Vittorino da Feltre - Département d`Informatique de l`ENS

MCCCXXIV
(1324)
Θεσσαλονίκη
birth of Demetrios Kydones
Demetrios Kydones (Δημήτριος Κυδώνης, 1324‐1397 in Crete) was
a Byzantine theologian, translator, writer and influential
statesman who served an unprecedented three terms as
Imperial Prime Minister or Chancellor of the Byzantine Empire
under three successive emperors: John VI Kantakouzenos, John
V Palaiologos and Manuel II Palaiologos.
As Imperial Premier, Kydones' effort during his second and third
stints was to bring about a reconciliation of the Byzantine and
Roman Churches, to cement a military alliance against the ever‐
encroaching Islam, a program that culminated in Emperor John
V Palaiologos' reconciliation with Catholicism.
Manuel Chrysoloras Manuel Chrysoloras (1355 –1415) was a pioneer in the introduction
of Greek literature to Western Europe during the late middle
ages.
He was born in Constantinople to a distinguished family. Kydones
was Crysolaras’ teacher. In 1390, he led an embassy sent to
Venice by the emperor Manuel II Palaeologus to implore the aid
of the Christian princes against the Muslim Turks. In 1396, the
University of Florence, invited him to come and teach Greek
grammar and literature, quoting Cicero:
– "The verdict of our own Cicero confirms that we Romans either made
wiser innovations than theirs by ourselves or improved on what we took
from them, but of course, as he himself says elsewhere with reference to
his own day: "Italy is invincible in war, Greece in culture." For our part, and
we mean no offence, we firmly believe that both Greeks and Latins have
always taken learning to a higher level by extending it to each other's
literature."
Manuel Chrysoloras Chrysoloras translated the works of Homer and Plato's Republic
into Latin. His his Erotemata Civas Questiones which was the
first basic Greek grammar in use in Western Europe, first
published in 1484 and widely reprinted, and which enjoyed
considerable success not only among his pupils in Florence, but
also among later leading humanists, being immediately studied
by Thomas Linacre at Oxford and by Desiderius Erasmus at
Cambridge; and Epistolæ tres de comparatione veteris et novæ
Romæ (Three Letters Comparing Ancient and Modern Rome).
Many of his treatises on morals and ethics and other philosophical
subjects came into print in the 17th and 18th centuries, because
of their antiquarian interest.
Manuel Chrysoloras Chrysoloras arrived to Florence in 1397. By the time there were
many teachers of law, but no one had studied Greek in Italy for
700 years. Chrysoloras remained only a few years in Florence,
from 1397 to 1400, teaching Greek, starting with the rudiments.
He moved on to teach in Bologna and later in Venice and Rome.
Among his pupils were numbered some of the foremost figures
of the revival of Greek studies in Renaissance Italy. These
alumni included Guarino da Verona.
When Chrysoloras died in 1413, his death gave rise to
commemorative essays of which Guarino da Verona made a
collection in Chrysolorina.
Guarino da Verona
Guarino da Verona (1370‐1460) was an early figure in the
Italian Renaissance.
He was born in Verona and later studied Greek at
Constantinople, during five years under Chrysoloras. When
he set out to return home, he had with him two cases of
precious Greek manuscripts which he had taken great pains
to collect.
It is said that the loss of one of these by shipwreck caused him
such distress that his hair turned grey in a single night. On
arriving back in Italy, he earned a living as a teacher of
Greek, in Verona, Venice and Florence. In 1436, he became a
professor of Greek at Ferrara through the patronage of
Lionel, the marquis of Este. His method of instruction was
renowned and attracted many students from Italy and the
rest of Europe. Many of them, notably Vittorino da Feltre,
afterwards became well‐known scholars.
Guarino da Verona
From 1438 on he interpreted for the Greeks at the councils of
Ferrara and Florence.
His principal works are translations of Strabo and of some of
the Lives of Plutarch, a compendium of the Greek grammar
of Chrysoloras, and a series of commentaries on Persius,
Martial, the Satires of Juvenal, and on some of the writings
of Aristotle and Cicero.
Vittorino da Feltre
Vittorino da Feltre (1378‐1446) was an Italian humanist and
teacher, born in Feltre. His real name was Vittorino
Ramboldini.
He studied at Padua and later taught there, but after a few
years he was invited by the marquis of Mantua to educate
his children. At Mantua, Vittorino set up a school at which
he taught the marquis's children and the children of other
prominent families, together with many poor children,
treating them all on an equal footing.
He not only taught the humanistic subjects, but placed special
emphasis on religious and physical education.
Vittorino da Feltre
He was one of the first modern educators to develop during
the Renaissance. Many of his methods were novel,
particularly in the close contacts between teacher and pupil
as he had with Gasparino da Barzizza and in the adaptation
of the teaching to the ability and needs of the child.
He lived with students and befriended them in the first secular
boarding school. Vittorino's school was well lit and built of
better construction than other schools of the time.
Vittorino also made school work more interesting, adding field
trips to his curricula.
He watched the health of his students very carefully, and
generally elevated the status of teachers. Schools
throughout Europe (especially England) copied Vittorino's
model.
Vittorino da Feltre
Many of fifteenth century Italy's greatest scholars, including
Guarino da Verona, sent their sons to study under Vittorino
da Feltre.
One of Vittorino's most noteworthy students was Theodorus
Gaza.
Theodorus Gaza Theodorus Gaza (1400–1475) was a Greek humanist and
translator of Aristotle, one of the Greek scholars who were
the leaders of the revival of learning in the 15th century (the
Palaeologan Renaissance).
He was born at Thessalonica. On the capture of his native city
by the Turks in 1430 he fled to Italy. During a three years
residence in Mantua he rapidly acquired a competent
knowledge of Latin under the teaching of Vittorino da
Feltre, supporting himself meanwhile by giving lessons in
Greek, and by copying manuscripts of the ancient classics.
In 1447 he became professor of Greek in the newly founded
University of Ferrara, to which students in great numbers
from all parts of Italy were soon attracted by his fame as a
teacher. His students there included Rodolphus Agricola.
