September 24, 1501 - September 21, 1576

GIROLAMO CARDANO

16 th Century Mathematician

Latin: Hieronymus Cardanus

Girolamo Cardano (Gerolamo),

(English: Jerome Cardan)

born on September 24, 1501 in

the city of Pavia, duchy of Milan

(Italy).

BIRTH

LIFE WITH MATHEMATICS

Cardano was the most outstanding

mathematician of his time.

Here are some of his works (books) in

Mathematics.

LIFE WITH MATHEMATICS

Practica Arithmetica et Mensurandi

Singularis (1539)

Ars Magna (1545)

Liber de Ludo Aleae (1663)

De Vita Propria

BOOKS

Practica Arithmetica et Mensurandi Singularis

(1539)

English: The Practice of Arithmetic and

Simple Mensuration

first mathematical publication

P r a c t i c a A r i t h m e t i c a e t M e n s u r a n d i S i n g u l a r i s ( 1 5 3 9 )

Ars Magna(Artis Magnæ sive

de regulis algebraicis liber

unus)(1545)

English: The Great Art; or, The Rules of Algebra

contained the solution of the cubic equation,

for which he was indebted to the Venetian

mathematician Niccolò Tartaglia, and also the

solution of the quartic equation found by

Cardano’s former servant , Lodovico Ferrari .

Ars Magna

This was probably the most important

mathematical achievement of the 16th

century.

This book contains a variety of methods for

solving polynomial equations, and anticipates

the discovery of complex numbers .

Ars Magna

He demonstrates for the first time that

solutions can be negative, irrational, and in

some cases may involve square roots of

negative numbers.

Ars Magna

In another book, Ars Magna Arithmetic ,

Cardano remarks that √(-9) is neither +3 nor

–3 but some “obscure third sort of thing”

(quaedam tertia natura abscondita ). This is

how complex numbers were announced to the

world.

Ars Magna

Liber de Ludo Aleae

(1663)

Caravaggio The Cardsharps c. 1594, oil on canvas, The Kimbell Art Museum, Fort Worth, Texas, USA.

English: The Book on Games of Chance

presents the first systematic computations of

probabilities

formulated the fundamentally important

concept of solving a probability problem by

identifying a sample space with equally likely

outcome

Liber de Ludo Aleae

When discussing the case of rolling two

symmetric dice he wrote:

. . . there are six throws with like faces, and

fifteen combinations with unlike faces, which

when doubled gives thirty, so that there are

thirty-six throws in all , . . .

Liber de Ludo Aleae

Cardano showed remarkable understanding

that the outcomes for two rolls should be taken

to be the 36 ordered pairs rather than the 21

unordered pairs.

Liber de Ludo Aleae

De Vita Propria

English: The Book of My Life

his autobiography; completed before he died

This book was an unvarnished and often

outrageous account of his character and

conduct .

Cardano displays the same unbounded

curiosity that made him a scientific pioneer.

De Vita Propria

“This I recognise as unique and outstanding

amongst my faults - the habit , which I persist

in, of preferring to say above all things what

I know to be displeasing to the ears of my

hearers. I am aware of this, yet I keep it up

wilfully, in no way ignorant of how many

enemies it makes for me.”

TRAGEDIESIN LIFE

Cardano's beloved son, Giambatista, confessed

that he poisoned his cuckolding wife. He was

then executed for murder (1560). Cardano

never recovered from the blow.

TRAGEDIES IN LIFE

In 1570 he was arrested on the accusation of

heresy (in part for casting the horoscope of

Jesus). After several months in jail , he was

permitted to abjure privately, but he lost his

position and the right to publish books.

TRAGEDIES IN LIFE

Cardano is reported to have correctly

predicted the exact date of his own death

but…

TRAGEDIES IN LIFE

… he committed suicide by drinking a glass

of poison on September 21, 1576 to ensure

his prediction would come true.

TRAGEDIES IN LIFE

“Quinquies exscriptus, maneat tot millibus annis.”

“I wrote it out five times, may it last

the same number of millennia.”

– final line of Ars Magna

QUOTATION

In what way/s can you

relate your life to

Cardano’s?

QUESTIONHe had been a hot tempered person, not well - l iked, a

compulsive gambler, but he st i l l stood outduring his t ime.