# Gerolamo Cardano: Lives of the Mathematical Ninja

It's been a while since I did a Ninja Lives post - let me put that right!

Gerolamo Cardano is just what the MacTutor archives call him: in France, he's Jerome Cardan; if you ask a Latinist, he's Hieronymus Cardanus. Some people call him Geronimo, which is a pretty awesome name, too. In any case, he was born early in the 16th century, in what is now Italy. His dad knew Leonardo.

Life wasn't easy for the young Cardano: an illegitimate child, his mother reputedly tried to abort him, before spending much of his childhood moving around to avoid the plague like the, um... you know. And for a while, the colleges wouldn't let him study medicine because he was illegitimate. That changed eventually, and he became a medic of some repute - he not only assuaged the Archbishop of St Andrews' asthma, but he said it three times drunk.

Mathematically, he was way ahead of his time. He developed a lot of the work behind the binomial expansion using Pascal's triangle - a good example of Stigler's Law, Pascal's triangle was well-known even before Cardano - and wrote about solutions to cubic equations using what is now known as Cardano's formula (discovered by Tartaglia). In the course of this, he was among the first to make systematic use of negative numbers, and almost certainly the first to try to do maths with complex numbers. (They crop up in Tartaglia's formula, but they cancel out.)

And, almost by the way, he invented probability. He was an incorrigible gambler, and won and lost several fortunes at the tables. In his Liber de Ludo Aleae, not published until nearly 100 years after he died, he outlined how to think about the possible outcomes of one, two or three dice, long before Pascal and Fermat got their hands on the ideas.

Cardano had trouble with his sons (one was executed for murdering his wife, and he turned another son into the police for burgling the family home) and spent time in prison himself after publishing a horoscope for Jesus1 He did eventually receive a pension from the Church and live well into his 70s.

He's reputed to have predicted the date of his death; however, he's also reputed to have committed suicide.

## Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

1. simultaneously managing to annoy both the Christians and the rationalists. []

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