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ON 8 September 1526, the Blessed Virgin鈥檚 birthday, Jerome Cardano was in Venice. While others were praying, Cardano was playing cards at the house of senator Thomas Lezun. He was confident that his recent invention 鈥� the mathematics of probability 鈥� was about to pay off. As well as money, he was hoping to win a night with a beautiful prostitute. Such an experience, he thought, might be just the thing to end his four-year streak of impotence.

He was nearly 25, and had recently graduated from medical school. Though Cardano would later become renowned across Europe for his skills as a physician, as well as a celebrated author, astrologer and mathematician, right now what he needed was money. The Milanese College of Physicians had denied him a licence to practice, possibly because of his illegitimate birth, although his rude, confrontational personality certainly didn鈥檛 help. It was this need for funds that drove him to gamble 鈥� and sparked his interest in all things mathematical.

Cardano grew up in Renaissance Milan, the son of a lawyer who counted Leonardo da Vinci among his associates. As a child, Cardano sometimes sat on da Vinci鈥檚 floor while the adults talked philosophy, law and culture. He was even taken to see The Last Supper, freshly painted on the wall of the convent of Santa Maria delle Grazie; when he saw it again years later, he was amazed at how 鈥渂lurred and colourless鈥� the once-vivid fresco had become.

It was as a student, during one of many nights in the local tavern playing dice and cards, that Cardano realised his time could be spent much more lucratively if he thought about stakes and the likelihood of certain numbers coming up when rolling several dice at once. Especially since everyone else was working under the assumption that dice rolls were determined by the Almighty and thus couldn鈥檛 be predicted.

In his spare time, Cardano began to jot down his insights. Later in life, he gathered these writings into The Book on Games of Chance. This told the reader how to work out various probabilities, such as the likelihood of any particular outcome of a dice roll. Cardano also developed what we now call the law of large numbers, showing that 1000 flips of a coin should turn up almost exactly 500 heads and 500 tails.

Gambling didn鈥檛 provide enough income, however, especially as Cardano鈥檚 grasp of probability wasn鈥檛 strong enough to make him unbeatable, or to make it clear exactly when he should stop. He also yearned for respectability, and took lecturing jobs in mathematics while studying philosophy and astronomy. The properties of the universe were a constant source of fascination. He speculated about the nature of light and the character of time, which he considered to be something that only flows within our universe. In the region outside, it 鈥渞emains eternal鈥�, he wrote in On Subtlety, his 鈥渃omplete account of the universe鈥�.

He was granted a medical licence eventually, and soon gained a reputation as a skilled and innovative physician. His mathematical skills meant he was repeatedly offered work in military research, though he always turned it down, and his texts teaching the basics of astronomy sold in significant numbers. Such was the demand that European publishing houses sometimes pirated his works. Shakespeare scholars even suggest that much of Hamlet鈥檚 鈥淭o be or not to be鈥� speech is Consolation, a lament on the death of his eldest son.

Cardano lived at a time when the works of great Islamic mathematicians such as Omar Khayyam had recently become widely available in Latin translation. He was entranced by them, and became obsessed with creating a guide to algebra 鈥� the Great Art, as he called it. It would explain how to solve quadratic equations (containing x² terms), as well as cubic (x³), quartic and quintic equations. These weren鈥檛 only of interest to mathematicians: they had applications in the military and financial sectors, and solutions were highly prized 鈥� and carefully guarded.

Cardano鈥檚 big problem was that the books available only provided a method for solving quadratic equations. Eventually (by somewhat questionable means) he 鈥渂orrowed鈥� a solution for the cubic equation and used this to develop solutions for the quartic and quintic equations. Along the way, Cardano discovered a puzzling phenomenon even more abstract than probability: imaginary numbers.

The most basic imaginary number, now denoted as i, is the square root of -1. It was even more alien and confounding then than it is to countless schoolchildren today. Negative numbers were themselves still a somewhat suspicious concept, and zero had only just become accepted as a mathematical object.

鈥淐ardano realised he could win more often at dice if he thought about probability鈥�

Cardano encountered square roots of negative numbers halfway through some of his algebraic workings. It didn鈥檛 really matter: he could keep them in, and since they were squared later in the process, the problem disappeared. But he found their existence curious, labelling them 鈥渋mpossible quantities鈥�. In The Great Art, he declares they are neither positive nor negative, but 鈥渟ome recondite third sort of thing鈥�.

These days, they are far from recondite. Engineers use i to develop electronic circuits, compression algorithms and myriad other facets of 21st-century life. Together with probability theory, i is also essential to our manipulations of the Schr枚dinger equation of quantum theory. Cardano鈥檚 two major mathematical finds have turned out to be the supporting pillars for our best explanation of how everything in the universe works.

Cardano鈥檚 lack of fame today may have something to do with his arrest by the Inquisition in 1570. The most likely reason is because he had presented a previous pope with a horoscope of the Son of God. At the time, astrology was widely accepted, and though Paul III had welcomed this gift from someone regarded as a talented astrologer, the papacy had since passed to Pius V, who had outlawed the practice. A horoscope of Christ was viewed by many in Pius鈥檚 court as an attempt to subjugate the Creator to his creation: if the stars foretell the life of Christ, that leaves no room for God to act as He chooses.

After a few months of incarceration, Cardano was released to house arrest. But he was forbidden to teach, publish books or even talk about why he had been arrested. He had to pay a significant lump sum to the church for this 鈥渇reedom鈥�, from which he received a meagre monthly income. With the smell of the Inquisition鈥檚 bonfires hanging around him, none of his former associates were comfortable in his company ever again, and his fame and esteem quickly waned.

It was during this time that Cardano wrote the autobiography that tells, among other tales, of that night鈥檚 gambling in Venice. He used his sense for probability to guess that his opponent was cheating by using marked cards. Having carefully won back the money he had lost, he drew his dagger and slashed Senator Lezun鈥檚 cheek in retribution before vanishing into the night. He didn鈥檛 mention what happened about the prostitute.

This article appeared in print under the headline 鈥淭he original chancer鈥