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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.

Henri Mondeux (1826-1862) was the son of a woodcutter near Tours. Sent to tend sheep at the age of 7, he amused himself by playing with pebbles, and thus learned mental arithmetic. Jacoby, a schoolmaster at Tours, hearing of him sought him out, offered to instruct him, and gave him his address in the city; but the boy's memory outside mathematics was so poor that he forgot both name and address, and found the schoolmaster only after a month's search.

He received instruction in arithmetic and other subjects, and in 1840 was exhibited before the Paris Academie des Sciences. In the committee's report on him we are told that he "carries on readily in his head not only the various arithmetical operations, but also, in many cases, the numerical solution of equations; he devises processes, sometimes remarkable, for solving a great number of different questions which are ordinarily treated by algebra, and determines in his own way the exact or approximate value of integral or fractional numbers which satisfy given conditions."

More specifically, he finds powers of numbers by rules of his own discovery which are equivalent to special cases of the binomial theorem; he has worked out formulas for the summation of the squares, cubes, etc., of the natural numbers, and for arithmetical progression and other series; he solves simultaneous linear equations by a method of his own, and sometimes equations of higher degree, especially where the root is a positive integer; and he solves such problems in indeterminate analysis as finding two squares whose difference is a given number. He "knows almost by heart the squares of all whole numbers under 100." learning a number of 24 figures, divided into four 6-figure periods, requires 5 minutes. He can solve a problem while attending to other things.

Mondeux's admirers hoped that he would one day distinguish himself in a scientific career; but this was not the case. Like his successor Inaudi, whom he closely resembles in several respects, he became a professional calculator; but he had no ability outside of mathematics, and even there his powers soon reached a limit beyond which they did not increase. He died in obscurity. If we may judge by the Academy report, he was almost the equal of Bidder in his insight into mathematical relations; but on the numerical side he was far excelled by Inaudi, who could, for example, memorize 24 figures in half a minute, a feat for which Mondeux required 5 minutes.