Theodorus Gaza He had taken some part in the councils which were held in
Siena (1423), Ferrara (1438), and Florence (1439), with the
object of bringing about a reconciliation between the Greek
and Latin Churches; and in 1450, at the invitation of Pope
Nicholas V, he went to Rome, where he was for some years
employed making Latin translations from Aristotle and
other Greek authors. In Rome, he continued his teaching
activities.
After the death of Nicholas (1455), being unable to make a
living at Rome, Gaza removed to Naples. Shortly afterwards
he was appointed by Cardinal Bessarion to a benefice in
Calabria, where the later years of his life were spent, and
where he died about 1475.
Theodorus Gaza His translations were superior, both in accuracy and style, to
the versions in use before his time. He devoted particular
attention to the translation and exposition of Aristotle's
works on natural science.
His Greek grammar (4 books), written in Greek, first printed at
Venice in 1495, and partially translated by Erasmus in 1521,
was for a long time the leading text‐book. His translations
into Latin were very numerous.
Rodolphus Agricola
Rodolphus Agricola (1443–1485) was a pre‐Erasmian humanist
of the northern Low Countries, famous for his supple Latin
and one of the first north of the Alps to know Greek well.
Agricola was a Hebrew scholar towards the end of his life,
an educator, musician and builder of a church organ, a poet
in Latin as well as the vernacular, a diplomat and a
sportsman of sorts (boxing). He is best known today as the
author of De inventione dialectica, as the father of northern
European humanism and as a zealous anti‐scholastic in the
late fifteenth century.
De inventione dialectica was very influential in creating a
proper place for logic in rhetorical studies, and was of great
significance in the education of early humanists. It is a
highly original, critical, and systematic treatment of all ideas
and concepts related to dialectics.
Rodolphus Agricola
Agricola's De formando studio ‐ his long letter on a private
educational program ‐ was printed as a small booklet and thus
influenced pedagogical insights of the early sixteenth century.
Erasmus greatly admired Agricola, eulogizing him in "Adagia";
Erasmus claimed him as a father/teacher figure and may have
actually met him through his own schoolmaster Alexander
Hegius, one of Agricola's students, at Hegius's school in
Deventer. Erasmus made it his personal mission to ensure that
several of Agricola's major works were printed posthumously.
Agricola's 'De inventione dialectica' has a huge impact on Deaf
community. He felt that a person born deaf can express
himself by putting down his thoughts in writing. The book was
not published until 100 years later. The statement that deaf
people can be taught a language is one of the earliest positive
statements about deafness on records.
Alexander Hegius
Alexander Hegius von Heek (1433–1498) was a German
humanist, so called from his birthplace Heek in Westphalia.
In 1474 he settled down at Deventer in Holland, where he
either founded or succeeded to the headship of a school,
which became famous for the number of its distinguished
alumni. First and foremost of these was Erasmus; another
famous alumnus of Hegius was Pope Adrian VI.
His writings, consisting of short poems, philosophical essays,
grammatical notes and letters, were published after his
death. They display considerable knowledge of Latin, but
less of Greek, on the value of which he strongly insisted.
Alexander Hegius
Hegius's chief claim to be remembered rests not upon his
published works, but upon his services in the cause of
humanism.
He succeeded in abolishing the old‐fashioned medieval
textbooks and methods of instruction, and led his pupils to
the study of the classical authors themselves.
His generosity in assisting poor students exhausted a
considerable fortune, and at his death he left nothing but
his books and clothes.
Erasmus
Desiderius Erasmus Roterodamus (1466–1536,) was a Dutch
Renaissance humanist and a Catholic Christian theologian.
Erasmus was a classical scholar who wrote in a "pure" Latin
style and enjoyed the sobriquet "Prince of the Humanists."
Using humanist techniques for working on texts, he prepared
important new Latin and Greek editions of the New
Testament. These raised questions that would be influential
in the Protestant Reformation and Catholic Counter‐
Reformation. He also wrote The Praise of Folly, Handbook
of a Christian Knight, On Civility in Children, and many other
works.
Erasmus
Erasmus lived through the Reformation period and he
consistently criticized some contemporary popular Christian
beliefs.
In relation to clerical abuses in the Church, Erasmus remained
committed to reforming the Church from within. He also
held to Catholic doctrines such as that of free will, which
some Protestant Reformers rejected in favor of the
doctrine of predestination.
His middle road disappointed and even angered many
Protestants, such as Martin Luther, as well as conservative
Catholics.
Erasmus
One of Erasmus’ best known works is Adagia, a collection of
4658 Greek and Latin adages. Many of which are common
today!
Make haste slowly One step at a time To be in the same boat To lead one by the nose A rare bird Even a child can see it To walk on tiptoe One to one Out of tune A point in time To call a spade a spade Hatched from the same egg Up to both ears (Up to his eyeballs) As though in a mirror Think before you start What's done cannot be undone We cannot all do everything Many hands make light work A living corpse Where there's life, there's hope To cut to the quick Time reveals all things Golden handcuffs Crocodile tears To show the middle finger To walk the tightrope We all live in a yellow submarine, yellow submarine
Cause we are living in a material world and I’m a material girl
To dangle the bait To swallow the hook The bowels of the earth From heaven to earth Erasmus
One of Erasmus’ best known works is Adagia, a collection of
4658 Greek and Latin adages. Many of which are common
today!
Make haste slowly One step at a time To be in the same boat To lead one by the nose A rare bird Even a child can see it To walk on tiptoe One to one Out of tune A point in time To call a spade a spade Hatched from the same egg Up to both ears (Up to his eyeballs) As though in a mirror Think before you start What's done cannot be undone We cannot all do everything Many hands make light work A living corpse Where there's life, there's hope To cut to the quick Time reveals all things Golden handcuffs Crocodile tears To show the middle finger To walk the tightrope We all live in a yellow submarine, yellow submarine
Cause we are living in a material world and I’m a material girl
To dangle the bait To swallow the hook The bowels of the earth From heaven to earth :
:
•The dog is worthy of his dinner •To weigh anchor •To grind one's teeth •Nowhere near the mark •Complete the circle •In the land of the blind, the one‐eyed man is king •No sooner said than done •A necessary evil •There's many a slip 'twixt cup and lip •To squeeze water out of a stone •To leave no stone unturned •Let the cobbler stick to his last (Stick to your knitting) •God helps those who help themselves •The grass is greener over the fence •The cart before the horse •Dog in the manger •One swallow doesn't make a summer •His heart was in his boots •To sleep on it •To break the ice •Ship‐shape •To die of laughing •To have an iron in the fire •To look a gift horse in the mouth •Neither fish nor flesh :
:
Jacob Milich
Jacob Milich (1501–1559) was a disciple of Erasmus, German
physician, mathematician, and astronomer.
