Free Why Beauty is Truth by Ian Stewart

exception. In the iconoclastic spirit of the age, Renaissance mathematicians were determined to overcome the limitations of classical mathematics. One of them had solved the mysterious cubic. Now he was accusing another of stealing his secret.
    The irate mathematician was Niccolo Fontana, nicknamed “Tartaglia,” the stammerer. The alleged thief of his intellectual property was a mathematician, a doctor, an incorrigible rogue, and an inveterate gambler. His name was Girolamo Cardano, aka Jerome Cardan. Around 1520, Girolamo, a true prodigal son, had worked his way through his father’s legacy. Broke, he turned to gambling as a source of finance, putting his mathematical abilities to effective use in assessing the chances of winning. He kept dubious company; once, when he suspected another player of cheating, he slashed the man’s face with a knife.
    They were hard times, and Girolamo was a hard man. He was also a highly original thinker, and he wrote one of the most famous and influential algebra texts in history.

    We know a lot about Girolamo because in 1575 he told us all about himself in The Book of My Life. It begins thus:
    This Book of My Life I am undertaking to write after the example of Antoninus the Philosopher, acclaimed the wisest and best of men, knowing well that no accomplishment of mortal man is perfect, much less safe from calumny; yet aware that none, of all ends which man may attain, seems more pleasing, none more worthy than recognition of the truth.
   No word, I am ready to affirm, has been added to give savor of vainglory, or for sake of mere embellishment; rather, as far as possible, mere experiences were collected, events of which my pupils . . . had some knowledge, or in which they took part. These brief cross-sections of my history were in turn written down by me in narrative form to become this my book.
    Like many mathematicians of the period, Girolamo practiced astrology, and he notes the astrological circumstances surrounding his birth:
    Although various abortive medicines—as I have heard—were tried in vain, I was normally born on the 24th day of September in the year 1500, when the first hour of the night was more than half run, but less than two thirds . . . Mars was casting an evil influence on each luminary because of the incompatibility of their positions, and its aspect was square to the moon.
   . . . I could easily have been a monster, except for the fact that the place of the preceding conjunction had been 29° in Virgo, over which Mercury is the ruler. And neither this planet nor the position of the moon or of the ascendant is the same, nor does it apply to the second decanate of Virgo; consequently I ought to have been a monster, and indeed was so near it that I came forth literally torn from my mother’s womb.
   So I was born, or rather taken by violent means from my mother; I was almost dead. My hair was black and curly. I was revived in a bath of warm wine which might have been fatal to any other child. My mother had been in labor for three entire days, and yet I survived.
    One chapter of The Book of My Life lists the books Girolamo wrote, and the first on the list is The Great Art , one of three “treatises in mathematics” that he mentions. He also wrote on astronomy, physics, morality, gemstones, water, medicine, divination, and theology.
    Only The Great Art plays a part in our tale. Its subtitle, The Rules of Algebra , explains why. In it, Girolamo assembled methods for solving not just the quadratic equation, known to the Babylonians, but newly discovered solutions for cubic and quartic equations. Unlike Khayyám’s solutions, which depended on the geometry of conics, those in The Great Art are purely algebraic.

    Earlier, I mentioned two kinds of mathematical symbol, both of which we see in an expression such as x 3 , for the cube of the unknown. The first kind of symbol is the use of