Girolamo Cardano was a 16th-century physician, mathematician, philosopher, scientist, encyclopedist, and inventor. During his life, he was beaten, imprisoned, survived a plague, suffered frequent illnesses, witnessed the execution of his son, was robbed by his other son, and was banned by the Church from engaging in any further scholarly work. This is his fascinating story – and an account of his unwavering optimism in the face of tragedy.
Cardano was born in 1501 in Pavia, Italy, to Chiara Micheri and Fazio Cardano. An illegitimate and initially unwanted child, he survived several abortion attempts before entering the world on 24 September 1501. Cardano had a difficult childhood: he was a sickly and accident-prone child, afflicted with a stutter, and his father often beat him. He contracted an unspecified plague and survived, but lost several of his half-siblings to the same disease. In the midst of this turbulent upbringing, the precocious Cardano found solace and comfort in the life of the mind.
Girolamo excelled at his university studies, graduating with his doctorate at the age of 25. A few years later, after finally overcoming a ten-year-long struggle with erectile dysfunction (his autobiography De vita propria liber (The Book of My Life, NYR) is disarmingly frank in places), he married a woman named Lucia Banderini. Finances were sometimes tight for the young couple, so Cardano supplemented their funds by gambling. This proved to be a lifelong habit that siphoned off considerable time and energy — he later called himself an “inordinately addicted” gambler and admitted to playing every single day for many years (Cardano & Stoner, 2002) – but one that ultimately helped him derive key insights that lay at the foundation of later probability theory.
Despite his doctorate in medicine, Cardano was repeatedly denied admission to the College of Physicians in Milan. He had a reputation as a difficult and sometimes arrogant young man, and the elite College didn’t approve of his illegitimate birth. Rejected and impecunious, he and his wife moved to a nearby town where he started practicing medicine. His private practice began to flourish. During this time, he also started teaching mathematics.
Cardano’s socio-professional status was finally improving. His success as a physician won him the respect and loyalty of some influential backers, a development that would be a major boon later in his career, as we shall see. But Cardano was still furious about his repeated rejections at the hands of the College of Physicians. So he did what any cautious young professional just setting out on his career would do – and published a no-holds-barred diatribe setting forth 72 scathing criticisms of the physicians of his time. Cardano attacked – to give you a flavor – “the tribal insecurities of men who banded themselves together and showed to the world a surface of pomp and learning that…concealed from the beholders the depth of ignorance beneath” (Wykes, 1969).
These were fighting words, and unlikely to endear him to the College of Physicians. Yet only one year after publishing his withering invective, Cardano thought it reasonable to apply again – and was unsurprisingly rejected a third time. Not long thereafter, however, the College relented to pressure exerted by Cardano’s influential supporters and finally agreed to admit him. The same year he finally became a member of the College (1539), Cardano published his first book on mathematics. This was the start of a new phase of his life, one in which he wrote prolifically on mathematics, medicine, philosophy, astrology, natural science, cryptology, music, and more.
Cardano became famous as a physician and a scholar, and was often sought after by European heads of state for his medical services. He agreed to journey to Scotland in 1552 to treat the Archbishop of St. Andrews, who was suffering from asthma attacks that were growing more frequent and more dangerous. His treatment of the archbishop was spectacularly successful, earning him a handsome reward, the loyalty of the archbishop, and the offer of a permanent place in the Scottish court (the last of which he refused, choosing to return to Italy instead). He returned to Italy a wealthy man and a renowned scholar, where he accepted the post of professor of medicine at Pavia University and enjoyed the support of many influential backers.
The rest of Cardano’s life was a combination of scholarship and repeated tragedy. He continued to publish influential books and treatises – by his own count, more than 200 in his lifetime – but personal catastrophes followed him around. The death of his wife left him lonely and isolated. His beloved eldest son, Giovanni Battista, had an acrimonious marriage with a woman who taunted him publicly about the fact that he was not really the father of his children. Enraged, Giovanni poisoned his wife and was caught by the authorities – who imprisoned, tortured, belimbed, and executed him. Cardano adopted his now-orphaned grandchildren, intending to rear them himself. One of them died tragically a few days later. Cardano never fully recovered from this series of events.
Cardano’s younger son, Aldo, presented his own problems. Cardano regarded Aldo as a dissolute reprobate; an awful youth of “base character” and “evil habits” (Cardano & Stoner, 2002). When Aldo lost all his savings and possessions to gambling, his next steps were to gamble away some of his father’s resources, and then break into his father’s house to rob him of cash and jewelry to finance more gambling. Cardano discovered this betrayal and alerted the authorities, who banished his youngest son from the city. This, too, was hard on Cardano.