He was born in Freiburg im Breisgau, where he received his
education starting in 1513.
He taught at Wittenberg, where he became a professor of
mathematics.
His most important student there was Erasmus Reinhold. He
became Dean of the Wittenberg university's philosophical
and medical branches, then served as Rector of the school
on several occasions.
The crater Milichius on the Moon is named after him.
Erasmus Reinhold
Erasmus Reinhold (1511 –1553) was a German astronomer and
mathematician, considered to be the most influential
astronomical pedagogue of his generation. He was born
and died in Saalfeld, Germany.
He was educated at the University of Wittenberg, where he
became dean and later rector. In 1536 he was appointed
professor of higher mathematics. In contrast to the limited
modern definition, "mathematics" at the time also included
applied mathematics, especially astronomy.
Reinhold catalogued a large number of stars.
Duke Albert of Brandenburg Prussia supported Reinhold and
financed the printing of Reinhold's Prutenicae Tabulae or
Prussian Tables. These astronomical tables helped to
disseminate calculation methods of Copernicus throughout
the Empire.
Erasmus Reinhold
Both Reinholds's Prutenic Tables and Copernicus' studies were
the foundation for the Calendar Reform by Pope Gregory
XIII in 1582.
However, Reinhold (like other astronomers before Kepler and
Galileo) translated Copernicus' mathematical methods back
into a geocentric system, rejecting heliocentric cosmology
on physical and theological grounds.
Reinhold tutored many disciples amongst whom was Valentin
Naboth.
Valentin Naboth
Valentin Naboth was born in Niederlausitz to a Jewish family.
In 1544, Valentin immatriculated at the University of
Wittenberg when Erasmus Reinhold taught there. In 1550
he transferred to the University of Erfurt.
From 1553 Naboth taught mathematics at the University of
Cologne. When he arrived at Cologne he began teaching
mathematics as Privatdozent, since that discipline was not
included in the university curriculum. He made such an
impression that he was offered a University position,
remunerated for his private lessons, and made ordinary
professor. Dutch mathematician Rudolph Snellius was one
of his students in Cologne.
Valentin Naboth
Naboth was the author of a general textbook on astrology
Enarratio elementorum astrologiae. Renowned for
calculating the mean annual motion of the Sun, his writings
are chiefly devoted to commenting upon Ptolemy and the
Arabian astrologers. Naboth teaches the calculation of the
movement of the planets according to the Prutenic Tables
of Erasmus Reinhold.
He advocated a measure of time, by which 0°59'09" (the mean
daily motion of the Sun in longitude) is equated to 1 year of
life in calculating primary directions. This was a refinement
of Ptolemy’s value of exactly 1 degree per year. This book
was banned by the Roman Catholic Church.
Ducunt volentem fata, nolentem trahunt!
In March 1564 Naboth resigned from his position at the University
of Cologne. He traveled to Italy, eventually settling in Padua.
There Naboth came to a bad end. He was living in Padua, Italy,
when he deduced from his own horoscope that he was about to
enter a period of personal danger, so he stockpiled an adequate
supply of food and drink, closed his blinds, and locked his doors
and windows, intending to stay in hiding until the period of
danger had passed.
Unfortunately, some thieves, seeing the house closed and the
blinds drawn, decided that the resident was absent. They
therefore broke into what they thought was an empty house,
and, finding Naboth there, murdered him to conceal their
identities. Thus he did not escape the fate predicted… by his
own astrological calculations.
Rudolph Snel van Royen
Rudolph Snel (latinized as Snellius, 1546‐1613) was a Dutch
linguist and mathematician.
Born to a wealthy family, Rudolf Snel grew up in Utrecht. At
maturity he left to study at the University of Cologne
(under Valentin Naboth) and the University of Heidelberg.
He soon received a teaching position at the University of
Marburg.
In 1578, he was offered, and accepted, a position as professor
of Hebrew and mathematics at the University of Leiden,
where he taught until his death in 1613.
Snel was an influence on some of the leading political and
intellectual forces of the Dutch Golden Age. Finally, not the
least of Snel’s influence was cast upon his son, Willebrord
Snellius, who would become the distinguished astronomer
and mathematician.
Willebrord Snellius
Willebrord Snellius (1580–1626, Leiden) was a Dutch
astronomer and mathematician. His name is attached to the
law of refraction of light (it is now known that this law was
discovered by Ibn Sahl in 984).
In 1613 he succeeded his father as professor of mathematics at
the University of Leiden. In 1615 he planned a new method
of finding the radius of the earth, by determining the
distance of one point on its surface from the parallel of
latitude of another, by means of triangulation. This work
describes the method and gives as the result of his
operations between Alkmaar and Bergen op Zoom which
he measured to be equal to 107.395 km. The actual distance
is approximately 111 km. Snellius also produced a new
method for calculating π, the first such improvement since
ancient times. He rediscovered the law of refraction in 1621.
The lunar crater Snellius is named after Willebrord Snellius.
Snell’s law
Snell’s Crater
Jacob van Gool
Jacob Golius (1596‐1667), was a Dutch Orientalist and mathematician.
Golius came to the University of Leiden in 1612 to study mathematics
(under Snel Jr.). In 1618 he registered again to study Arabic and
other Eastern languages. In 1622 he accompanied the Dutch
embassy to Morocco. On his return he got a professorship. In the
following year he set out on a Syrian and Arabian tour from which
he did not return until 1629. The remainder of his life was spent at
Leiden where he held the chair of mathematics as well as that of
Arabic.
