Gerolamo Cardano

Gerolamo Cardano (Italian: [dʒeˈrɔːlamo karˈdaːno]; also Girolamo or Geronimo; French: Jérôme Cardan; Latin: Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Italian polymath whose interests and proficiencies ranged through those of mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, music theorist, writer, and gambler.

He became one of the most influential mathematicians of the Renaissance and one of the key figures in the foundation of probability; he introduced the binomial coefficients and the binomial theorem in the Western world. He wrote more than 200 works on science.

Cardano became embroiled in a significant controversy over the publication of solutions to cubic and quartic equations in his 1545 work, Ars Magna.
The core of the dispute stemmed from his use of a method for solving cubic equations that he had learned from Niccolò Tartaglia in 1539. Tartaglia had shared the solution with Cardano under a strict oath of secrecy, promising not to publish it until Tartaglia himself had done so.
However, Cardano later discovered that the solution had been previously found by Scipione del Ferro, which he felt justified breaking his oath. He published the method in Ars Magna, crediting both Tartaglia and del Ferro, but this action enraged Tartaglia.

The controversy is emblematic of Cardano’s complex legacy, where his revolutionary contributions to mathematics were intertwined with personal and ethical transgressions. His work also introduced the first systematic treatment of complex numbers, though he found them “as refined as it is useless”.
This paradox—being both a groundbreaking innovator and a transgressor of intellectual trust—defines much of the narrative surrounding Cardano’s life and work

Today, Cardano is well known for his achievements in algebra. In his 1545 book Ars Magna he made the first systematic use of negative numbers in Europe, published (with attribution) the solutions for cubic and quartic equations, and acknowledged the existence of imaginary numbers.