One year later, in 1570, Cardano was arrested by the Inquisition on unspecified charges (but all indications point to heresy). What did the Inquisition want with Cardano, who was by all accounts a pious man and on good terms with the Church? Like many physicians and scholars of the 1500s, Cardano believed in the utility of astrology as a valid predictive science and a useful supplement to medical prognosis. (In fact, during his tour meeting important people in northern Europe, Cardano cast 14-year-old King Edward VI’s horoscope, predicting that he would enjoy a long and prosperous future. The adolescent king died a year later.)
The Church didn’t have a problem with astrology per se – the problem was that Cardano had cast the horoscope of Jesus Christ, attributing the events of his life to the positions of various celestial bodies. This blasphemy provoked the ire of the Vatican and earned 70-year-old Cardano a prison sentence. He was released after a few months, but only because a powerful archbishop interceded on his behalf (according to some accounts, it was an Italian archbishop whose mother Cardano had cured of disease; according to others, it was the Scottish archbishop mentioned earlier). Had it not been for this intercession, Cardano’s fate might have turned out very differently. The Church placed Cardano under house arrest, eventually freeing him but prohibiting him from holding a university post and banning him from publishing any more books.
Hamstrung but free, Cardano retired to Rome, where he lived off a pension and wrote his autobiography. Legend has it that, much as he had done with figures such as King Edward VI, Jesus Christ, and Martin Luther, Cardano cast his own horoscope – this time predicting the day of his own death, 21 September 1576. When that day arrived and he was neither sick nor dying, he is alleged to have killed himself so as not to falsify the prediction. This tidbit remains unverified, and is almost certainly apocryphal. But even myths can reveal something interesting about how an important figure was perceived in the public eye. This particular myth is an intriguing suggestion for an eccentric polymath whose life was an odd mix of science and superstition, success and tragedy.
Cardano was a true Renaissance polymath. Apparently unencumbered by all the Sturm und Drang in his life, he wrote two encyclopedias of natural science that were very popular in his time. These encyclopedias “contain a little of everything, from cosmology to the construction of machines, from the usefulness of natural sciences to the evil influence of demons, from the laws of mechanics to cryptology” (Gliozzi, 2008). Cardano made contributions to algebra, probability theory, medicine, hydrodynamics, mechanics, and geology. He invented many devices, including the universal joint, which we still use in cars today. He offered the first clinical description of typhus fever.
Not least, he was one of the first Europeans to make systematic use of negative numbers and to deal with problems involving imaginary numbers. Imaginary numbers were unthinkable and almost heretical in the 16th century – Cardano was ahead of his time in accepting their existence, but they disturbed him so deeply that he described working with them as “mental torture”. Cardano’s prolific and wide-ranging contributions made him a famous and highly regarded scholar during his time. A century later, German polymath Gottfried Leibniz said of him, “Knowledge exerts a magic that is comprehensible only to those who have been seized by it. [I am referring to] that kind of knowledge which Cardano possessed. He was a truly great man, despite his numerous misconceptions. If not for them, he would have been unequaled” (Fierz, 1983).
Cardano was also an inveterate gambler, a penchant that earned him the moniker “the gambling scholar” (Ore, 1953). In the 1500s, a vexing problem of dice games was a variant of the following: people reasoned that if you threw two dice, you should see 9 and 10 occur with equal frequency: after all, you can make 9 from 4+5 or 6+3, and you can make 10 from 5+5 or 6+4. But in reality, gamblers observed that 9 appeared significantly more often than 10, and nobody understood why. People were perplexed.
Cardano applied himself to this problem, eager to understand the reason for the discrepancy between prediction and observation – an issue that was also central to his interest in astrological prediction and medical prognosis. Cardano solved the problem with a key insight, realizing that 9 can be made from 5+4 or 4+5, as well as 6+3 or 3+6. By contrast, 10 can only be made from 5+5, 6+4, or 4+6. We now recognize this as the distinction between combinations and permutations, and it is no longer a surprising idea in the 21st century, but it was a major intellectual leap forward in Cardano’s time. As philosopher Roy Sorensen notes, “it [took] a Cardano to fight his way up to the vantage point that makes the paradox seem like a trivial mistake” (Sorensen, 2003).
Perhaps more importantly, this solution illustrated Cardano’s larger belief that there were scientific-probabilistic laws underlying games of chance, and that these laws could be formulated and studied. This groundbreaking idea led him to write the book Liber de Ludo Aleae (Book on Games of Chance).