His most important work is the Lexicon Arabico‐Latinum (1653) which
was only superseded in 1837. Among his earlier publications may
be mentioned editions of various Arabic texts.
After his death, there was found among his papers a Dictionarium
Persico‐Latinum which was published in 1669. Golius also edited,
translated and annotated the astronomical treatise of Alfragan in
1669.
van Gool’s most famous student is René Descartes
However, we will continue with another, less brilliant, yet famous,
student of Gool: Franciscus van Schooten
Franciscus van Schooten
Franciscus van Schooten (1615–1660) was a Dutch mathematician
known for popularizing the analytic geometry of René Descartes.
Schooten read Descartes' Géométrie (an appendix to his Discours de
la méthode) while it was still unpublished. Finding it hard to
understand, he went to France to study the works of other
important mathematicians of his time, such as François Viète and
Pierre de Fermat. When he returned to his home in Leiden in 1646,
he became a professor having Christiaan Huygens as a student.
Schooten's 1649 Latin translation and commentary of Descartes'
Géométrie made the work comprehensible to the broader
mathematical community, and thus was responsible for the spread
of analytic geometry to the world. Over the next decade he
expanded the commentaries to two volumes, published in 1659
and 1661. This edition and its extensive commentaries was far
more influential than the 1649 edition. It was this edition that
Gottfried Leibniz and Isaac Newton knew.
Franciscus van Schooten
Schooten was one of the first to suggest, in exercises published in
1657, that these ideas be extended to three‐dimensional space.
His efforts made Leiden the centre of the mathematical community
for a short period in the middle of the seventeenth century.
Christiaan Huygens
Christiaan Huygens (1629–1695) was a prominent Dutch
mathematician, astronomer, physicist, horologist, and writer of
early science fiction. His work included early telescopic studies
elucidating the nature of the rings of Saturn and the discovery
of its moon Titan, investigations and inventions related to time
keeping and the pendulum clock, and studies of both optics
and the centrifugal force.
Huygens achieved note for his argument that light consists of
waves, now known as the Huygens–Fresnel principle, which
became instrumental in the understanding of wave‐particle
duality. He generally receives credit for his discovery of the
centrifugal force, the laws for collision of bodies, for his role in
the development of modern calculus and his original
observations on sound perception.
Huygens is seen as the first theoretical physicist as he was the first
to use formulae in physics.
Named After Christiaan Huygens
• The Huygens probe: The lander for the Saturnian moon Titan,
part of the Cassini‐Huygens Mission to Saturn
• Asteroid 2801 Huygens
• A crater on Mars
• Mons Huygens, a mountain on the Moon
• Huygens Software, a microscope image processing package.
• Achromatic two element eyepiece designed by him.
• The Huygens–Fresnel principle, a simple model to understand
disturbances in wave propagation.
• Huygens wavelets, the fundamental mathematical basis for
scalar diffraction theory
Named After Christiaan Huygens
• W.I.S.V. Christiaan Huygens: Dutch study guild for the
studies Mathematics and Computer Science at the Delft
University of Technology
• Huygens Laboratory: Home of the Physics department at
Leiden University, The Netherlands
• Huygens Supercomputer: National Supercomputer facility
of The Netherlands, located at SARA in Amsterdam
• The Huygens‐building in Noordwijk, The Netherlands, first
building on the Space Business park opposite Estec (ESA)
• The Huygens‐building at the Radboud University, Nijmegen,
The Netherlands. One of the major buildings of the science
department at the university of Nijmegen.
• etc…
Huygens: Mechanics
Huygens formulated what is now known as the second law of motion
of Isaac Newton in a quadratic form. Newton reformulated and
generalized that law. In 1659 Huygens derived the now well‐known
formula for the centrifugal force, exerted by an object describing a
circular motion, for instance on the string to which it is attached, in
modern notation:
with m the mass of the object, v the velocity and r the radius.
Furthermore, Huygens concluded that Descartes' laws for the elastic
collision of two bodies must be wrong and formulated the correct
laws.
Huygens: Wave Theory and Optics
Huygens is remembered especially for his wave theory of light,
expounded in his Traité de la lumière (see also Huygens‐Fresnel
principle).
The later theory of light by Isaac Newton in his Opticks proposed a
different explanation for reflection, refraction and interference
of light assuming the existence of light particles.
The interference experiments of Thomas Young vindicated
Huygens' wave theory in 1801, as the results could no longer be
explained with light particles.
Huygens experimented with double refraction in Icelandic crystal
(calcite) and explained it with his wavetheory and polarised
light.
Huygens: Clocks
He also worked on the construction of accurate clocks, suitable for
naval navigation. In 1658 he published a book on this topic called
Horologium. His invention of the pendulum clock, patented in
1657, was a breakthrough in timekeeping.
Huygens discovered that the cycloid was an isochronous curve
and, applied to pendulum clocks in the form of cycloidal cheeks
guiding a flexible pendulum suspension, would ensure a regular
(i.e isochronous) swing of the pendulum irrespective of its
amplitude, i.e. irrespective of how it moved side to side. The
mathematical and practical details of this finding were published
in "Horologium Oscillatorium" of 1673.
Huygens: Clocks
Huygens was the first to derive the formula for the period of the
mathematical pendulum (with massless rod or cable), in modern
notation:
with T the period, l the length of the pendulum and g the
gravitational acceleration.
In 1675, Christiaan Huygens patented a pocket watch.
Huygens: Astronomy
In 1655, Huygens proposed that Saturn was surrounded by a solid
ring, "a thin, flat ring, nowhere touching, and inclined to the
ecliptic." Using a 50 power refracting telescope that he designed
himself, Huygens also discovered the first of Saturn's moons,
Titan. In the same year he observed and sketched the Orion
Nebula. His drawing, the first such known of the Orion nebula,
was published in Systema Saturnium in 1659. Using his modern
telescope he succeeded in subdividing the nebula into different
stars. He also discovered several interstellar nebulae and some
double stars.
In 1661, he observed planet Mercury transit over the Sun.
