Gerolamo Cardano (French
Jérôme Cardan; Latin
Hieronymus Cardanus) (24 September 1501 – 21 September 1576) was an
ItalianItaly , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
RenaissanceThe Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...
mathematicianA mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
,
physicianA physician is a health care provider who practices the profession of medicine, which is concerned with promoting, maintaining or restoring human health through the study, diagnosis, and treatment of disease, injury and other physical and mental impairments...
,
astrologerAn astrologer practices one or more forms of astrology. Typically an astrologer draws a horoscope for the time of an event, such as a person's birth, and interprets celestial points and their placements at the time of the event to better understand someone, determine the auspiciousness of an...
and gambler. His gambling led him to formulate elementary rules in probability, making him one of the founders of the field.
Early life and education
He was born in
PaviaPavia , the ancient Ticinum, is a town and comune of south-western Lombardy, northern Italy, 35 km south of Milan on the lower Ticino river near its confluence with the Po. It is the capital of the province of Pavia. It has a population of c. 71,000...
, Lombardy, the illegitimate child of
Fazio CardanoFazio Cardano was an Italian jurist and mathematician. He was a profound student of perspective. Cardano was also a professor at the University of Pavia, and was devoted to hermetical science and the world of the occult. He was a friend of Leonardo da Vinci.It was said that Cardano was always...
, a mathematically gifted
lawyerA lawyer, according to Black's Law Dictionary, is "a person learned in the law; as an attorney, counsel or solicitor; a person who is practicing law." Law is the system of rules of conduct established by the sovereign government of a society to correct wrongs, maintain the stability of political...
, who was a friend of
Leonardo da VinciLeonardo di ser Piero da Vinci was an Italian Renaissance polymath: painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer whose genius, perhaps more than that of any other figure, epitomized the Renaissance...
. In his autobiography, Cardano claimed that his mother had attempted to
abortAbortion is defined as the termination of pregnancy by the removal or expulsion from the uterus of a fetus or embryo prior to viability. An abortion can occur spontaneously, in which case it is usually called a miscarriage, or it can be purposely induced...
him. Shortly before his birth, his mother had to move from
MilanMilan is the second-largest city in Italy and the capital city of the region of Lombardy and of the province of Milan. The city proper has a population of about 1.3 million, while its urban area, roughly coinciding with its administrative province and the bordering Province of Monza and Brianza ,...
to
PaviaPavia , the ancient Ticinum, is a town and comune of south-western Lombardy, northern Italy, 35 km south of Milan on the lower Ticino river near its confluence with the Po. It is the capital of the province of Pavia. It has a population of c. 71,000...
to escape the
PlagueThe Black Death was one of the most devastating pandemics in human history, peaking in Europe between 1348 and 1350. Of several competing theories, the dominant explanation for the Black Death is the plague theory, which attributes the outbreak to the bacterium Yersinia pestis. Thought to have...
; her three other children died from the disease.
In 1520, he entered the
University of PaviaThe University of Pavia is a university located in Pavia, Lombardy, Italy. It was founded in 1361 and is organized in 9 Faculties.-History:...
and later in
PaduaPadua is a city and comune in the Veneto, northern Italy. It is the capital of the province of Padua and the economic and communications hub of the area. Padua's population is 212,500 . The city is sometimes included, with Venice and Treviso, in the Padua-Treviso-Venice Metropolitan Area, having...
studied medicine. His eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after his studies ended. In 1525, Cardano repeatedly applied to the College of Physicians in Milan, but was not admitted owing to his combative reputation and illegitimate birth.
Eventually, he managed to develop a considerable reputation as a physician and his services were highly valued at the courts. He was the first to describe
typhoid feverTyphoid fever, also known as Typhoid, is a common worldwide bacterial disease, transmitted by the ingestion of food or water contaminated with the feces of an infected person, which contain the bacterium Salmonella enterica, serovar Typhi...
.
Mathematics
Today, he is best known for his achievements in
algebraAlgebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
. He published the solutions to the cubic and quartic equations in his 1545 book
Ars MagnaThe Ars Magna is an important book on Algebra written by Gerolamo Cardano. It was first published in 1545 under the title Artis Magnæ, Sive de Regulis Algebraicis Liber Unus . There was a second edition in Cardano's lifetime, published in 1570...
. The solution to one particular case of the cubic equation 0= ax^3+bx^2+c (in modern notation), was communicated to him by
Niccolò Fontana TartagliaNiccolò Fontana Tartaglia was a mathematician, an engineer , a surveyor and a bookkeeper from the then-Republic of Venice...
