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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.

Ugo Zaneboni (b. 1867), an Italian, born in the same year as his countryman Inaudi, received a fair education. His interest in numbers began at the age of 12, and when 14 he could solve any problem his teacher proposed to him. While serving his term in the army he was for a time stationed at a railroad depot, where he amused himself by gradually committing to memory a vast body of statistics relating to timetables, distances between different cities, population, tariffs, etc. When he later took to the stage as a professional calculator, questions based on these statistics formed part of his regular programme. Among his other usual feats are the repetition, either forwards or backwards, of a memorized number of 256 figures, the squaring of numbers up to 4 figures and the cubing of numbers up to 3 figures, finding the 5th powers of 2-figure numbers, and, conversely, extracting the 5th root of any number of 10 figures or less, the cube root of any 9-figure number, and the square root of any number of 7 figures or less, whether the given number is a perfect power or not. In these problems he is aided by his knowledge of many perfect squares, cubes, etc., as well as by various properties of 2-figure endings, with which he is thoroughly familiar. He possibly has a number-form, in which the numbers from 1 to 10, from 10 to 100, and from 100 to 1000 are arranged along three horizontal lines. This number-form, however, if it really exists, plays little or no part in his actual calculations.