He began his study of Chinese characters circa 1942, and took courses in spoken Chinese circa 1989 at West Virginia University. He subscribed to Pravda, Izvestia and Krokodil in order to practice reading Russian. His interests have included artificial languages, word studies and cryptography. Learning from his father to count in Arabic at an early age, and with a deep interest in the Middle East, Gould served for three years as Faculty Adviser to the WVU Arab Students Club 1958-61.

Some general articles relating to Gould's life and work:

  1. Susannah Grimm, "WVU-China Correspondence Resumes After President's Visit", WVU Magazine,
      Vol. 4, No. 3, Fall 1972, pp. 20-21. (with photo)
  2. Earl Lemley Core, "The Monongalia Story. A Bicentennial History", 5 Volumes, 1974-1984, Published
      by the McClain Printing Co., Parsons, W. Va.  Gould is credited in several volumes for information
      about the history of the WVU Mathematics Department and the old WVU Observatory (1901-1919).
  3. Elsa Nadler, "The Case for Vectors", Inquiry (WVU magazine), Spring 1986, pp. 25-27. (photo)
  4. Ira M. Gessel, Louis W. Shapiro and Douglas Rogers (Editors). Biographical notes about Henry Gould,
      Discrete Mathematics,Volume 204(1999), front pages, Entire volume was dedicated in honor of Gould.
  5. Norman Julian, "Numbers are No. 1 in this math professor's life", Dominion Post, Morgantown, WV,
      Sunday, 2 April, 2000.
  6. by the editors,  Photo and short story about Half Professors Charlie Brown and Spotsie Ann,
      Bull. Inst. Combinatorics and its Appls., 36(2002), Sept., p. 102.
  7. Scott H. Brown, "An Interview with H. W. Gould", College Mathematics Journal, Vol. 37, No. 5,
       November, 2006, pp. 370-379. (eight photos)
  8. Mary Ellen Mazey, Dean, Eberly College, "Our Accomplished Faculty", The Eberly College Magazine,
      Spring 2008, p. 1, contains remarks about Gould's work at WVU.
  9. Katherine Kline, story about Henry Gould retiring, The Eberly College Magazine, Spring 2008,
10. Malinda Reinke, Man + Math = Love, Retired Professor Heney W. Gould Knows Formulas,
      Dominion Post newspaper, Mon. Nov 7, 2011, Section: Front Page and page 4.
11. The Modern Renaissance Man, by Dave Carl and Wayne Haviland,
12. Henry Gould, Sherlockian Who’s Who 2016,

Some Theses directed at WVU:

Allen Taylor Hopper, Generalized Hermite Polynomials, M.S., 1961.
Herbert Kirk Fallin, Jr., Cauchy's Integral Theorem, M.A., 1964
       (Co-directed with Prof. Charles H. Vehse).
Charles F. Waiveris, Jr., Factorials: Their History, Generalizations, and Characterizations, M.A., 1973.
Michael J. Kuchinski, Catalan Structures and Correspondences, M.S., 1977. This thesis is linked to
       Gould's 1971 bibliography of Catalan Numbers for the references.
Michael M. Watts, An Examination of Mine Valuation Formulas, M.B.A., 1977
       (data on W. Va. coal mines collected by Jairo Velez).
Stephen A. Ford, Analyses of Formulas for Coal Tax Evaluation (Hoskold-Bondurant Formulas),
       M.S., Computer Science, 1977.
John P. Ryan, An Historical Consideration of the Theory of Primitive Roots, M.S., 1980.
Louis Worthy Kolitsch, A Relationship Between the Partition Function and and the Bracket Function,
       Master's Project Paper, 1981 (Co-directed with Prof. Michael E. Mays).
Temba Shonhiwa, Investigations in Number Theory Functions, Ph.D. Dissertation, 1996.
Stephen L. Richardson, Jr., Enumeration of the Generalized Catalan Numbers, M.S., 2005.

Updated 23 Oct. 2016