[130] De Morgan would have rejoiced in the rôle played by Intuition in the mathematics of to-day, notably among the followers of Professor Klein.
[131] Colburn was the best known of the calculating boys produced in America. He was born at Cabot, Vermont, in 1804, and died at Norwich, Vermont, in 1840. Having shown remarkable skill in numbers as early as 1810, he was taken to London in 1812, whence he toured through Great Britain and to Paris. The Earl of Bristol placed him in Westminster School (1816-1819). On his return to America he became a preacher, and later a teacher of languages.
[132] The history of calculating boys is interesting. Mathieu le Coc (about 1664), a boy of Lorraine, could extract cube roots at sight at the age of eight. Tom Fuller, a Virginian slave of the eighteenth century, although illiterate, gave the number of seconds in 7 years 17 days 12 hours after only a minute and a half of thought. Jedediah Buxton, an Englishman of the eighteenth century, was studied by the Royal Society because of his remarkable powers. Ampère, the physicist, made long calculations with pebbles at the age of four. Gauss, one of the few infant prodigies to become an adult prodigy, corrected his father's payroll at the age of three. One of the most remarkable of the French calculating boys was Henri Mondeux. He was investigated by Arago, Sturm, Cauchy, and Liouville, for the Académie des Sciences, and a report was written by Cauchy. His specialty was the solution of algebraic problems mentally. He seems to have calculated squares and cubes by a binomial formula of his own invention. He died in obscurity, but was the subject of a Biographie by Jacoby (1846). George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an arithmetical prodigy at the age of ten, and did not attend school until he was twelve. Of the recent cases two deserve special mention, Inaudi and Diamandi. Jacques Inaudi (born in 1867) was investigated for the Académie in 1892 by a commission including Poincaré, Charcot, and Binet. (See the Revue des Deux Mondes, June 15, 1892, and the laboratory bulletins of the Sorbonne). He has frequently exhibited his remarkable powers in America. Périclès Diamandi was investigated by the same commission in 1893. See Alfred Binet, Psychologie des Grands Calculateurs et Joueurs d'Echecs, Paris, 1894.
[133] John Flamsteed's (1646-1719) "old white house" was the first Greenwich observatory. He was the Astronomer Royal and first head of this observatory.
[134] It seems a pity that De Morgan should not have lived to lash those of our time who are demanding only the immediately practical in mathematics. His satire would have been worth the reading against those who seek to stifle the science they pretend to foster.
[135] Ismael Bouillaud, or Boulliau, was born in 1605 and died at Paris in 1694. He was well known as an astronomer, mathematician, and jurist. He lived with De Thou at Paris, and accompanied him to Holland. He traveled extensively, and was versed in the astronomical work of the Persians and Arabs. It was in his Astronomia philolaica, opus novum (Paris, 1645) that he attacked Kepler's laws. His tables were shown to be erroneous by the fact that the solar eclipse did not take place as predicted by him in 1645.
[136] As it did, until 1892, when Airy had reached the ripe age of ninety-one.
[137] Didaci a Stunica ... In Job commentaria appeared at Toledo in 1584.
[138] "The false Pythagorean doctrine, absolutely opposed to the Holy Scriptures, concerning the mobility of the earth and the immobility of the sun."
[139] Paolo Antonio Foscarini (1580-1616), who taught theology and philosophy at Naples and Messina, was one of the first to champion the theories of Copernicus. This was in his Lettera sopra l'opinione de' Pittagorici e del Copernico, della mobilità della Terra e stabilità del Sole, e il nuovo pittagorico sistema del mondo, 4to, Naples, 1615. The condemnation of the Congregation was published in the following spring, and in the year of Foscarini's death at the early age of thirty-six.