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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.

Pericles Diamandi (b. 1868), the son of a Greek grain merchant, attributes his calculating gift to his mother, who "has an excellent memory for all sorts of things." One brother and one sister, out of a family of fourteen, share his aptitude for mental arithmetic. He entered school at the age of 7, and remained there until he was 16, always standing at the head of the class in mathematics. But it was only after entering the grain business himself, in 1884, that he discovered his powers of mental calculation, which he now found very useful. He knows five languages, - English, French, German, Roumanian, and his native Greek, - and is a great reader; he has read all he can find on the subject of mental calculation; and he has written novels and poetry, concerning whose quality, however, Binet does not enlighten us. It will thus be seen that Diamandi's education is much better than Inaudi's, and his range of interests correspondingly wider, but that he was far less precocious in calculation than his rival.

Diamandi is of the visual memory type. He has a number-form of a common variety, running zigzag from left to right and giving most space to the smaller numbers. This number-form he sees as localized within a peculiar grayish figure which also serves as a framework for any particular number or other object which he visualizes. He has colored audition for the names of various persons, the days of the week, etc., and if a few figures in a given number differ in color from the rest he remembers the colors without effort. If the color scheme is more complicated, however, he first memorizes the number and then learns the colors of the individual figures. He always sees numbers as written in his own handwriting, and preferably, if the numbers are large, in a rectangle as nearly square as possible, rather than in one or two long Hues. He learns spoken figures (in French) much less readily than written, since in the case of spoken figures he must not only call forth the corresponding visual images, but translate the numbers into his native Greek, in which all his calculations are carried on. Where he seeks to learn the figures very accurately, for purposes of calculation, he is only about half as fast as Inaudi; but where he is concerned with speed rather than accuracy his times are much shorter. In the one case he learned 10 figures in 17 seconds; in the other, 11 figures in 3 seconds.

In calculation Diamandi is considerably slower than Inaudi, whether the numbers concerned are large or small. His time was 127 seconds for a 4-figure multiplication, whereas Inaudi could accomplish the same feat in 21 seconds. Diamandi finds the various figures of the product in order, from right to left, by cross-multiplication; thus in such an example as

he finds the figures of the partial products not in the horizontal lines of the ordinary method, but in vertical lines, - first 7, then 5, 6, then 4, 4, 1, then 6, 5, 1, etc., - and adds each column before he proceeds to find the numbers that compose tire next column. This method has the advantage that the various figures of the partial products can be forgotten almost as fast as obtained, since that figure of the total product which depends on a given column of the partial product is found and recorded as soon as the column is known, and the numbers in that column therefore play no further part in the calculation. On Diamandi's performances in other operations than multiplication Binet gives us no data.

Source:  Rivista sperimentale di Freniatria, etc., XXIII, 1897, pp. 132-159, 407-429. A summary of these articles, in German, is found in the Zeitschrift fur Psychologie und Physiologie der Sinnesorgane, XVI, 1898, p. 314. The writer is indebted to Mrs. Rose Harrington for a translation of considerable portions of the original Italian articles.