Gottfried Wilhelm Leibniz It is impossible to present Leibniz’ (1646‐1716) contribution to
humanity without devoting to it at least an entire workshop.
He is remembered for work in infinitesimal calculus, calculus, a new
formula for π, Leibniz’ harmonic triangle, Leibniz formula for
determinants, Leibniz integral rule, Leibniz differential, Notation
for differentiation, Differential calculus, Proof of Fermat's little
theorem and Kinetic energy.
Other contributions, in the fields of humanity or philosophy, are
less known to the mathematical community. These nonetheless
include: Monadology, Theodicy, Optimism, Principle of sufficient
reason, Diagrammatic reasoning,
Principle of Sufficient Reason • For every entity x, if x exists, then there is a sufficient explanation why x exists. • For every event e, if e occurs, then there is a sufficient explanation why e occurs. • For every proposition p, if p is true, then there is a sufficient explanation why p is true. Diagrammatic reasoning
Reasoning can be symbolized as icons visually related using lines
to represent relations and combinations of basic components
(the ancestor of today’s flowchart).
Theodicity (θεός + δίκη)
Why evil happens?
Leibniz thought that the evil in the world does not conflict with the
goodness of God, and that notwithstanding its many evils, the
world we know is the best of all possible worlds.
Leibniz wrote his Théodicée as a criticism of Pierre Bayle's
Dictionnaire Historique et Critique, that argued that the sufferings
experienced in this earthly life prove that God could not be good
and omnipotent
Gottfried Wilhelm Leibniz Jacob Bernoulli Jacob Bernouilli (1654‐1705) was a disciple of Leibniz.
He studied theology and entered the ministry. But contrary to the
desires of his parents, he also studied mathematics and
astronomy.
He traveled throughout Europe from 1676 to 1682, learning about
the latest discoveries in mathematics and the sciences.
He published papers on transcendental curves (1696) and
isoperimetry (1700, 1701). In 1690, Jacob became the first
person to develop the technique for solving separable
differential equations.
Jacob Bernoulli Upon returning to Basel in 1682, he founded a school for
mathematics and the sciences. He was appointed professor of
mathematics at the University of Basel in 1687, remaining in
this position for the rest of his life.
He is the author as the law of large numbers. The terms Bernoulli
trial and Bernoulli numbers result from this work. The lunar
crater Bernoulli is also named after him jointly with his brother
Johann.
Bernoulli chose a figure of a logarithmic spiral and the motto
Eadem mutata resurgo for his gravestone; the spiral executed
by the stonemasons was, however, an Archimedean spiral.
Jacob had five daughters and three sons.
Jacob Bernoulli Johann Bernoulli Johann (1667–1748) was the brother of Jacob.
Johann began studying medicine but did not enjoy it and began
studying mathematics on the side with Jacob. The Bernoulli
brothers worked together spending much of their time
studying the newly discovered calculus.
After graduating from Basel University Johann Bernoulli moved to
teach differential equations and in 1694, became a professor of
mathematics at the University of Groningen. As a student of
Leibniz’s calculus, Johann Bernoulli sided with him in 1713 in the
Newton–Leibniz debate over who deserved credit for the
discovery of calculus. Johann Bernoulli defended Leibniz by
showing that he had solved certain problems with his methods
that Newton had failed to solve.
Johann Bernoulli In 1691 Johann solved the problem of the catenary presented by
Jakob.
In 1696 Johann proposed the problem of the brachistochrone,
despite already having solved the problem himself. Within two
years he received five answers, one of which was from his
older brother, Jakob.
Johann Bernoulli Johann Bernoulli Johann was hired by Guillaume François Antoine de L'Hôpital to
tutor him in mathematics. Bernoulli and L'Hôpital signed a
contract which gave L'Hôpital the right to use Bernoulli’s
discoveries as he pleased. L'Hôpital authored the first textbook
on calculus, which mainly consisted of the work of Bernoulli,
including what is now known as L'Hôpital's rule.
Johann educated the great mathematician Leonhard Euler in his
youth
Leonhard Paul Euler Leonhard Paul Euler (1707–1783) was a pioneering Swiss
mathematician and physicist who spent most of his life in
Russia and Germany.
Euler made important discoveries in fields as diverse as calculus
and graph theory. He also introduced much of the modern
mathematical terminology and notation, particularly for
mathematical analysis, such as the notion of a mathematical
function. He is also renowned for his work in mechanics, fluid
dynamics, optics, and astronomy.
Euler is considered to be the preeminent mathematician of the
18th century and one of the greatest of all times. He is also one
of the most prolific; his collected works fill 60–80 quarto
volumes.
The city of Kaliningrad (Russia) was set on both sides of the
Pregel River, and included two large islands which were
connected to each other and the mainland by seven bridges.
The problem was to find a walk through the city that would cross
each bridge once and only once. The islands could not be
reached by any route other than the bridges, and every bridge
must have been crossed completely every time (one could not
walk halfway onto the bridge and then turn around to come at it
from another side).
V − E + F = 2 relates the number of vertices, edges, and faces of
a convex polyhedron
The asteroid 2002 Euler was named in his honor. He is also
commemorated by the Lutheran Church on their Calendar of Saints
on 24 May ‐ he was a devout Christian (and believer in biblical
inerrancy) who wrote apologetics and argued forcefully against the
prominent atheists of his time.
Joseph Lagrange
Joseph‐Louis Lagrange, born Giuseppe Lodovico Lagrangia (1736–
1813) was an Italian‐born mathematician and astronomer, who
lived most of his life in Prussia and France, making significant
contributions to all fields of analysis, to number theory, and to
classical and celestial mechanics. On the recommendation of
Euler and D'Alembert, in 1766 Lagrange succeeded Euler as the
director of mathematics at the Prussian Academy of Sciences in
Berlin, where he stayed for over twenty years, producing a
large body of work and winning several prizes of the French
Academy of Sciences.
Lagrange's treatise on analytical mechanics (Mécanique
Analytique, 1888), written in Berlin and first published in 1788,
offered the most comprehensive treatment of classical
mechanics since Newton and formed a basis for the
development of mathematical physics in the nineteenth
century.
