The celebrated mathematician Alexis Claude Clairault (now Clairaut)[478] was certainly born in May, 1713. His treatise on curves of double curvature (printed in 1731)[479] received {220} the approbation of the Academy of Sciences, August 23, 1729. Fontenelle, in his certificate of this, calls the author sixteen years of age, and does not strive to exaggerate the wonder, as he might have done, by reminding his readers that this work, of original and sustained mathematical investigation, must have been coming from the pen at the ages of fourteen and fifteen. The truth was, as attested by De Molieres,[480] Clairaut had given public proofs of his power at twelve years old. His age being thus publicly certified, all doubt is removed: say he had been--though great wonder would still have been left--twenty-one instead of sixteen, his appearance, and the remembrances of his friends, schoolfellows, etc., would have made it utterly hopeless to knock off five years of that age while he was on view in Paris as a young lion. De Molieres, who examined the work officially for the _Garde des Sceaux_, is transported beyond the bounds of official gravity, and says that it "ne merite pas seulement d'etre imprime, mais d'etre admire comme un prodige d'imagination, de conception, et de capacite."[481] That Blaise Pascal was born in June, 1623, is perfectly well established and uncontested.[482] That he wrote his conic sections at the age of sixteen might be difficult to establish, though tolerably well attested, if it were not for {221} one circumstance, for the book was not published. The celebrated theorem, "Pascal's hexagram,"[483] makes all the rest come very easy. Now Curabelle,[484] in a work published in 1644, sneers at Desargues,[485] whom he quotes, for having, in 1642, deferred a discussion until "cette grande proposition nommee le Pascale verra le jour."[486] That is, by the time Pascal was nineteen, the _hexagram_ was circulating under a name derived from the author. The common story about Pascal, given by his sister,[487] is an absurdity which no doubt has prejudiced many against tales of early proficiency. He is made, when quite a boy, to invent geometry _in the order of Euclid's propositions_: as if that order were natural sequence of investigation. The hexagram at ten years old would be a hundred times less unlikely.