GEROLAMO CARDANO: BIOGRAPHY, CONTRIBUTIONS, INVENTIONS - ARTE - 2025

Gerolamo Cardano (1501-1576) was an Italian-born mathematician, physician, physicist, philosopher, and astrologer, recognized primarily for his contributions to mathematics, mechanics, and physics.

His book Ars Magna is considered one of the pillars of the history of algebra and the work that spread the general formula for solving third degree equations. He is also credited with the invention of the cardan mechanical component, essential for the automotive industry.

Portrait of Gerolamo Cardano. Source:

He led a life full of controversies, in which he was even declared a heretic, and accumulated many enemies due to his uncompromising nature. Of course, no one can deny that his ability to perform calculations and process knowledge was rare.

Cardano published more than 200 works from different areas and two natural science encyclopedias. He also presented the first systematic calculations of probabilities, a century before Blaise Pascal and Pierre de Fermat.

Biography

In September 1501, Gerolamo Cardano was born in the city of Pavia, in northern Italy. He was the illegitimate son of Fazio Cardano and Chiara Micheria, a widow in her 30s who was struggling to raise her three children.

His father was a learned jurist from Milan, but a great fan of mathematics. It is said that he gave lectures on geometry and that even Leonardo Da Vinci at some point consulted him in the area.

Little is known of the early years of Cardano's life, but it is said that he was a child in poor health. In his youth he became an assistant to his father, who opened the door to the world of mathematics with his teachings.

Although at first his father refused to allow him to attend university, he finally gave in with the hope that he would study law at the University of Pavia, but he opted for a career in Medicine.

When war broke out in the area and before the study center closed, he had to move to the University of Padua to complete his studies. During that time his father died and left him a small legacy, which Cardano squandered on his fondness for gambling. He was a brilliant but difficult student, being excessively outspoken, uncompromising, and critical.

Difficult beginnings

In 1525 he received his medical degree and submitted his application to enter the Milan Medical College, but was rejected three times with the excuse of his illegitimate birth. It is then that he decides to move to the small town of Sacco and practices medicine a few kilometers from Padua.

In 1531 he married Lucía Bandarini and a year later they must move to Gallarate, due to having insufficient income from their medical practice. In 1533 the economic problems continued and Cardano, pressed by debts, decided to return to gambling, which led him to end up pawning his wife's jewelry and some furniture.

Among their desperate attempts to improve their fortune, they moved to Milan and end up falling into poverty, being forced to enter a welfare asylum.

However, a surprising twist allowed them to get out of that terrible situation, when the Piatti Foundation in Milan granted him the position of professor of mathematics that his father once held.

During that period he was able to treat some patients and was gaining recognition in the practice of medicine, although he was still rejection of the medical institution. He even published a book in 1537 scathingly criticizing it and judging the character of its members.

Years of great contributions

Cardano's medical practice and some near-miraculous cases were so prominent that they earned him an excellent reputation and the admiration of many. This served as a pressure factor for the Milan Medical College, which modified the clause of his birth and ended up admitting him in 1539, after having rejected him three times.

That same year his first book on mathematics Practica arithmetice et mensurandi singularis was published and he had an approach to Niccolò Fontana Tartaglia, an Italian mathematician and engineer, who had gained fame by solving cubic equations.

This marked a period, approximately six years, in which Cardano, knowing the Tartaglia method, dedicated himself to working and studying the solution of third degree equations. During those years, he did not disclose the procedure due to a promise he made to Niccolò.

Between 1540 and 1542, after resigning from his position as professor of mathematics, he also abandoned his studies and relapsed into his addiction to gambling, this time spending the whole day playing chess.

However, in 1543 he managed to get out of this vicious circle and spent almost the next ten years giving medical lectures at the universities of Milan and Pavia.

During that period, specifically in the year 1545, Cardano published his main contribution to mathematics Ars Magna, in which he explained the methods for solving cubic and quartic equations.

This book was published after Cardano found out that Tartaglia was not the father of this discovery, but Scipione dal Ferro, so he felt released from his promise and decided to spread his studies.