French or Italian?
Born Giuseppe Lodovico Lagrangia in Turin of Italian parents,
Lagrange had French ancestors on his father's side. In 1787 he
became a member of the French Academy, and he remained in
France until the end of his life. Therefore, Lagrange is
alternatively considered a French and an Italian scientist.
Lagrange survived the French Revolution and became the first
professor of analysis at the École Polytechnique upon its
opening in 1794. Napoleon named Lagrange to the Legion of
Honour and made him a Count of the Empire in 1808. He is
buried in the Panthéon.
Some of Lagrange’s Results
Lagrange (1766–1769) was the first to prove that Pell's equation x2
− ny2 = 1 has a nontrivial solution in the integers for any non‐
square natural number n.
He proved the theorem, stated by Bachet without justification,
that every positive integer is the sum of four squares, 1770.
He proved Wilson's theorem that if n is a prime, then (n − 1)! + 1 is
always a multiple of n, 1771.
His papers of 1773, 1775, and 1777 gave demonstrations of several
results enunciated by Fermat, and not previously proved.
His Recherches d'Arithmétique of 1775 developed a general theory
of binary quadratic forms to handle the general problem of
when an integer is representable by the form ax2 + by2 + cxy.
Joseph Lagrange
Siméon Poisson
Siméon Poisson entered the École Polytechnique in 1798. In 1800,
less than two years after his entry, he published two memoirs,
one on Étienne Bézout's method of elimination, the other on
the number of integrals of a finite difference equation.
The latter was examined by Legendre, who recommended that it
should be published in the Recueil des savants étrangers, an
unprecedented honor for a youth of eighteen. This success at
once procured entry for Poisson into scientific circles.
Lagrange, who lectured at the École Polytechnique, recognized
Poisson’s talent, and also became his friend. Laplace, in whose
footsteps Poisson followed, regarded him almost as his son.
Poisson was made deputy professor in 1802, and, in 1806 full
professor succeeding Fourier. In 1808 he became astronomer
to the Bureau des Longitudes; and professor of rational
mechanics in 1809.
Siméon Poisson
He became a member of the Institute in 1812, examiner at the
military school of Saint‐Cyr in 1815, graduation examiner at the
École Polytechnique in 1816, councillor of the university in 1820,
and geometer to the Bureau des Longitudes succeeding Laplace
in 1827.
His father, whose early experiences had led him to hate aristocrats,
bred him in the creed of the First Republic. Throughout the
Revolution, the Empire, and the following restoration, Poisson
was not interested in politics, concentrating on mathematics.
He was appointed to the dignity of baron in 1821; but he neither
took out the diploma or used the title.
Siméon Poisson
The revolution of July 1830 threatened him with the loss of all
his honors; but this disgrace to the government of Louis‐
Philippe was adroitly averted by François Arago, who, while
his "revocation" was being plotted by the council of
ministers, procured him an invitation to dine at the Palais
Royal, where he was openly and effusively received by the
citizen king, who "remembered" him. After this, of course,
his degradation was impossible, and seven years later he was
made a peer of France, not for political reasons, but as a
representative of French science.
Notwithstanding his many official duties, he found time to
publish more than three hundred works, several of them
extensive treatises.
Siméon Poisson’s Works
Memoirs on the theory of electricity and magnetism, which
virtually created a new branch of mathematical physics.
Next in importance stand the memoirs on celestial mechanics.
The most important of these are his memoirs Sur les
inégalités séculaires des moyens mouvements des planètes,
Sur la variation des constantes arbitraires dans les questions
de mécanique, (1809); Sur la libration de la lune, (1821), and
Sur le mouvement de la terre autour de son centre de gravité
(1827).
Poisson Distribution
In probability the Poisson distribution is a discrete probability
distribution that expresses the probability of a number of
events occurring in a fixed period of time if these events occur
with a known average rate and independently of the time since
the last event. The Poisson distribution can also be used for
the number of events in other specified intervals such as
distance, area or volume.
The distribution was discovered by Poisson and published,
together with his probability theory, in 1838 in his work
Recherches sur la probabilité des jugements en matières
criminelles et matière civile. The work focused on certain
random variables N that count, among other things, the
number of discrete occurrences (sometimes called "arrivals")
that take place during a time‐interval of given length.
Poisson Distribution
If the expected number of occurrences in this interval is λ,
then the probability that there are exactly k occurrences is
equal to
λ is a positive real number, equal to the expected number of
occurrences that occur during the given interval. For
instance, if the events occur on average 4 times per minute,
and you are interested in the number of events occurring in
a 10 minute interval, you would use as your model a Poisson
distribution with λ = 10×4 = 40.
As a function of k, this is the probability mass function. The
Poisson distribution can be derived as a limiting case of the
binomial distribution.
The Poisson distribution can be applied to systems with a
large number of possible events, each of which is rare. A
classic example is the nuclear decay of atoms.
Siméon Poisson
Michel Chasles Michel Floréal Chasles (1793–1880) studied at the École
Polytechnique under Poisson. In the War of the Sixth Coalition
he was drafted to fight in the defence of Paris in 1814. After the
war, he gave up on a career as an engineer or stockbroker in
order to pursue his mathematical studies.
In 1837 he published his Historical view of the origin and
development of methods in geometry, a study of the method of
reciprocal polars in projective geometry. The work gained him
considerable fame and respect and he was appointed Professor
at the École Polytechnique in 1841, then he was awarded a chair
at the Sorbonne in 1846.
Jakob Steiner had proposed the problem of enumerating the
number of conic sections tangent to each of five given conics,
and had answered it incorrectly. Chasles developed a theory of
characteristics that enabled the correct enumeration of the
conics (there are 3264).
Michel Chasles He established several important theorems (all called Chasles'
theorem). That on solid body kinematics was seminal for
understanding their motions, and hence to the development of
the theories of dynamics of rigid bodies.
In 1865 he was awarded the Copley Medal.
