# Mathematics and Statistics

## The Ohio Section: Beginnings

It all started in Ohio. Not in Columbus, but in Fairfield County. Benjamin Franklin Finkel was born there in 1865. He attended the Ridge country school in Fairfield County, where "disorder reigned supreme" until a new teacher used his muscle to subdue the older boys. When Finkel was fifteen he encountered a "very superior country school teacher," George W. Bates, who had more influence on him than anyone else besides his mother. "Though small in stature and crippled in limb," Bates was a man of courage, honesty, firmness, and judgement, who strove to instill these character traits in his students. It was at this time that Finkel's interest in mathematics was aroused.

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:

1. To provide organized activity in the large field between the fields of secondary school mathematics and the field of pure research.
2. To form a medium of communication and a forum for exchange of ideas between teachers and others interested in collegiate mathematics.
3. To furnish a place for publication of scientific articles and papers adapted to this intermediate field.
4. To publish historical articles, book reviews, notes and news, and indeed any matters of interest to the great body of men and women related to this field. [Jones, in The MAA: Its First Fifty Years, p. 20.]

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 [1915]. 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.]

#### The Organizational Meeting for the MAA

The organizational meeting took place in room 101 of Page Hall on the campus of Ohio State University. There were two sessions, the first on Thursday morning, December 30, 1915, and the second on the following morning. The meeting was attended by 104 individuals, many of whose names are recognized today, including: R. D. Carmichael (University of Illinois), L. E. Dickson (University of Chicago), B. F. Finkel (Drury College), Henry S. White (Vassar College), and Alexander Ziwet (University of Michigan), to name but a few. When the meeting was called to order, E. R. Hedrick, of the University of Missouri, was elected temporary Chairman and W. D. Cairns, of Oberlin College, temporary Secretary. Hedrick immediately asked H. E. Slaught, who was acting on behalf of the board of editors of the Monthly, who had called the meeting, to discuss the history of the movement to found a new organization devoted to collegiate mathematics.

The meeting then resolved into a committee of the whole to consider, section by section, a constitution and by-laws which had been drafted in advance. It took three hours of painstaking deliberation to resolve all issues but one: What should the new organization be called? Eighteen names had been suggested, so a committee was given the task of deciding. The three committee members decided to act independently on choosing a name. When they reconvened they had all chosen the same name, and this was accepted unanimously by the whole group the next morning. Thus it was that our society became known as The Mathematical Association of America.

On Friday morning, December 31, 1915, the Constitution and By-laws were officially adopted. They were first printed in the January, 1916, issue of the Monthly, an issue that was delayed in mailing. E. R. Hedrick was elected the first President of the MAA, E. V. Huntington of Harvard and G. A. Miller of Illinois were chosen as Vice-Presidents, and Cairns was continued as Secretary-Treasurer (a post in which he served until 1943). Twelve individuals, representing as many states, were elected to the executive committee. A committee was appointed to negotiate with the owners of the Monthly to make it the official journal of the Association, and thus it was that the Monthly began its twenty-third year of continuous service to the mathematical community.

As one would expect of any mathematical meeting, the organizational meeting was not devoid of mathematics. There was only one speaker, the distinguished historian of mathematics from the University of Michigan, Louis C. Karpinski, who gave an illustrated lecture on the "Story of Algebra." E. R. Hedrick wrote that that Karpinski's erudite and interesting lecture would not have been given at one of the other mathematical organizations. The lecture emphasized the point that "serious and dignified study of no matter what topic in the mathematical field might constitute research in a newer sense." [School and Society, 3, 396.]

More mathematics was discussed by the other societies. Henry S. White gave his retiring address as Vice-President of section A of the AAAS on "Poncelet Polygons." In addition, twenty-six papers were presented at the AMS meeting which was held at Ohio State the same weekend.