Fame and misfortunes

De propria vita, Cardano's autobiography. Source: European Library of Information and Culture

Cardano accepted an offer to travel to Scotland in 1552 to serve the Archbishop of St. Andrews, John Hamilton, who had suffered from asthma for ten years and his attacks were getting worse in frequency and severity without finding a cure.

The doctors of the courts of the French king and the German emperor had failed to improve his health condition, which brought him to the brink of death.

The journey in the midst of fame that Cardano was experiencing was extremely successful as he achieved the first signs of improvement within two months of his arrival. He was also received by medical societies and recognized as a scientific leader wherever he attended.

Upon his return, with more than two thousand gold crowns that he received from the archbishop, he was appointed professor of medicine at the University of Pavia, for which he continued to reap fame and fortune.

However, in 1557 her eldest son Giambatista secretly married Brandonia di Seroni, who according to some versions was only interested in family fortune and publicly cheated on her husband.

Giambatista poisoned his wife and later confessed to the crime. The subsequent torture and execution of his son in 156, generated terrible regret for Cardano, from which he was never able to recover.

In addition to blaming himself for not avoiding the suffering of his first-born son, his prestige was strongly affected, so he had to move to Bologna, where he applied for a chair of medicine in 1562.

Controversies and heresy

This period was full of controversies and enmities for his arrogant and critical attitude. In addition to this, he had problems with his other son, Aldo, who was a hardcore gamer. Aldo lost all his possessions and even broke into his father's house to deal with gambling, so his father denounces him.

In 1570, Cardano was accused of heresy and imprisoned for publishing the horoscope of Jesus Christ and attributing the events of his life to the stars. It is said that it was an attempt to regain notoriety and perpetuate his name, since previously the church had received his full support.

After a few months he was released, but as he was forbidden to publish his work and occupy a university position, he moved to Rome the following year. There he received membership in the College of Physicians and a lifetime pension from the Pope. During this period he wrote his autobiography which would be published posthumously in 1643.

In September 1576, a few days before his 75th birthday, one of the most brilliant mathematicians of that time passed away. Historians indicate that he used to give himself the ability to project his spirit out of the body, have premonitory dreams and even predict the date of his death; Some even consider that he stopped eating in a suicidal practice because he did not miss his last prediction.

Contributions and inventions

Cardano wrote more than 200 works on medicine, mathematics, physics, philosophy, religion. He also made contributions in the areas of mechanics, geology, hydrodynamics, probability, and, of course, algebra.

In his work Ars magna he disseminates what would later become known as the Cardano Method or Cardano Rule. It is the general formula for solving a cubic equation of any type.

His outstanding calculus ability, his observations on the roots and coefficients of the equation, as well as the use of imaginary numbers, later gave him the authorship of the theory of algebraic equations.

He was also the first to venture into probability theory, studying the throwing of the dice with the intention of showing that the results were governed by scientific principles and not by chance.

He not only introduced the concept of probability, but also stated one of his fundamental theorems, the law of large numbers. He also presented the so-called power law, which assumed the probability that a certain event would be repeated.

Cardano is credited with the invention of the gimbal, a mechanical component that allows two non-coaxial shafts to join and transmit a rotary movement. The so-called cardan joint is a basic automotive part, which was first implemented in 1908 by the Mercedes-Benz automobile house.

Finally his reflections in the fields of geology, hydrodynamics and physics did not go unnoticed. Among them is his statement about the impossibility of perpetual motion, except in heavenly bodies.

His observation on the trajectory of the projectiles also stands out, which he assured was not straight, but in the shape of a parabola.

References

1. Encyclopædia Britannica (2019, May 27). Girolamo Cardano. Recovered from britannica.com
2. "Cardano, Girolamo." Complete Dictionary of Scientific Biography. Recovered from Encyclopedia.com
3. NNDB (2019). Girolamo Cardano. Recovered from nndb.com
4. O'Connor, J and Robertson, E. (nd). Girolamo Cardano. MacTutor History of Mathematics archive, University of St Andrews. Recovered from history.mcs.st-andrews.ac.uk
5. Izquierdo, AF (2018, November 12). The great Gerolamo Cardano. Recovered from laverdad.es
6. M Gliozzi, Biography in Dictionary of Scientific Biography (New York 1970-1990).