16th Century Mathematician

1. September 24, 1501 - September 21, 1576
GIROLAMO CARDANO
16th Century Mathematician

2. Latin: Hieronymus Cardanus
Girolamo Cardano (Gerolamo),
(English: Jerome Cardan)
born on September 24, 1501 in
the city of Pavia, duchy of Milan
(Italy).
BIRTH

4. Cardano was the most outstanding
mathematician of his time.
Here are some of his works (books) in
Mathematics.
LIFE WITH MATHEMATICS

5.  Practica Arithmetica et Mensurandi
Singularis (1539)
 Ars Magna (1545)
 Liber de Ludo Aleae (1663)
 De Vita Propria
BOOKS

7.  English: The Practice of Arithmetic and
Simple Mensuration
 first mathematical publication
Practica Arithmetica et
Mensurandi Singularis (1539)

9.  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

10.  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

11.  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

12.  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

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

15.  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

16.  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

17.  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

19.  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

20. “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.”

22.  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

23.  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

24.  Cardano is reported to have correctly
predicted the exact date of his own death
but…
TRAGEDIES IN LIFE

25.  … he committed suicide by drinking a glass
of poison on September 21, 1576 to ensure
his prediction would come true.
TRAGEDIES IN LIFE

26. “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

27. In what way/s can you
relate your life to
Cardano’s?
QUESTION
He had been a hot tempered person, not well -liked, a
compulsive gambler, but he still stood out
during his time.