As described in A Treasury of Deception, by Michael Farquhar,
between 1861 and 1869 Chasles purchased over 27,000 forged
letters from Frenchman Vrain‐Denis Lucas. Included in this trove
— all apparently written in modern French — were letters from
Alexander the Great to Aristotle, from Cleopatra to Julius Caesar
(written in French!), and from Mary Magdalene to a revived
Lazarus.
Chasles' name is one of 72 that appears on the Eiffel Tower.
The Gullible Chasles « Ce grand mathématicien collectionnait les documents anciens et fut
une victime un peu naïve et complaisante d’un faussaire qui lui vendit
des fausses lettres de Pascal prouvant soi‐disant que Pascal avait
découvert la gravitation universelle avant Newton. L’histoire de cette
fraude scientifique a fait l’objet d’un téléfilm très réussi en 1998, avec
Michel Piccoli.
A partir de juillet 1867, le mathématicien présenta à l'Académie des
sciences une série de lettres inédites prétendument de Pascal, que le
faussaire Vrain‐Lucas venait de fabriquer. Elles voulaient établir
qu'avant Newton, l'auteur des Pensées avait découvert le principe de
l'attraction universelle. Un savant anglais fit observer qu'on y
trouvait des mesures astronomiques bien postérieures à la mort de
Pascal. Approvisionné une nouvelle fois par Vrain‐Lucas, Chasles
montra alors des lettres où Galilée communiquait à Pascal les
résultats de ses observations…
The Gullible Chasles … Le savant anglais remarqua cette fois que dans une lettre de 1641,
Galilée se plaignait de sa mauvaise vue, alors qu'il était
complètement aveugle depuis près de quatre ans. Surgit alors une
nouvelle lettre, postérieure à la précédente et datée de décembre
1641, dans laquelle un autre savant italien apprenait à Pascal que
Galilée, dont la vue n'avait cessé de baisser, avait fini par la perdre
entièrement.
Ses collègues de l'Institut prirent la chose avec bonne humeur, mais à
l'étranger — à Londres en particulier — on fit des gorges chaudes
du manque d'esprit critique des scientifiques français. Quant à
Chasles, il se montra désespéré de s'être fait ainsi mystifier.
D'autant que, comme on l'apprit plus tard, il avait acheté à Vrain‐
Lucas d'autres lettres, d'Alexandre le Grand à Aristote, de Jules
César à Vercingétorix, de César à Cléopâtre, toutes rédigées dans un
faux vieux français. Chasles légua à sa mort sa collection à l'Institut,
y compris les faux fabriqués par Vrain‐Lucas. »
Michel Chasles Michel Chasles AB + BC = AC
Jean‐Gaston Darboux
Jean‐Gaston Darboux (1842‐1917) was a French mathematician
who made important contributions to geometry and
mathematical analysis. He was a biographer of Henri Poincaré
and edited the Selected Works of Joseph Fourier.
Darboux received his Ph.D. from ENS in 1866. His thesis, written
under the direction of Chasles, was titled Sur les surfaces
orthogonales. In 1884, Darboux was elected to the Académie
des Sciences. In 1900, he was appointed the Academy's
permanent secretary of its Mathematics section.
Among his students were Charles‐Emile Picard, Emile Borel and
Élie Cartan.
In 1902, he was elected to the Royal Society; in 1916, he received
the Sylvester Medal from the Society.
Jean‐Gaston Darboux
Many mathematical objects are named after Darboux:
Darboux’s equation, frame, integral, function, net invariants,
formula, vector, problem, cubic, transformation, theorem in
symplectic geometry, theorem in real analysis (related to
Intermediate value theorem),
or after Darboux and others:
Christoffel‐Darboux identity,
Christoffel‐Darboux formula,
Euler‐Darboux equation,
Euler‐Poisson‐Darboux equation,
Darboux‐Goursat problem etc
Jean‐Gaston Darboux
Charles‐Emile Picard
Charles Émile Picard (1856‐1941) was a French mathematician. He was
elected the fifteenth member to occupy seat 1 of the Académie
Française in 1924.
Picard's mathematical papers, textbooks, and many popular writings
exhibit an extraordinary range of interests, as well as an impressive
mastery of the mathematics of his time. Modern students of
complex variables are probably familiar with two of his named
theorems. His lesser theorem states that every nonconstant entire
function takes every value in the complex plane, with perhaps one
exception. His greater theorem states that an analytic function
with an essential singularity takes every value infinitely often, with
perhaps one exception, in any neighborhood of the singularity.
Charles‐Emile Picard
Picard also made important contributions in the theory of differential
equations, including work on Painlevé transcendents and his
introduction of a kind of symmetry group for a linear differential
equation, the Picard group. In connection with his work on
function theory, he was one of the first mathematicians to use the
emerging ideas of algebraic topology. In addition to his path‐
breaking theoretical work, Picard made important contributions to
applied mathematics, including the theories of telegraphy and
elasticity. His collected papers run to four volumes.
Like his contemporary, Henri Poincaré, Picard was much concerned
with the training of mathematics, physics, and engineering
students. He wrote a classic textbook on analysis, one of the first
textbooks on the theory of relativity. Picard's popular writings
include biographies of many leading French mathematicians,
including his father in law, Charles Hermite.
Charles‐Emile Picard
Jacques Salomon Hadamard
Jacques Salomon Hadamard (1865–1963) was a made major
contributions in number theory, complex function theory,
differential geometry and partial differential equations.
The son of a teacher, Amédée Hadamard, of Jewish descent, and
Claire Marie Jeanne Picard, Hadamard attended the Lycée
Charlemagne and Lycée Louis‐le‐Grand, where his father
taught.
In 1884 Hadamard entered the ENS, having been placed first in the
entrance examinations both there and at the École
Polytechnique. His teachers included Hermite, Darboux and
Picard. He obtained his doctorate in 1892 and in the same year
was awarded the Grand Prix des Sciences Mathématiques for his
prize essay on the Riemann zeta function.