#### The Organizational Meeting for the Ohio Section

The twenty-five Ohio teachers of collegiate mathematics who were registered at the organizational meeting of the MAA met together to form a Section of the national organization. They adopted a constitution which is reproduced in Appendix E below. Most importantly, they applied to the national Association for a charter, which was granted on March 1, 1916.

They also elected the first section officers. Professor R. B. Allen of Kenyon College was elected Chairman, G. N. Armstrong of Ohio Wesleyan University was chosen as Secretary-Treasurer, and C. C. Morris of Ohio State University became the third member of the Executive Committee.

#### The First Annual Meeting of the Ohio Section

The first meeting of the Ohio Section of the MAA was held April 21-22, 1916, at The Ohio State University in conjunction with The Ohio College Association, the Ohio Academy of Science, The Ohio Society of College Teachers of Education, and the Association of Ohio Teachers of Mathematics and Science. Such joint meetings were common in this day when all of the organizations were small.

The meeting was attended by forty individuals from twenty-two colleges and universities. Few of these names would be recognized today by any but the most careful student of the history of American mathematics. No school had more than two people in attendance, except Ohio State, which had nine. It is encouraging to note that eight of the participants were women. But it is a sign of the times that all of those were "Miss."

In reading the report of the meeting published in the Monthly [23, 189-193] we are struck by the fact that a number of things which we today consider standard at a meeting were already a part of the first meeting. They had a banquet, but the written report of the meeting expressed it rather more eloquently than we would today: "The members of the Section dined together." Later on Friday evening, Professor Charles H. Judd, of the University of Chicago, spoke on "The more complete articulation of higher institutions with the high school." This indicates how little things have changed, for this same topic has been discussed at some of our meetings in the 1980s.

At the business meeting three new officers were elected, and the group also passed three resolutions. There was to be one meeting in the spring of each year, and it was to be held in conjunction with the Ohio College Association. Naturally, money reared its ugly head: "a collection of twenty-five cents each be taken to meet the expenses of this meeting for printing and postage." This seems ridiculously cheap, but a quarter then was dearer than our five dollars today. The final resolution asked the national Association to remit five per cent of the annual dues, and at least one half of the initiation fees of new members. The annual dues were three dollars, an amount that was barely sufficient to pay for the copies of the Monthly that each member received. Amazingly, the national Association decided to remit all of the initiation fees for new members to the sections.

The heart of the program consisted of the talks. The Chairman's address, by R. B. Allen, was entitled "Hypercomplex Number Systems." He stated the fundamental theorems and gave "enough of the proofs to indicate their elementary character." Using these results, he showed that "the only real number systems in which division is unambiguous [are] the real system, the ordinary complex system, and the real quaternion system." From the brief abstract it appears that this was a sound exposition of a fairly recent mathematical result.

In addition there were five "formal papers," but only one of those was mathematical. C. N. Moore of the University of Cincinnati discussed the history of divergent series, the principal methods of summing them, and some applications of divergent series. The other talks dealt with pedagogy. A. E. Young of Miami University spoke on "What elective courses following the calculus should the average college offer?" He classified courses as "algebraic, geometric, functional, or applied mathematics," and suggested that the average student take those from the first and second category, "a functional course for the exceptionally brilliant," and applied courses for the prospective engineer. Unfortunately, the abstract does not explain what is meant by a functional course. The twelve-hour program beyond calculus (yes, far fewer courses were taken then) should include "without question a course in differential equations." He also pleaded that there should be "a well-defined connectivity in the post calculus courses, both with the different fields of mathematics and the applications of science."

Rereading the report of this meeting, and of the other early meetings of the Ohio Section, one is struck with how little things have changed. We would like to think that we have made great strides in pedagogy and curriculum design, yet we are still faced with the same problems that our forebears were. Perhaps success is measured by how hard we struggle.

#### Which section was first?

This question is one that periodically haunts three sections: Missouri, Kansas and Ohio. Our aim here will be to try to give an objective answer to this recurring puzzle, by carefully examining the extant documents from the Monthly.

