## Section 2.8 Profile: Joseph Benson Reynolds (1881-1975)

Joseph B. Reynolds was not only one of the three founders of our section, he was the one who initially proposed the idea of forming an MAA

^{ 1 }section in the Lehigh Valley. Although he was a productive scholar, he is perhaps the least likely of the trio to be involved in such an undertaking, because the other two had much deeper connections in the American mathematical community.J. B. Reynolds was born in New Castle, in the western part of Pennsylvania, on May 17, 1881, to Peter Stafford and Lydia Ann (Kemp) Reynolds. He was educated in public schools, graduating from New Castle High School in 1903. Considering his later accomplishments, graduation at age 22 is certainly not due to lack of intelligence; rather it was probably due to the need to work on the family farm. Upon graduation he crossed the state to enroll at Lehigh University, where he earned an A.B. degree four years later. The title of his undergraduate thesis portends an interest in applied mathematics, as well as the inclination of the Department of Mathematics and Astronomy at the time – “The temperature compensation of the Bond sidereal clock of Sayre Observatory at Lehigh University”.

Reynolds loved this part of the state from the outset of his undergraduate days. Indeed, he was associated with Lehigh in various capacities for the rest of his career. The first position occurred upon graduation when he accepted an instructorship. His bond to the area was cemented when he met and married Chloey B. Graham on July 2, 1908. The couple had three children: Peter Graham, Jane Niblock, and Joseph Benson Jr.

Reynolds continued his studies while teaching at Lehigh, earning a masters degree in 1910. Once again he wrote a thesis with an astronomical theme, “The determination of the elements of the orbit of a minor planet: Taunton no. 94, ‘Lehigh’.” In 1928 he was promoted to professor of mathematics and theoretical mechanics. Could his role in the founding of the Philadelphia Section have played a part in the promotion? If it did, it probably was not so important as time spent as Acting Head of the department during 1924-1925.

J. B. Reynolds was an active participant in sectional affairs. He was the first person to present an invited lecture at the organizational meeting in 1926, he served as chairman of the section in 1938-1939, and he represented the MAA

^{ 2 }officially at the 1949 inauguration of the new president at Moravian College.The Monthly accounted for almost all of Reynolds’ publications, with roughly 90 of the 100 entries appearing in its Problems Department. His first endeavor with the journal occurred when he proposed two problems for solution in the May 1915 issue, one on calculus and one in mechanics. In the remainder of that year he was credited with solving three problems; his solution to a problem on mechanics posed by Monthly founder B. F. Finkel was published as the most elegant of the correct solutions received. The following year Reynolds proposed three other problems and solved one more. But 1917 was a banner year for submissions to the Problems Department, as he was cited for 19 items – five posed problems, three solutions to problems posed earlier, four printed solutions, and seven solutions listed under “also solved by”. His last solution appeared in 1965, exactly 50 years after his first one. He was 84 years old at the time!

The succession of Reynolds’ other contributions to the Monthly traces his development as a mathematician. In the banner year 1917 he published a small note in the Discussions Department. However, it would be another six years before his first refereed paper would appear. Altogether Reynolds published eight refereed articles in the Monthly, his last three appearing in Classroom Notes. Not all of his papers appeared in the Monthly; two were published in the Tohuku Mathematical Journal and one in Agricultural Engineering.

Reynolds’ connection to theoretical mechanics is reflected in four of the six books he wrote. The first one, Elementary Mechanics, was published in 1928 and revised six years later. In between those editions he published Analytic Mechanics in 1931. It took eight more years to write Forty Lessons in Analytic Mechanics (1939), suggesting five lessons per year. His last book, Elements of Mechanics, written with his colleague, G. E. Raynor, was published in 1943.

It is this proclivity toward applied mathematics that makes Reynolds seem like an improbable candidate to play such a vital role in founding the Philadelphia Section of the MAA

^{ 3 }. Yet the very notion of such a section was his alone. In this sense the role that Reynolds played in the founding of the Philadelphia section is reminiscent of the roles played by the first five presidents of the AMS^{ 4 }, none of whom was a pure mathematician.In addition to works on mechanics, Reynolds and his colleague Frank M. Weida published Analytic Geometry and the Elements of Calculus in 1930. (Another successful calculus author from Lehigh was Lloyd L. Smail.) Overall Reynolds published three other books between 1918 and 1935, one of which appeared in two editions. The remaining work not yet described is The Peter Reynolds Family of Lawrence County Pennsylvania, which he published in 1940.

Reynolds’ enduring interest in both pure and applied mathematics can be seen in the very last note he published in the Monthly in 1944. Titled “Reversion of series with applications,” it dealt with a method for solving differential equations he felt was appropriate for “every student who is trained for engineering or other scientific work.”

Reynolds died in Wilmington, Delaware, in 1975 at age 94. His example shows a competent teacher and administrator who, though he found some time for original investigations, contributed mainly to the Problems Department of the Monthly. His shared interests with astronomy and applied mathematics hearken back to an earlier period in the history of mathematics in America.

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