A problem had been making the rounds, and Finkel's older half-brother heard it at the village store, and brought it home:
There is a ball 12 feet in diameter on top of a pole 60 feet high. On the ball stands a man whose eye is six feet above the ball. How much ground beneath the ball is invisible to him?
Finkel asked his teacher, Bates, about the problem, who explained that it might be solved by geometry. But since Finkel saw neither an algebra nor a geometry book till he was seventeen, this advice was of little help. He had studied Ray's Third Part Arithmetic, so attempted to solve it using the rules of mensuration in that book. It was several years before he succeeded, but a problem solver was born. In 1931, Finkel reminisced that "this perfectly senseless problem, with no value whatsoever from the standpoint of modern educational theory, nevertheless was the borax in the mortar which retarded mental hardening until a time arrived when other elements could play their part in the active materials of a life, and it seems to me that such a result should be the test by which the value of a problem should be gauged."
At eighteen Finkel left the county school to attend Ohio Normal University in Ada, Ohio, a school now called - after Finkel's suggestion - Ohio Northern University. He received his B.S. in 1888 and a M.S. in 1891. While a student there, and for several years afterwards, Finkel conducted a mathematical column in the University Herald. After a year of college he began teaching in the the rural schools of Ohio, while continuing work on his degrees. He taught first in Fostoria, and later in Gibson, Tennessee. Then he became superintendent in North Lewisburg and finally West Middleburg. Sadly, Finkel "became thoroughly discouraged and disheartened because of the dishonorable political methods used in securing positions in most of the city schools in Ohio," and so in 1892 joined his friend, G. W. Shaw, Principle of Kidder School in Kidder, Missouri, where he often taught forty-five three-quarter-hour periods per week. (Later, at the college level, he only taught from nineteen to twenty-seven hours per week.) However, the Kidder School was free of the "petty politics so deadening to intellectual honesty and spiritual development," so Finkel was finally able to "ascend to the mountain heights of imagination and get glimpses of things unseen."
During his years as teacher in Ohio, Finkel devoted his leisure time to solving and posing problems in a variety of periodicals which contained columns on mathematics, including the Ohio Educational Monthly, The School Messenger, the Monthly of Davenport, Iowa, the Mathematical Magazine, the Mathematical Visitor, and the School Visitor. Finkel awaited these magazines anxiously and was disappointed when they did not appear with regularity. Finkel's variety of teaching experience made him keenly aware that the "mathematical teaching in our high schools and academies was very deplorable and even worse in the rural schools." Consequently he had "the ambition to publish a journal devoted solely to mathematics and suitable to the needs of teachers of mathematics in these schools." The editor and publisher of the local newspaper in Missouri was daring enough to agree to print the new journal. Finkel also secured the assistance of John M. Colaw of Monterey, Virginia, whom he knew through his contributions to the School Visitor, to assist him as co-editor. In the fall of 1893, Finkel decided to give his journal an ambitious and prophetic title, The American Mathematical Monthly.
Finkel and Colaw then began writing high school teachers of mathematics and professors in the colleges and universities in order to solicit subscribers and contributions. The first response came from the superintendent of the Kansas City schools, who enclosed his check for $2.00, and a promise that he would bring the new journal to the attention of all his mathematics teachers. The first response from the university level came from George Bruce Halsted of the University of Texas, the "stormy petrel" in the mathematical world, who was "in his element when in the midst of a violent verbal storm initiated by himself or otherwise." Halsted promised contributions for publication and sent a check for $30.00, an amount he contributed each year until he was fired at Texas for one of his verbal storms. Unfortunately, the school teachers of mathematics saw no need for such a journal and so the Monthly "became occupied with a more virile race of mathematicians," adopting itself as a repository of articles of permanent wealth to teachers of collegiate mathematics.
The first issue of The American Mathematical Monthly appeared in January, 1894. Finkel's introduction to the issue proclaimed the purpose of the journal and indicated that there would be a problem section - a section which has been a mainstay of the Monthly for almost a century. His words are both modest and autobiographical:
While realizing that the solution of problems is one of the lowest forms of Mathematical research, and that, in general, it has no scientific value, yet its educational value cannot be over estimated. It is the ladder by which the mind ascends into higher fields of original research and investigation. Many dormant minds have been aroused into activity through the mastery of a single problem. The American Mathematical Monthly will, therefore, devote a due portion of its space to the solution of problems, whether they be the easy problems in Arithmetic, or the difficult problems in the Calculus, Mechanics, Probability, or Modern Higher Mathematics.One of the most amazing things about the Monthly under Finkel's editorship is that, in order to save money, he carved most of the woodcuts himself. Simultaneously, his wife proofed the work of the inexperienced typesetters and addressed the mailing wrappers.
