276 CALCULATING PEODIGIES [CH. XIII 



that in his mental arithmetic he worked with pictures of the 

 figures, and said "If I perform a sum mentally it always 

 proceeds in a visible form in my mind ; indeed I can conceive 

 no other way possible of doing mental arithmetic": this it 

 will be noticed is opposed to his father's method. Two of 

 his children, one son and one daughter representing a third 

 generation, have inherited analogous powers. 



I mention next the names of Henri Mondeux, and Tito 

 Mangiamele. Both were born in 1826 in humble circumstances, 

 were sheep-herds, and became when children, noticeable for 

 feats in calculation which deservedly procured for them local 

 fame. In 1839 and 1840 respectively they were brought to 

 Paris where their powers were displayed in public, and tested 

 by Arago, Cauchy, and others. Mondeux's performances were 

 the more striking. One question put to him was to solve the 

 equation a? + 84 = 37a; : to this he at once gave the answer 3 

 and 4, but did not detect the third root, namely, — 7. Another 

 question asked was to find solutions of the indeterminate 

 equation a? — y i = 133 : to this he replied immediately 66 

 and 67 ; asked for a simpler solution he said after an instant 

 6 and 13. I do not however propose to discuss their feats in 

 detail, for there was at least a suspicion that these lads were not 

 frank, and that those who were exploiting them had taught 

 them rules which enabled them to simulate powers they did not 

 really possess. Finally both returned to farm work, and ceased 

 to interest the scientific world. If Mondeux was self-taught we 

 must credit him with a discovery of some algebraic theorems 

 which would entitle him to rank as a mathematical genius, but 

 in that case it is inconceivable that he never did anything more, 

 and that his powers appeared to be limited to the particular 

 problems solved by him. 



Johann Martin Zacharias Dase, whom I next mention, is 

 a far more interesting example of these calculating prodigies. 

 Dase was born in 1824 at Hamburg. He had a fair education, 

 and was afforded every opportunity to develop his powers, but 

 save in matters connected with reckoning and numbers he 

 made little progress and struck all observers as dull. Of 