(who later claimed that Cardano had sworn not to reveal it, and engaged Cardano in a decade-long fight), and the quartic was solved by Cardano's student
Lodovico FerrariLodovico Ferrari was an Italian mathematician.Born in Milan, Italy, grandfather, Bartholomew Ferrari was forced out of Milan to Bologna. He settled in Bologna, Italy and he began his career as the servant of Gerolamo Cardano. He was extremely bright, so Cardano started teaching him mathematics...
. Both were acknowledged in the foreword of the book, as well as in several places within its body. In his exposition, he acknowledged the existence of what are now called
imaginary numberAn imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...
s, although he did not understand their properties (described for the first time by his Italian contemporary
Rafael BombelliRafael Bombelli was an Italian mathematician.Born in Bologna, he is the author of a treatise on algebra and is a central figure in the understanding of imaginary numbers....
, although mathematical field theory was developed centuries later). In
Opus novum de proportionibus he introduced the
binomial coefficientIn mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written \tbinom nk , and it is the coefficient of the x k term in...
s and the
binomial theoremIn elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with , and the coefficient a of...
.
Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and
chessChess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
player. His book about games of chance,
Liber de ludo aleae ("Book on Games of Chance"), written in 1526, but not published until 1663, contains the first systematic treatment of
probabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
, as well as a section on effective cheating methods. Cardano invented several mechanical devices including the
combination lockA combination lock is a type of lock in which a sequence of numbers or symbols is used to open the lock. The sequence may be entered using a single rotating dial which interacts with several discs or cams, by using a set of several rotating discs with inscribed numerals which directly interact with...
, the
gimbalA gimbal is a pivoted support that allows the rotation of an object about a single axis. A set of two gimbals, one mounted on the other with pivot axes orthogonal, may be used to allow an object mounted on the innermost gimbal to remain immobile regardless of the motion of its support...
consisting of three concentric rings allowing a supported
compassA compass is a navigational instrument that shows directions in a frame of reference that is stationary relative to the surface of the earth. The frame of reference defines the four cardinal directions – north, south, east, and west. Intermediate directions are also defined...
or
gyroscopeA gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation...
to rotate freely, and the
Cardan shaftA drive shaft, driveshaft, driving shaft, propeller shaft, or Cardan shaft is a mechanical component for transmitting torque and rotation, usually used to connect other components of a drive train that cannot be connected directly because of distance or the need to allow for relative movement...
with
universal jointA universal joint, universal coupling, U joint, Cardan joint, Hardy-Spicer joint, or Hooke's joint is a joint or coupling in a rigid rod that allows the rod to 'bend' in any direction, and is commonly used in shafts that transmit rotary motion...
s, which allows the transmission of rotary motion at various angles and is used in vehicles to this day. He studied
hypocycloidIn geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle...
s, published in
de proportionibus 1570. The generating circles of these hypocycloids were later named Cardano circles or cardanic circles and were used for the construction of the first high-speed printing presses.
He made several contributions to hydrodynamics and held that
perpetual motionPerpetual motion describes hypothetical machines that operate or produce useful work indefinitely and, more generally, hypothetical machines that produce more work or energy than they consume, whether they might operate indefinitely or not....
is impossible, except in celestial bodies. He published two
encyclopediaAn encyclopedia is a type of reference work, a compendium holding a summary of information from either all branches of knowledge or a particular branch of knowledge....
s of natural science which contain a wide variety of inventions, facts, and occult superstitions. He also introduced the
Cardan grille-History:In 1550, Girolamo Cardano , known in French as Jérôme Cardan, proposed a simple grid for writing hidden messages. He intended to cloak his messages inside an ordinary letter so that the whole would not appear to be a cipher at all....
, a cryptographic tool, in 1550.
Someone also assumed to Cardano the credit for the invention of the so called
Cardano's Rings, also called
Chinese Ringsright|thumb|200pxBaguenaudier is a mechanical puzzle featuring a double loop of string which must be disentangled from a sequence of rings on interlinked pillars. The puzzle is thought to have been invented originally in China...
, but it is very probable that they are more ancient than Cardano.
Significantly, in the history of education of the deaf, he said that deaf people were capable of using their minds, argued for the importance of teaching them, and was one of the first to state that deaf people could learn to read and write without learning how to speak first. He was familiar with a report by Rudolph Agricola about a deaf mute who had learned to write.