Article V of the Constitution of the MAA is entitled "Sections," and the first item reads:

Any group of members of this Association may petition the Council for authority to organize a Section of the Association for the purpose of holding local meetings. The Council shall have power to specify the conditions under which such authority shall be granted.

In the report of the Organizational Meeting we find that this section of the Constitution was quickly put into use:

The Council received formal applications from duly authorized representatives of three states requesting authority for organizing Sections of the Association; namely, from Kansas, Missouri and Ohio. The Kansas meeting was held early in the Autumn, the Missouri meeting at Thanksgiving time, and the Ohio meeting on Thursday afternoon at Columbus, the latter having some thirty-five delegates present. The Council appointed a committee consisting of E. R. Hedrick, Alexander Ziwet, and K. D. Schwartzel, to formulate the terms under which such petitions may be granted, as provided by the Constitution, and to act with power on these and other similar petitions which may be received before the next meeting.

The February, 1916, issue of the Monthly indicated that the committee on the organization of sections was working out the details and would report in the March issue, and so they did. After stating the newly formulated "Regulations for Sections," it was reported that:

The first body to make application for admission as a section was in Kansas. A meeting was held in the autumn of 1915 at which the Kansas teachers of collegiate mathematics organized and appointed Professor U. G. Mitchell, of the University of Kansas, as their delegate to present their application at the Columbus meeting as soon as the national Association should give them an opportunity. They held their first meeting as a Section of the Mathematical Association of America at the University of Kansas on March 18, 1916. [AMM 23(1916), p. 95.]

Interestingly enough, Ulysses Grant Mitchell was the only mathematician from Kansas at the Organizational meeting in December. The report of this first meeting of the Kansas section, as a Section of the MAA, is printed in the May, 1916, Monthly. It indicated that they had now become a section of the national organization, but no date for the acceptance of their charter is given. The report repeats the statement that the Kansas section was the first section to make application for admission to the MAA. The program for this meeting is reproduced in the Kansas Section of the Mathematical Association of America, 65 Years (1915-1980), which was prepared by Elaine L. Tatham in 1980. This program carries the line "The Kansas Association has now become a section of the national organization, The Mathematical Association of America, recently organized at Columbus, Ohio." Again, no date is given.

The full report of the first meeting of the Ohio Section is in the July issue of the Monthly and contains the information that the section was granted a Charter by the national organization on March 1, 1916.

The first meeting of the Ohio Section of the Association was held at Columbus, on April 21, 22, 1916. This section was formed at Columbus at the same time that the national association was organized and application for admission was made then [p. 185].

We have already discussed the program of this meeting in detail above.

The next mention of Sections is in the November Monthly, p. 361. At this time there were four sections, Kansas, Ohio, Missouri, and Iowa. (It is not clear if there is any significance to this order). The Ohio and Kansas sections had held their first meetings (besides their organizational meetings), and the Missouri section had one planned for November 16, 1916. This was the first mention of a meeting of the Missouri section, so it seems clear that they were definitely not the first section of the MAA.

In "The Association and Its Sections", H. E. Slaught gave a ten year history of the sections, of which there were seventeen by that time. He reported:

It will be recalled that Ohio and Missouri were contestants for the honor of securing the first charter for a section and that Ohio won by the margin of a few minutes, both petitions being presented within an hour after the final adoption of the constitution at the organization meeting of the Association in Columbus, Ohio, in December, 1915. [AMM 34(1927), 225.]

We should remember that Slaught was an editor of the Monthly at the time the Association was founded in 1915, was present at the organizational meeting in Columbus, and, being from the University of Chicago, does not have a favorite son in the dispute over which section was first. Consequently, considerable weight must be given to his statement.

