Artemas Martin, a self-taught mathematician whose activity covered almost six decades, has been described as 'a unique example of what an inherent love of the solution of mathematical problems can do to a man even if he has not the advantages of advanced schooling'. He lived in rural Pennsylvania until he was fifty, edited columns of mathematical puzzles, worked enthusiastically and relentlessly on mathematical problems that he found interesting, corresponded with other mathematicians, and founded two journals: 'The Mathematical Visitor' (1878 - 1894) and 'The Mathematical Magazine' (1882 - 1884). Although these publications were short-lived, they helped prepare the ground for others such as 'The American Mathematical Monthly' (1894), the first official publication of the Mathematical Association of America. Thus it is quite appropriate that one of the first articles in that periodical was a short biography of Martin .As the above quote states, Martin lived in rural Pennsylvania until he was fifty, mostly in Erie. There he earned his living farming, drilling oil wells and chopping wood. He did teach mathematics in local schools during four of the winters he spent there. He certainly could have had a much higher status for in 1881 he was offered the position of professor of mathematics at the Normal School in Warrensburg, Missouri. He turned this down but in 1885, at the age of fifty, he did accept the offer of a job as librarian with the United States Coast and geodetic Survey in Washington, D.C. In taking the position of librarian Martin was following the second passion of his life, namely that of being a book collector. He possessed by far the most extensive collection of American texts on algebra and arithmetic, so it was natural for him to publish a work called Notes on the history of American textbooks on arithmetic in 1899. He wrote this work jointly with J M Greenwood. His book collection extended well beyond mathematics, however, with many texts on poetry, as well as botany and natural history. He left his collection of 5000 books to the American University and it is now housed in its Special Collection. With his library there is a number of notebooks which contain his solutions to mathematical problems and well as lists of books that he was trying to purchase.
Martin published a very large number of problems and solutions to problems in a wide range of publications :-
In his writings and problem-solving, Martin dealt mostly with Diophantine analysis, probability, elliptic integrals, logarithms, and properties of numbers and triangles.For example, he published thirteen articles entitled On Average in The Wittenberger (A Journal Devoted to the Interests of Wittenberg College), between the years 1877 and 1879. To see the type of problems he was examining we quote a problem from the first of these articles:-
Required the average area of all right-angled triangles whose hypotenuses are a.Here is another example, this time from the second of the thirteen articles:-
A point is taken at random in the surface of the circle, and a chord is drawn through it at random, and then a point is taken at random on the chord and another chord drawn to it at right angles to the first. Find the average area of the quadrilateral formed by joining the extremities of the chords.Finally a problem from the third On averages article:-
Two equal spheres intersect; find the average of the volume common to both.He did publish one research level article, namely On fifth power numbers whose sum is a fifth power to the International Mathematical Congress in Chicago in 1893. By describing this as his only research article we do not mean to suggest that some of his problems were not very challenging. For example try solving the problems he proposed in 1878:-
Find the average distance of one corner of a rectangle from all the points on its surface.Martin was the first American subscriber to the Educational Times and the first American to contribute to its mathematical section. He was a member of many mathematical societies. He was a member of the New York Mathematical Society and later of the American Mathematical Society. He was also a member of the London Mathematical Society, the Edinburgh Mathematical Society, the French Mathematical Society, the German Mathematical Society, and the Mathematical Circle of Palermo. He was a fellow of the American Association for the Advancement of Science. In 1877 he was awarded an honorary M.A. from Yale, then an honorary Ph.D. from Rutgers in 1882, and finally an LL.D. from Hillsdale College in 1885.
Find the average distance of one corner of a rectanglar solid from all the points in its interior.
Finkel, writing in  nearly twenty-five years before Martin's death, says that he:-
... has that rare and happy faculty of presenting his solutions in the simplest mathematical language, so that those who have mastered the elements of the various branches of mathematics, are able to understand his reasoning.
Article by: J J O'Connor and E F Robertson