Family
Cardano's eldest and favorite son was executed in 1560 after he confessed to having
poisonIn the context of biology, poisons are substances that can cause disturbances to organisms, usually by chemical reaction or other activity on the molecular scale, when a sufficient quantity is absorbed by an organism....
ed his
cuckoldCuckold is a historically derogatory term for a man who has an unfaithful wife. The word, which has been in recorded use since the 13th century, derives from the cuckoo bird, some varieties of which lay their eggs in other birds' nests...
ing wife. His other son was a gambler, who stole money from him. He allegedly cropped the ears of one of his sons. Cardano himself was accused of
heresyChristian heresy refers to non-orthodox practices and beliefs that were deemed to be heretical by one or more of the Christian churches. In Western Christianity, the term "heresy" most commonly refers to those beliefs which were declared to be anathema by the Catholic Church prior to the schism of...
in 1570 because he had computed and published the
horoscopeIn astrology, a horoscope is a chart or diagram representing the positions of the Sun, Moon, planets, the astrological aspects, and sensitive angles at the time of an event, such as the moment of a person's birth. The word horoscope is derived from Greek words meaning "a look at the hours" In...
of
JesusJesus of Nazareth , commonly referred to as Jesus Christ or simply as Jesus or Christ, is the central figure of Christianity...
in 1554. Apparently, his own son contributed to the prosecution, bribed by
TartagliaNiccolò Fontana Tartaglia was a mathematician, an engineer , a surveyor and a bookkeeper from the then-Republic of Venice...
. He was arrested, had to spend several months in prison and was forced to abjure his
professorA professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
ship. He moved to Rome, received a lifetime annuity from
Pope Gregory XIIIPope Gregory XIII , born Ugo Boncompagni, was Pope from 1572 to 1585. He is best known for commissioning and being the namesake for the Gregorian calendar, which remains the internationally-accepted civil calendar to this date.-Youth:He was born the son of Cristoforo Boncompagni and wife Angela...
(after first having been rejected by
Pope Pius VPope Saint Pius V , born Antonio Ghislieri , was Pope from 1566 to 1572 and is a saint of the Catholic Church. He is chiefly notable for his role in the Council of Trent, the Counter-Reformation, and the standardization of the Roman liturgy within the Latin Church...
) and finished his
autobiographyAn autobiography is a book about the life of a person, written by that person.-Origin of the term:...
.
Miscellaneous
Richard Hinckley Allen tells of an amusing reference made by Boteler in his book
HudibrasHudibras is an English mock heroic narrative poem from the 17th century written by Samuel Butler.-Purpose:The work is a satirical polemic upon Roundheads, Puritans, Presbyterians and many of the other factions involved in the English Civil War...
:
Cardan believ'd great states depend
Upon the tip o'th' Bear's tail's end;
That, as she wisk'd it t'wards the Sun,
Strew'd mighty empires up and down;
Which others say must needs be false,
Because your true bears have no tails.
Alessandro ManzoniAlessandro Francesco Tommaso Manzoni was an Italian poet and novelist.He is famous for the novel The Betrothed , generally ranked among the masterpieces of world literature...
's novel
I Promessi Sposi portrays a pedantic scholar of the obsolete, Don Ferrante, as a great admirer of Cardano. Significantly, he values him only for his superstitious and astrological writings; his scientific writings are dismissed because they contradict
AristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
, but excused on the ground that the author of the astrological works deserves to be listened to even when he is wrong.
Works
- De malo recentiorum medicorum usu libellus, Venice, 1536 (on medicine).
- Practica arithmetice et mensurandi singularis, Milan, 1539 (on mathematics).
- Artis magnae, sive de regulis algebraicis
The Ars Magna is an important book on Algebra written by Gerolamo Cardano. It was first published in 1545 under the title Artis Magnæ, Sive de Regulis Algebraicis Liber Unus . There was a second edition in Cardano's lifetime, published in 1570...
(also known as Ars magna), Nuremberg, 1545 (on algebra).
- De immortalitate (on alchemy).
- Opus novum de proportionibus (on mechanics) (Archimedes Project).
- Contradicentium medicorum (on medicine).
- De subtilitate rerum, Nuremberg, Johann Petreius, 1550 (on natural phenomena).
- De libris propriis, Leiden, 1557 (commentaries).
- De varietate rerum, Basle, Heinrich Petri, 1559 (on natural phenomena).
- De Methodo medendi, 1565
- Opus novum de proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum. Item de aliza regula, Basel, 1570.
- De vita propria, 1576 (autobiography
An autobiography is a book about the life of a person, written by that person.-Origin of the term:...
).
- Liber de ludo aleae, ("On Casting the Die
A die is a small throwable object with multiple resting positions, used for generating random numbers...
") posthumous (on probability).
- De Musica, ca 1546 (on music theory), posthumously published in Hieronymi Cardani Mediolensis opera omnia, Sponius, Lyons, 1663
- De Consolatione, Venice, 1542
External links