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The American Journal of Psychology XVIII April 1907 – Mathematical Prodigies – Frank D Mitchell

By a "mathematical prodigy" we shall mean a person who shows unusual ability in mental arithmetic or mental algebra, especially when this ability develops at an early age, and without external aids or special tuition. We shall use the word "calculator" in the sense of "mental calculator," as a synonym for "mathematical prodigy," and shall usually mean by "calculation" "mental calculation," unless the contrary is clearly indicated by the context. A "professional calculator" will be taken to mean a mental calculator who gives public exhibitions of his talent. "Computer," however, will be restricted to mean one who calculates on paper. All problems mentioned as solved by the mathematical prodigies will be understood to be done mentally, unless otherwise indicated.

Truman Henry Safford (1836-1901) was, like Zerah Colburn, the son of a Vermont farmer; but both his parents were former school-teachers, and persons of some education, father had a strong interest in mathematics, and the mother we are told, was of an "exquisite nervous temperament." Young Safford showed a remarkable all-round precocity, similar to that of Ampere. In his 3rd year "the grand bias of his mind was suspected"; later his parents "amused themselves with his power of calculating numbers"; and when he was 6 years old he was able to calculate mentally the number of barleycorns, 617,760, in 1040 rods.

At the age of 7 he had "gone to the extent of the famous Zerah Colburn's powers." About this time he began to study books on algebra and geometry, and soon afterwards higher mathematics and astronomy. Wanting some logarithms, he found them himself by the formulas; and in his loth year he published an almanac computed entirely by himself. The following year he published four almanacs, one of which, computed for Cincinnati at once reached a sale of 24,000 copies. In this almanac he used a new and original rule for obtaining moon risings and settings, accompanied by a table which saved a quarter of the work of their computation. About this time he also discovered a new rule for calculating eclipses, with a saving of one-third in the labor of computing.

Such feats at once made the boy a public character, and in the same year (1846) he was examined by the Rev. H. W. Adams, a skillful mathematician. He solved a number of difficult algebraic problems, doubtless in the main by algebraic methods rather than by the trial and error method of most of the other prodigies. Problems in the mensuration of solids caused him no trouble, though in one case, where the answer was a 12-figure number, he "used a few [written] figures." He extracted the cube roots of 7-figure exact cubes "instantly," doubtless by the use of 2-figure endings. Finally, he squared 365.365.365.365.365.365, entirely in his head, in "not more than one minute," though with evident effort. A three-hour examination convinced Adams that the boy had mastered and gone beyond all his text-books.

Like Ampere, Safford had a wide range of interests, and an encyclopedic memory. Chemistry, botany, philosophy, geography, and history, as well as mathematics and astronomy, were included in his field of study. He took his degree at Harvard in 1854, and became an astronomer. After holding various positions he became professor of astronomy in Williams College in 1376, where he remained until his death in 1901.

Safford early outstripped Bidder in a range of mental calculation, but with the aid of books, whereas Bidder's methods were entirely of his own discovery. It is to be regretted that we have not more detailed information about Safford's calculations; but except for the examination whose results have been given above, all we can say is that later he acquired considerable skill in factoring large numbers, seeming to be able to recognize almost at a glance what numbers were likely to divide any given number, and remembering the divisors of any number he had once examined.

Source  Scripture, op, cit., p. 29; Appleton's Cyclo. of Am. Siog., art. Safford; Chambers's Edinburgh Journal, N. S. VIII, 1847, p. 265; Belgravia, XXXVIII, 1879, p. 456.