Girolamo Cardano

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Girolamo Cardano — Latinized as Hieronymus Cardanus, anglicized as Cardan — was an Italian physician, mathematician, and astrologer whose career spans the full range of sixteenth-century learning, from the algebra of cubic equations to the casting of horoscopes and the interpretation of dreams. Born in Pavia on 24 September 1501, the illegitimate son of the Milanese jurist Fazio Cardano — a lecturer in geometry, an editor of the medieval optical writer John Peckham, and a friend of Leonardo da Vinci — he rose from a disputed start to become one of the most sought-after physicians in Europe and one of its most prolific authors, leaving some two hundred works at his death in Rome on 21 September 1576, the eve of his seventy-fifth birthday.

Engraved portrait of Girolamo Cardano (1501–1576), physician and mathematician — Bibliothèque interuniversitaire de santé, via Wikimedia Commons (Licence Ouverte 1.0).

The disputed start was the shape of everything that followed. Cardano took his doctorate in medicine at Padua in the mid-1520s and applied to the College of Physicians of Milan, which barred him: the bar of birth out of wedlock served where dislike of the man would not have been a sufficient pretext. He practiced for a time in the small town of Sacco, treated patients the licensed faculty could not, and forced his way back into Milanese medicine by the only door open to a man without standing — print and reputation. By the 1530s and 1540s his consultations were sought across the continent; in 1552 he traveled as far as Scotland to treat the asthma of John Hamilton, Archbishop of St Andrews, a cure that made his name. He held chairs of medicine at Pavia and then at Bologna. The illegitimate son refused a license came to sit, by his own reckoning, among the first physicians of the age — a reversal he never stopped narrating.

The algebra that opened a science

His enduring place in the history of the Renaissance rests on the Ars Magna of 1545 — Artis magnae sive de regulis algebraicis — which gave the first printed general solution to the cubic and the quartic, the work conventionally taken to open modern algebra. Behind it lies one of the most famous priority quarrels in the history of mathematics. The cubic had first been solved, decades earlier and never published, by Scipione del Ferro of Bologna; the method passed privately to a pupil, Antonio Maria Fior, whose 1535 public contest with Niccolò Tartaglia drove Tartaglia to rediscover the solution under pressure. In 1539 Tartaglia disclosed his method to Cardano, who swore an oath of secrecy to obtain it. Cardano then went further — his pupil and servant Lodovico Ferrari extended the technique to the quartic — and in 1543, visiting Bologna, the two examined del Ferro’s surviving notebook and saw that the cubic had been solved there first, before Tartaglia. On that ground Cardano judged the oath void, and published in 1545 with credit assigned to del Ferro, to Tartaglia, and to Ferrari by name. Tartaglia answered with accusations of theft; the quarrel ran on through public cartelli and ended in a 1548 disputation at Milan between Ferrari and Tartaglia from which Ferrari emerged the victor and Tartaglia the diminished man.

The Ars Magna did more than collect solutions. Forced by his own cases into roots that were neither positive nor real — the square roots of negative quantities he met and gingerly manipulated — Cardano set down the first European reckoning with what would later be called complex numbers, even while he called the procedure subtle and as refined as it was useless. He wrote on mechanics, and the gimbal mounting he described in De subtilitate (1550) and the ring-suspension of his later work still carry his name as the Cardan joint and the Cardan suspension, though he neither invented the device — it is far older, known in antiquity and in China — nor claimed to. And in the Liber de ludo aleae, the book on games of chance, he reasoned about dice and fortune as a working gambler who had lost and won at the tables for years: the fraction of equally possible outcomes favorable to a throw, the multiplication of chances across repeated throws, the notion of a fair stake. It stands among the earliest sustained pieces of mathematical reasoning about probability, written around 1564 but printed only in 1663, long after Pascal and Fermat had been credited with the founding of the field he had quietly anticipated.

The cosmos as a legible text

These pursuits were, for Cardano, of a piece with his astrology, not opposed to it. He held the heavens to be a legible order whose influences a careful observer could read, and he cast nativities throughout his life. He did not treat the stars as one curiosity among his many subjects; he treated number, medicine, the variety of nature, dreams, and the sky as a single continuous science — the project of reading the one ordered book of the world in whatever script a given page happened to use. The encyclopedic De subtilitate (1550) and its companion De rerum varietate (1557) catalog the powers latent in metals, stones, plants, weather, and stars as a connected economy of natural forces, the same forces a physician manages in the body and an astrologer charts in the heavens.

Title page of Cardano’s encyclopedic De subtilitate (1559 edition, Lyon), his survey of the powers latent in nature — BEIC (Biblioteca Europea di Informazione e Cultura), via Wikimedia Commons (public domain).

His astrological practice was, above all, documentary. He compiled and printed collections of genitures — the nativities of emperors, popes, poets, heretics, and physicians — with running commentaries explaining how a life had unfolded under its stars; he revised them across editions as new lives and new deaths gave him fresh data, and he set his own nativity among them, treating his own biography as a case to be read. In 1554 he published an immense commentary on Claudius Ptolemy’s Tetrabiblos, the canonical ancient defense of astrology, planting his practice in the authority of the oldest technical tradition. Into that commentary he set the horoscope he is most remembered for: a nativity of Christ, in which the events of the life — the nature of the teaching, the manner of the death — were read as unfolding under the configuration of the heavens at the birth. He cast it not to demean the subject but, on the contrary, to crown astrology with the most exalted nativity conceivable; the gesture nonetheless put the life of Christ inside the reach of the stars, and that reach is what would later be turned against him.

