Problems and Solutions from
The Mathematical Visitor 1877-1896
Foreword
In his introduction to the first issue of The Mathematical Visitor, October 1877, founding editor Artemas Martin commented that, "In England and Europe periodical publications have contributed much to the diffusion of mathematical learning.'' Martin further noted that "some of the greatest scientific characters of those countries commenced their mathematical career by solving the problems proposed in such works.''
Indeed, the periodical literature in mathematics has been especially rich in the tradition of publishing challenging problems and subsequent solutions. From simple computational problems sent in by people needing help, to problems and solutions whose consequences cast their shadows across centuries of mathematics, the periodicals have provided a special forum for the dynamic exchange of ideas.
A study of the problems in a single periodical reveals much about the mathematical spirit of the time. In 1817, Thomas Leybourn published a massive four volume collection containing over 1,300 problems and solutions from the famous Ladies' Diary. Over its long run, the Ladies' Diary inspired an enormous amount of mathematical interest. A casual look at the problems will surprise the reader. The names of renowned 17th and 18th century mathematicians appear time and again as problemists and commentators, often referred to as venerated masters held in high esteem. Similarly, in The Mathematical Visitor, we find contributors such as Benjamin Pierce, E. B. Seitz, J. J. Sylvester, and G. B. M. Zerr.
The British tradition of publishing problems in periodicals was well established by the time America achieved its independence. A glance at the early American periodicals proves revealing. Even among those not primarily devoted to mathematical or scientific themes, there is evidence of ongoing interest in and fascination with puzzles and mathematical problems. On occasion, newspapers offered tempting teasers for their readers, with solutions appearing in later issues. One British newspaper, the Educational Times, had a mathematical problem column that survived for over a hundred years.
At the beginning of the 19th century, periodicals devoted entirely to mathematics emerged in America, and problems and solutions contributed by readers began to fill their pages. Among these periodicals were The Mathematical Correspondent, (which began in 1804), The Mathematical Museum, The Analyst, and The Mathematical Diary.
In a variety of cultural areas, including fine art and music, early America was somewhat insecure in its ability to produce an indigenous product worthy of comparison with its European counterpart. By midcentury, however, even the British were impressed with what was called Yankee Ingenuity and the American flair for practicality. Especially manifest in New England and the northeastern states, American efficiency in manufacturing and industry were world-renowned and respected. The passion for the practical, the getting down to the business of doing it quickly and efficiently, can even be seen in problems posed in the mathematical periodicals.
There was much fascination with exhaustive computation and deft manipulation of masses of symbols. Among the hundreds of problems in The Mathematical Visitor, there is one calling for a solution in integers to x2-9781y2=1 (the least positive value of x contains 156 digits), and another requesting "an expeditious method of approximating the cube root of 2 to at least 100 places.'' Both problems are solved diligently and proudly, and without modern calculators. There are also many graceful geometric miniatures, ingenious number theoretic excursions with sophisticated analyses, and old chestnuts we've all seen before.
The Mathematical Visitor, over its nearly twenty-year run, was devoted almost entirely to problems and solutions. Its energetic founding editor was deeply convinced of its value to the mathematical community and invited "professors, teachers, students and all lovers of the 'bewitching science' to contribute their best problems and solutions for its pages.'' Its wide range of readership and diversity of contributors bear testimony to his vision.
Lawrence Zimmerman
Brooklyn, New York
March, 1994
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