Mainländer had a grandfather who, after the death of a son, carried religious mysticism to the extent of insanity, and died of inflammation of the brain at the age of thirty-three. A brother, also insane, wished to embrace Buddhism. As a youth, looking at the sea at Sorrento, he felt impelled to throw himself in, merely attracted by the purity of the water. He educated himself and wrote his celebrated book, _Die Philosophie der Erlösung_, but to realize his theories entirely, he adopted a rule of absolute chastity, and on the day on which his book was published hanged himself, the better to confirm a passage which said: “In order that man may be redeemed it is necessary that he should recognize the value of not-being, and desire intensely not to be.”[162] The great Auguste Comte, the initiator of the positivist philosophy, was for ten years under the care of Esquirol, the famous alienist; he recovered, but only to repudiate, without any cause, the wife who had saved him; later, he--who had wished to abolish all priest-craft--believed himself the priest and apostle of a materialistic religion. In his works, amidst stupendous elucubrations, genuinely maniacal ideas may be found, as, for example, the prophecy that one day women will be fecundated without the help of the male.[163] It is said that mathematicians are exempt from psychical derangements, but this is not true; it is sufficient to recall not only Newton and Enfantin, of whom I will speak at length, but the two famous distractions of Archimedes, the hallucination of Pascal, and the vagaries of the mathematician Codazzi (not to be confounded with Codazza). Codazzi was sub-microcephalic, oxycephalic, alcoholic, sordidly avaricious; to affective insensibility he added vanity so great that while still young he set apart a sum for his own funeral monument, and refused the least help to his starving parents; he admitted no discussion of his judgment even if it only concerned the cut of a coat; and he had taken it into his head that he could compose melodic music with the help of the calculus. All mathematicians admire the great geometer Bolyai, whose eccentricities were of an insane character; thus he provoked thirteen officials to duels and fought with them, and between each duel he played the violin, the only piece of furniture in his house; when pensioned he printed his own funeral card with a blank date, and constructed his own coffin--a vagary which I have found in two other mathematicians who died in recent years. Six years later he had a similar funeral card printed, to substitute for the other which he had not been able to use. He imposed on his heir the obligation to plant on his grave an apple-tree, in remembrance of Eve, of Paris, and of Newton.[164] Such was the great reformer of Euclid.