On October 15, 1966, when Kenneth O. May was preparing The Mathematical Association of America: Its First Fifty Years (published in 1972), he wrote to Foster Brooks, then Secretary of the Ohio Section, asking for information about the history of the section. Brooks replied on November 18, 1966, indicating that he had "the complete file of papers of the section." (The present whereabouts of these files is unknown [These were recovered in 2004 from Ray Rolwing]). He indicated that he would try to get Professor Barnett of the University of Cincinnati and Professor Musselman at Western Reserve to write a history of the Section, since they were both charter members of the MAA. Neither are listed as charter members of the Ohio Section in the April, 1916, Monthly, but there is a J. R. Musselman, of Johns Hopkins University, who was present at the organizational meeting, and who was a charter member from Maryland. Brooks was unable to get any charter members to write a history at that time, and so was forced to write a brief history himself. He sent this to May on June 16, 1967.

"The official account of these events, as recorded in the minutes of the Section" indicates that twenty-five members of the Ohio Teachers of Collegiate Mathematics met December 30, 1915, at 2 P.M. and passed a resolution that the Ohio Teachers of Collegiate Mathematics favor forming themselves into a section of "The Mathematical Association of America."

The use of the official name here before it was approved the next day indicates how universal the agreement was about the name of the new Association. This group appointed Professor Allen of Kenyon College as Temporary Secretary. More importantly, "Professor Allen was appointed a delegate to represent the section at the adjourned meeting of the parent organization to be held Friday, December 31 at 9 A.M." From the information reported in the Monthly, it appears that Allen dutiful carried out this responsibility, even being the first to apply for membership as a Section.

Also at this organizational meeting of the Section, a committee of five was appointed to, among other things, "formulate a scheme of organization" and "to report to an adjourned meeting [of the Section] to be held December 31 at 2 P.M." The next day this committee proposed the Constitution of "The Ohio Section of the Mathematical Association of America," which is reproduced in Appendix E below. It was immediately accepted.

The next item dealt with in the history by Foster Brooks contains information that has never been reported in the Monthly :

Under date of January 3, 1916, the Secretary-Treasurer of the Ohio Section notified the Secretary of the parent Organization of the formation of the Ohio Section, and made application for recognition and the granting of a charter. Notification of the granting of this request under date of March 1, 1916, was received in the attached letter from the President of the parent Association.

It is not clear whether the Secretary-Treasurer referred to above was the Temporary Secretary, R. B. Allen of Kenyon, or G. N. Armstrong of Ohio Wesleyan, who was elected December 31, 1915, as the first Secretary-Treasurer of the Ohio Section. But the March 1, 1916, letter of E. R. Hedrick, first President of the MAA, indicating that the Ohio Section had been approved, was sent to Armstrong, with a copy to Allen. The really surprising information was that the official letter requesting sectionhood was not sent until January 3, 1916.

Professor Brooks also wrote about the first meeting of the Ohio Section. His report is substantially different that that which appears in the June, 1916, Monthly. This raises the question of how much, if at all, the required reports which were submitted to the national organization were edited by the secretary before they appeared in the Monthly. We suspect that they were printed verbatim - at least this would account for the discrepancies over which section was first. Moreover, the Secretary of the national organization was an Ohioan, so he certainly would not have removed the statements in the Kansas reports that they were first.

In summary, Ohio may well have been the first section to apply for membership in the MAA. We surmise that, on December 31, 1915, they were recognized first at the meeting and made an oral application for membership, and that Kansas got to speak next. But, since Mitchell was acting as a committee of one from Kansas, he was able to submit a letter asking for admission immediately after the meeting. This would allow both sections to claim that they were first. But Ohio was not the first Section to hold a meeting as a recognized Section of the MAA.

Hopefully, the publication of this history will prompt people to search deeply into their files and into the archives of their schools and find further documentation concerning the history of the Ohio Section. In any case, one thing is certain, as is amply documented by this history: The Ohio Section of the Mathematical Association of America has a firm claim on consistently being one of the most active and best Sections.