This is the same conviction that runs through the Somniorum Synesiorum libri IIII (Basel, 1562), his four books on dreams, named for the late-antique bishop and Neoplatonist Synesius of Cyrene whose short treatise on dreams Cardano took as a charter. Where the popular Greco-Roman dream-key of Artemidorus had decoded the dream as a sign of coming events, Cardano built a fuller theory: a classification of dreams, an account of their causes in the body and in the soul, and a final book of worked examples drawn from his own nights — for the dream, on his reading, was another channel through which the ordered cosmos disclosed itself to an attentive reader, no different in kind from a chart or a symptom. The work, conceived in the 1530s and reshaped after the catastrophe of 1560, became the most ambitious treatment of the dream produced in the Renaissance.

The attendant spirit

Across his late writings Cardano described a personal attendant spirit — a genius or daimon, in the long classical and Neoplatonic lineage of the guiding spirit, the lineage that runs from the daimonion of Socrates through the tutelary genii of Plotinus and Synesius. To it he attributed his warnings, his strange immunities, the premonitions that crossed his sleep, and the turns of fortune he could not otherwise account for; he held that his father Fazio had been accompanied by such a spirit before him, and that its communications came to him not as plain voices or visions but as half-glimpsed signs — an obscurity he took, characteristically, as evidence of their genuineness rather than against it. The figure of the personal genius was not eccentric in his century. It belonged to a Renaissance argument about the powers ruling the sublunary world that his contemporaries Pietro Pomponazzi and Jean Bodin pursued in the same key — Pomponazzi reducing apparent marvels to natural celestial causes, Bodin populating the world with active demons — and that the magia naturalis of Marsilio Ficino and Cornelius Agrippa framed as the manipulation of a living, ensouled nature. Cardano stands inside that Renaissance current of natural magic and its divinatory arts, alongside Paracelsus the physician-magus and the later mathematician-magi John Dee, Giordano Bruno, and Johannes Kepler, in whose work — as in his — the line later drawn between astronomy and astrology, between mathematics and magic, had not yet been cut.

The Inquisition, and the reckoning

The horoscope of Christ stood at the center of the case the Roman Inquisition brought against him. On 6 October 1570 Cardano was arrested at Bologna by the local Inquisitor and imprisoned; the investigation had gathered through the spring and summer of that year, and the charge was heresy. As scholarship on the trial sets out — most fully Monica Azzolini’s reconstruction from the surviving records — the gravamen was less the existence of the nativity than what it implied: that in extending the reach of celestial influence so far, and in the cosmological claims of De rerum varietate, Cardano appeared to make the stars govern even sacred history, and so to crowd out the direct action of God in the order of nature. In December he was moved to house arrest; in February 1571 the verdict came down. He abjured — not as a convicted heretic, but as one vehemently suspected of heresy, the lighter of the formal categories — and the sentence stripped him of his chair, forbade him to teach in the Papal States, and barred him from publishing. He went then to Rome, where he secured a papal pension and, against the odds, the protection of the very institution that had condemned him.

There, in his last months — from September 1575 to May 1576 — he wrote the book by which he is most vividly known. De vita propria liber, the book of his own life, is modeled on the lives of Suetonius: not a chronicle but a portrait assembled by topic — his body, his ailments, his enemies, his gambling, his dreams, his fortunes and reverses, the spirit that accompanied him. Into it he set, without much shielding, the worst of his life: the execution in 1560 of his elder son Giovanni Battista, beheaded for poisoning his wife, a blow Cardano said his attendant spirit had foretold and which broke the center of his years; the dissolute younger son he was driven to disinherit; the disfigurements and diseases he catalogs with a physician’s detachment and a sufferer’s exactness. It was printed only in 1643, by the librarian and skeptic Gabriel Naudé, who appended his own cool judgment of the author. The book remains the closest thing to seeing a Renaissance mind take its own measure — a man who counted the stars and the dice alike, and was sure both were trying to tell him something.

The record and its readers

The recovery of Cardano as a coherent figure rather than a cabinet of curiosities is largely the work of the last century. His collected Opera omnia was gathered in ten folio volumes at Lyon in 1663 by the physician Charles Spon, the corpus from which most later study has worked. The standard modern account of his life — and the argument that his astrology was a rational practice continuous with his science rather than a lapse from it — is Anthony Grafton’s Cardano’s Cosmos: The Worlds and Works of a Renaissance Astrologer (Harvard, 1999), which reads the genitures, the self-commentary, and the print career as a single enterprise; Grafton also introduced the standard English autobiography. The trial has its own dedicated study in Monica Azzolini’s reconstruction in Isis (2019), which works directly from the Inquisition’s records to show how a cosmology, not merely a horoscope, was put on trial. The probability work was brought into the modern history of mathematics by Øystein Ore’s Cardano: The Gambling Scholar (Princeton, 1953), which carried S. H. Gould’s English translation of the Liber de ludo aleae; the horoscope of Christ and its place in the sixteenth-century defense of the art is treated by James H. Holden’s survey of the early nativities of Jesus. The autobiography that anchors all of this — The Book of My Life — was Englished by Jean Stoner in 1930 and has stayed in print, last reissued with Grafton’s introduction; it is the document through which every later reader has met the man who treated his own life as one more text the cosmos had written and left for a careful reader to construe.

→ Related: Pietro Pomponazzi · Jean Bodin · The Renaissance · Divination · Astrology · Neoplatonism · Renaissance Magic · Marsilio Ficino · Cornelius Agrippa · Paracelsus · John Dee · Giordano Bruno · Johannes Kepler · Hermes Trismegistus · Cecco D Ascoli