Jacques Salomon Hadamard
In 1892 Hadamard got married (he had 5 children). The following
year he took up a lectureship in the University of Bordeaux,
where he proved his celebrated inequality on determinants,
which led to the discovery of Hadamard matrices when equality
holds. In 1896 he made two important contributions: he proved
the prime number theorem, using complex function theory and
he was awarded the Bordin Prize of the French Academy of
Sciences for his work on geodesics in the differential geometry
of surfaces and dynamical systems. In the same year he was
appointed Professor of Astronomy and Rational Mechanics in
Bordeaux. For his cumulative work, he was awarded the Prix
Poncelet in 1898.
After the Dreyfus affair, which involved him personally because
his wife was related to Dreyfus, Hadamard became politically
active and a supporter of Jewish causes though he professed to
be an atheist in his religion.
Jacques Salomon Hadamard
In 1897 he moved to Paris, holding positions at Sorbonne and Collège
de France (appointed Professor of Mechanics in 1909). In addition,
he was appointed to chairs of analysis at the École Polytechnique
in 1912 and at the École Centrale in 1920, succeeding Jordan. In
Paris Hadamard concentrated on the problems of mathematical
physics, in particular partial differential equations, the calculus of
variations and the foundations of functional analysis.
He introduced the idea of well‐posed problem and the method of
descent in the theory of partial differential equations, culminating
in his book on the subject, based on lectures given at Yale in 1922.
He was elected to the French Academy of Sciences in 1916, in
succession to Poincaré. He was awarded the CNRS Gold medal for
lifetime achievements in 1956.
His students included Maurice Fréchet, Szolem Mandelbrojt and
André Weil.
Jacques Salomon Hadamard
Szolem Mandelbrojt
Szolem Mandelbrojt (1899–1983) was a Jewish‐Polish mathematician.
He worked mainly in classical analysis; he was a student of Jacques
Hadamard, and became Hadamard's successor as Professor at the
Collège de France.
He was an early member of the Bourbaki group. In fact his direction
was very different, as his publications show, with an interest in
Dirichlet series, lacunary series, entire functions and other major
topics in complex analysis and harmonic analysis.
During World War II he was in Houston, USA at the Rice Institute
from 1940, being one of many French scientists helped by the
program of Louis Rapkine after the fall of France in June.
Benoît Mandelbrot is his nephew, and Jean‐Pierre Kahane one of his
students.
Jean‐Pierre Kahane
Jean Pierre Kahane (born in 1926) is a french mathematician. He
attended ENS and obtained his mathematics agrégation in
1949. He then worked for the CNRS from 1949 to 1954, and
defended his PhD in 1954; his advisor was Szolem Mandelbrojt.
He was assistant professor and professor of mathematics in
Montpellier from 1954 to 1961 and a professor from 1961 until
his retirement (1994) at Université de Paris‐Sud in Orsay.
He was elected corresponding member of the French Academy of
Sciences in 1982 and full member in 1998. In 2002 he became
commander in the order of the Légion d'Honneur.
Jean‐Pierre Kahane
Jean‐Louis Krivine
Jean‐Louis Krivine
Jacques!
Demetrios Kydones
Jacob Bernoulli Manuel Chrysoloras Johann Bernoulli Guarino da Verona
Leonhard Paul Euler Vittorino da Feltre
Joseph Lagrange
Theodorus Gaza Siméon Poisson
Rodolphus Agricola
Michel Chasles Alexander Hegius
Jean‐Gaston Darboux
Erasmus
Charles‐Emile Picard
Jacob Milich
Jacques Salomon Hadamard
Erasmus Reinhold
Szolem Mandelbrojt
Valentin Naboth
Jean‐Pierre Kahane
Rudolph Snel van Royen
Jean‐Louis Krivine
Willebrord Snellius
Jacques Stern Jacob van Gool
Franciscus van Schooten
Christiaan Huygens
Gottfried Wilhelm Leibniz
Jacques’ students
with no descendents as yet
Jacques’ students
with descendents
Industry: 32
VeriSign
Nagra (2)
EADS
Cryptolog (2)
Clipperton Fidequity
HSBC (2)
Apple
CryptoExperts
BNP Paribas
SAGEM
Gemalto
Orange (7)
SwissSign
Siemens
Oberthur
Google Irisresearch, Norway.
Thales (2)
Ingénico (2)
plus two unspecified occupations.
State Services: 11
CELAR
Défense (5)
DCSSI (3)
DGA
Ministère des Affaires Etrangères
Full‐Time Researchers : 7
DR CNRS ‐ LRI
DR CNRS ‐ Caen
DR CNRS – ENS DR INRIA ‐ ENS
CR CNRS ‐ LRI
CR CNRS ‐ LIX
CR CNRS ‐ Caen
Full Time Researchers, Abroad: 1
CONICET (CNRS Argentina), Buenos Aires
Educators, France : 24
Pr. Caen (2)
Pr. UVSQ Pr. Paris II
Pr. 3iL Limoges
Pr. Paris 7
Pr. UVSQ
Pr. Univ. Dauphine
Pr. LIF Marseilles
MC Paris 6
MC Telecom ParisTech
MC ENS
MC Paris 8
MC GREYC, Caen (4)
MC LIF, Marseilles (2)
MC LATP, Marseille
MC LINA, Nantes
plus two classe prépatoire professors.
Educators, Abroad: 5
Pr. EPFL Pr. Morocco
Pr. Luxembourg
Pr. HES‐SO: Haute école Pr. spécialisée de Suisse occidentale
Pr. UCL, London
Postdocs and other humanitarian volunteers: 7
Humanitarian mission at Burkina Fasso
Post‐doc at Univ. Reims
Post‐doc at ENS (2)
Post‐doc at Univ. Catholique de Louvain‐la‐Neuve
Post‐doc at Univ. Grenoble
Post‐doc at LORIA
A Variety of Contributions
I asked each of the descendents to send me his/her most important
scientific contribution.
Not all responded but all answers I got were compiled in a « full list »,
available upon request.
As This Presentation Ends
I voice all these descendents’ thanks, respect and recognition.
Thank you Jacques!
Thank you for your contributions to science.
Thank you for your contributions to education.
Thank you for your mentoring and caring guidance.
You helped many become researchers, it is our challenge to live up
to this heritage, transmit it and enrich it by writing the book’s next
pages!
A Small Token of Recognition…