Interesting as it would be to discuss the early issues of the Monthly in great detail, that would be a digression from our story. For further information, and the source of all of the above quotations, see the text of a talk that Finkel gave at an annual MAA meeting in Cleveland on "The Human Aspect in the Early History of The American Mathematical Monthly" [AMM 38(1931), 305-320].
In June of 1895 Finkel became professor of mathematics and physics at Drury College in Springfield, Missouri, where he remained until his death in 1947. Immediately after being hired, he set off to attend the summer session at the recently founded University of Chicago. That summer he met and became friends with Leonard Eugene Dickson. Two years earlier, as a nineteen year old graduate student of Halsted at Texas, Dickson had published an article on Pythagorean Triples in the very first issue of the Monthly. Later, in 1900, Finkel secured Dickson's assistance as co-editor (Colaw having become involved in writing elementary textbooks), and also a subsidy of $50.00 per year from the University of Chicago to support publication. When Dickson resigned in 1906, he "suggested that his mantle be placed upon the shoulders of the aggressive, indomitable, and persevering Professor H. E. Slaught." "After a very conscientious debate with himself, he decided to devote his life to the promotion and improvement of the teaching of mathematics rather than to a research career." Consequently, Slaught accepted, and so the journal continued in strong mathematical hands.
But there were problems. The typesetting was very difficult, and there were often delays. There were fears that the publisher would quit and, of course, there were constant financial worries. Finkel was afraid that he might have to cease publication. Consequently, in the summer of 1912, Finkel traveled to Chicago to visit Slaught and discuss these problems. Slaught was successful in enlisting the cooperation of other institutions and, beginning with Volume XX, the Monthly was published under the auspices of a dozen universities and two colleges. This arrangement was satisfactory, but not permanent, so Slaught approached the American Mathematical Society to see if they would take over the journal.
In April, 1914, the Chicago Section of the American Mathematical Society set up a committee of five to investigate whether the Society should take over publication of the Monthly. The next April, by a vote of three to two, the committee deemed it unwise to take over the Monthly, but declared their support for any additional organization that might be formed to support collegiate mathematics.
Professor Slaught conceived the idea of a new mathematical organization to support collegiate mathematics. He wrote hundreds of letters to professors of mathematics in the United States and Canada setting forth his plan. In June, 1915, Slaught sent out a form letter requesting the return of a postcard if the recipient believed a new organization with the following four goals should be formed:
In the October, 1915, Monthly Slaught reported - and this is the first mention of the Association that appeared there - that he had received approximately 350 replies, only a half dozen of which were in any way opposed to the proposal. Eventually 450 replies were received, representing every state in the Union [AMM22(1915), 352]. It was proposed to hold an organizational meeting in conjunction with the annual meeting of the American Association for the Advancement of Science in Columbus, Ohio, on December 30-31, 1915. "The name of the new society, its precise character and policy, its relation to The American Mathematical Monthly, etc., will be questions for full discussion and determination at the organization meeting." [AMM, October 1915, p. 253]
However, not all of the interest in new mathematical organizations was being generated at the national level.
The first meeting of the Kansas Association of Teachers of College Mathematics was held at Topeka, Kansas, November 12 . This meeting was the result of a movement initiated in the spring of 1915 for the improvement of teaching collegiate mathematics in the colleges of Kansas. It is a part of a nation wide movement having the same end. . . .
This action of the college teachers of mathematics in Kansas is the first step in a movement that promises to grow rapidly. Definite plans are already formed for a similar organization in Ohio during the Christmas holidays, in conjunction with the meeting to be called for organizing a new national mathematical association, which is to be held at Columbus on Thursday, December 30, at ten o'clock in Page Hall of Ohio State University. [AMM, 22(1915), 324, November issue.]
Article excerpted from The
Ohio Section: 1915-1990,
edited by David E. Kullman.