Welcome back to our series on Italian Masters of math and science. Last week I wrote about Galileo’s extensive accomplishments both in the field of astronomy and beyond. This week, I’ll take a look at another renaissance polymath who dabbled in astronomy, along with his work in mathematics, medicine, biology, chemistry, philosophy, and gambling (yes, seriously): Girolamo Cardano. Cardano is a less well-known figure than Galileo or some of the other scientists I’ve written about who have famous equations or units of measurement named after them, like Volta or Torricelli. He is regarded as one of the greatest mathematicians of his age, however, and made a great many contributions to science, mathematics and mechanical engineering, despite his reputation as a disrespectful, gambling misanthrope.
Girolamo Cardano (1501-1576)
Born in 1501 in Pavia, Cardano was the illegitimate son of a Milanese lawyer and mathematician. Although his father hoped Cardano would follow in his footsteps and study law, he was too intrigued by the sciences, and pursued a path in academics, starting with a degree in medicine in 1526. He lived a hard life, as the circumstances of his birth, his perpetual gambling habits, and his irascible temperament always stood in his way. It took him 14 years to gain admission as a professor at the College of Physicians in Milan, due to being a bastard in more ways than one: besides his illegitimate birth, he also penned scathing critiques of the physicians at the College as vain and talentless hacks. Ultimately, he was awarded a professorship at a series of universities throughout his life, though his troubles never ceased. Of his three children, his older son was executed in 1560 for poisoning his wife and his younger son was banished and disowned in 1569 for gambling away Cardano’s money and burglarizing his house to pay overdue debts. Not long after in 1570, Cardano found himself under arrest by the Catholic Church on charges of heresy. He was only imprisoned for a few months, but after his release he was nonetheless forbidden from holding a university post or publishing any work for the rest of his life. He finally passed away in 1576, and many believe he intentionally committed suicide in order to fulfil a horoscope he had cast for his own life years earlier.
Mathematics and Probability
Cardano spent a great deal of time tackling the mathematical unknowns of his time. His biggest impacts on the field of mathematics arose from his work on algebra and probability. Cardano derived solutions for a number of significant problems in algebra, including methods for determining the roots of cubic and quartic equations and expanding binomial equations. His solutions are all the more impressive considering that European mathematicians were not yet acknowledging that negative numbers could exist and had not yet developed a theory for complex numbers. His methods may seem needlessly complex by today’s standards, considering how broad our mathematical toolbox is, but the fact that his solutions worked despite such handicaps is testament to his brilliance.
That brilliance also found its way into his life in dice halls and chess games. His insight into the nature of these games of strategy and chance led him to the development of the first systematic exploration of probability and statistics. He based his theory on the ratios of favorable outcomes to non-favorable outcomes, which we now call “odds” in both gambling and statistics. His initial forays into determining the combined probabilities of multiple events with their own odds set the stage for later mathematicians to develop the rules we still use in statistics today. Indeed, the very examples he used in his treatise Book on Games of Chance would still be familiar to students 5 centuries later, as he used throws of 6-sided die to demonstrate the likelihood of certain outcomes.
Cardano was also an accomplished mechanical engineer, constructing devices that were the predecessors to tools we still use today. Some of his inventions are so tied to his work that they still bear his name. The cardan gear, for instance, is an efficient method for converting rotational motion into linear motion. He is sometimes credited with inventing a combination lock, the three-ringed gimbal method for stabilizing compasses, and the universal joint, the last of which is still sometimes called the Cardan joint. There is some debate as to whether he independently arrived at these inventions or was just improving ideas by previous scientists and inventors. Regardless, the fact that so many inventions are credited to his experimentation goes to show how much respect his peers and successors had for his creativity.
In his own autobiography, Cardano described himself as “hot-tempered, single-minded, and given to women,” and considered himself “cunning, crafty, sarcastic, diligent, impertinent, sad, treacherous, magician and sorcerer, miserable, hateful, lascivious, obscene, lying, obsequious.” While he wasn’t proud of his own gambling or abrasive personality, he did take great pride in his work as a physician, mathematician, scientist, and inventor. People tend to focus on Cardano’s hard living and the scandals he was involved in, while unfortunately overlooking his many achievements. Steeped as we are in math and science, we can surely appreciate the accomplishments of a man who burned the candle at both ends as brightly as Cardano did.