It was not published until a century later, but it represents the first-ever foray (at least in Europe) into the beautiful and complex world of probability theory. A full century before Pascal and Fermat, Cardano defined probability as the ratio of favorable outcomes to possible ones and anticipated the law of large numbers. For this reason, Cardano has also been called “the father of probability”.
Cardano enjoyed scholarly success and a measure of wealth and renown, but his life was also marked by repeated suffering. He endured sickness, accidents, rejection, the execution of one son and betrayal by the other, the death of his grandson, imprisonment at the hands of the Inquisition, and intellectual shackling by the Church. Cardano describes his life’s greatest sadnesses in this way:
“The first was my marriage; the second, the bitter death of my son; the third, imprisonment; the fourth, the base character of my youngest son.” (Cardano & Stoner, 2002).
This litany of things-gone-wrong would be enough to put many of us out of commission. By contrast, Cardano kept putting his best foot forward. His cantankerous side sometimes shines through his writing, but he appears to have remained thankful until the end. Here is a snippet from his autobiography, written toward the end of his life and infused with serene gratitude:
How quietly uplifting this is, especially coming from somebody who suffered as much as Cardano did.
Today, Girolamo Cardano is no longer a key figure in our public intellectual discourse. By one author’s estimation, he was unfortunate enough to have lived during a time when major advances in some of his fields of expertise were difficult to come by (as was the case in medicine), or where his advances were important, but necessarily overshadowed by those of future thinkers (as was the case in mathematics). As a result, many of us have never even heard of him. Our mathematics and medicine have superseded his, it has been hundreds of years since the intelligentsia last regarded astrology as a genuinely predictive science, and Cardano’s beliefs in demons, spirits, and the occult now seem quaint and anachronistic. But it has been 500 years since he lived, so this is to be expected. Tempus edax rerum indeed. Even if you were an important and original thinker in your time, it is easy for the passage of the centuries to consign you to obscurity.
Cardano nonetheless remains important in many ways, and perhaps he deserves to be talked about more. He was a key Renaissance figure, bridging the medieval period with the later Enlightenment. Despite being a Catholic in post-Reformation Europe, he collaborated with Protestant astronomers and praised Muslim thinkers, extolling Ibn Sina’s (Avicenna’s) virtues at a time when the continent was convulsing with religious wars. He had an insatiable curiosity and wrote about everything under the sun, from mechanics to morality. He laid the foundations of probability theory. He invented devices that we still use today. When he treated patients, he was circumspect and erred on the side of caution, often eschewing medicine in favor of common-sense prescriptions centered on diet and exercise.
He understood the relevance of mood and emotions to the physical well-being of his patients – an understanding that was crucial to his successful treatment of the Archbishop of St. Andrews, for whom anxiety was a major trigger of asthma attacks. His interpretation of dreams – yes, he did that too – was an entertaining mix of the supernatural (demons, spirits), the now-antiquated-but-then-current (Galenic humors), and reasonable, quotidian observations (bodily states can affect dreams, dreams often reflect memories of one’s recent past).
This combination is most characteristic of Cardano – he was a stimulating and eclectic farrago of Classical Greek ideas, medieval supernatural beliefs, and cutting-edge Renaissance math and science. This seems a strange mix to the 21st century eye, but was not such a shocking combination in the 1500s. And it makes for highly entertaining reading.
Cardano’s unusual story is worth recounting for its own colorful sake. But we can also draw a few lessons from the life of this 16th century polymath. First, Cardano’s accomplishments are an encouraging reminder of how far curiosity, intelligence, and hard work can get you despite turbulent beginnings and repeated heartbreak. Second, Cardano illustrates quite vividly that it is possible to be very wrong about some things and very right about others. This may seem obvious. But in today’s vociferous political antagonisms and culture wars, the point is often lost or ignored – instead, it is often assumed that a stance is wholly right or wholly wrong, a person entirely good or entirely bad. And third, perhaps Cardano’s calm gratitude and serene optimism – evidenced in the excerpt from his autobiography – can serve as a reminder-by-example that there is good in the world, and we should try to enjoy it while we still can, even if we are beset by tragedy. In the words of Max Ehrmann’s eloquent poem Desiderata, “With all its sham, drudgery, and broken dreams, it is still a beautiful world. Be cheerful. Strive to be happy.”
This is doubtless easier said than done, but we should probably resist the temptation to mock such thinking. Yes, the advice is difficult to follow, and yes, it has been offered before. So what? It is a valuable psychological lesson from a colorful, beleaguered polymath who kept on giving it his best despite an omnipresent cloud of heartbreak and tragedy. Cardano’s story serves as an inadvertent lesson from 500 years ago that’s still worth heeding today.