Cardan was a great mathematician. His main job was as a physician, and he became renowned throughout Europe for his medical skills. But he also published a number of important mathematical texts.
Ars Magna, published in 1545, gave the first method of solving cubic and quartic equations. Controversy rages over this book as much of the methodology came from Tartaglia. His way of solving cubic equations was divulged to Cardan under a strict oath of secrecy. Cardan on discovering that Tartaglia was not first with the proof, only the first to make the knowledge public, felt released from his obligations.
The book was a triumph and went further than Tartaglia anyway, presenting the first calculations for complex numbers, looking at quartic equations and being the first European maths book to focus on algebra.
Cardan is also known for making the first forays into examining probability. Cardan made one of the first studies of die rolling.
Cardan’s later years should have been triumphant - he was rich, lauded as a great mathematician and the finest physician in Europe. Instead he was arrested for heresy and although leniently treated for the time, was dismissed from his University position and not allowed to publish any further work.