MCCCXXIV(1324)

Θεσσαλονίκη

birth of Demetrios KydonesDemetrios Kydones (Δημήτριος Κυδώνης, 1324‐1397 in Crete) was

a Byzantine theologian, translator, writer and influentialstatesman who served an unprecedented three terms asImperial Prime Minister or Chancellor of the Byzantine Empireunder three successive emperors: John VI Kantakouzenos, JohnV Palaiologos and Manuel II Palaiologos.

As Imperial Premier, Kydones' effort during his second and thirdstints was to bring about a reconciliation of the Byzantine andRoman Churches, to cement a military alliance against the ever‐encroaching Islam, a program that culminated in Emperor JohnV 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 middleages.

He was born in Constantinople to a distinguished family. Kydoneswas Crysolaras’ teacher. In 1390, he led an embassy sent toVenice by the emperor Manuel II Palaeologus to implore the aidof the Christian princes against the Muslim Turks. In 1396, theUniversity of Florence, invited him to come and teach Greekgrammar 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 tookfrom them, but of course, as he himself says elsewhere with reference tohis own day: "Italy is invincible in war, Greece in culture." For our part, andwe mean no offence, we firmly believe that both Greeks and Latins havealways taken learning to a higher level by extending it to each other'sliterature."

Manuel Chrysoloras Chrysoloras translated the works of Homer and Plato's Republic

into Latin. His his Erotemata Civas Questiones which was thefirst basic Greek grammar in use in Western Europe, firstpublished in 1484 and widely reprinted, and which enjoyedconsiderable success not only among his pupils in Florence, butalso among later leading humanists, being immediately studiedby Thomas Linacre at Oxford and by Desiderius Erasmus atCambridge; and Epistolæ tres de comparatione veteris et novæRomæ (Three Letters Comparing Ancient and Modern Rome).

Many of his treatises on morals and ethics and other philosophicalsubjects came into print in the 17th and 18th centuries, becauseof 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 for700 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 figuresof the revival of Greek studies in Renaissance Italy. Thesealumni included Guarino da Verona.

When Chrysoloras died in 1413, his death gave rise tocommemorative essays of which Guarino da Verona made acollection in Chrysolorina.

Guarino da VeronaGuarino 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. Whenhe set out to return home, he had with him two cases ofprecious Greek manuscripts which he had taken great painsto collect.

It is said that the loss of one of these by shipwreck caused himsuch distress that his hair turned grey in a single night. Onarriving back in Italy, he earned a living as a teacher ofGreek, in Verona, Venice and Florence. In 1436, he became aprofessor of Greek at Ferrara through the patronage ofLionel, the marquis of Este. His method of instruction wasrenowned and attracted many students from Italy and therest of Europe. Many of them, notably Vittorino da Feltre,afterwards became well‐known scholars.

Guarino da VeronaFrom 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 grammarof Chrysoloras, and a series of commentaries on Persius,Martial, the Satires of Juvenal, and on some of the writingsof Aristotle and Cicero.

Vittorino da FeltreVittorino da Feltre (1378‐1446) was an Italian humanist and

teacher, born in Feltre. His real name was VittorinoRamboldini.

He studied at Padua and later taught there, but after a fewyears he was invited by the marquis of Mantua to educatehis children. At Mantua, Vittorino set up a school at whichhe taught the marquis's children and the children of otherprominent families, together with many poor children,treating them all on an equal footing.

He not only taught the humanistic subjects, but placed specialemphasis on religious and physical education.

Vittorino da FeltreHe 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 pupilas he had with Gasparino da Barzizza and in the adaptationof the teaching to the ability and needs of the child.

He lived with students and befriended them in the first secularboarding school. Vittorino's school was well lit and built ofbetter construction than other schools of the time.

Vittorino also made school work more interesting, adding fieldtrips to his curricula.

He watched the health of his students very carefully, andgenerally elevated the status of teachers. Schoolsthroughout Europe (especially England) copied Vittorino'smodel.

Vittorino da FeltreMany of fifteenth century Italy's greatest scholars, including

Guarino da Verona, sent their sons to study under Vittorinoda Feltre.

One of Vittorino's most noteworthy students was TheodorusGaza.

Theodorus Gaza Theodorus Gaza (1400–1475) was a Greek humanist and

translator of Aristotle, one of the Greek scholars who werethe leaders of the revival of learning in the 15th century (thePalaeologan Renaissance).

He was born at Thessalonica. On the capture of his native cityby the Turks in 1430 he fled to Italy. During a three yearsresidence in Mantua he rapidly acquired a competentknowledge of Latin under the teaching of Vittorino daFeltre, supporting himself meanwhile by giving lessons inGreek, and by copying manuscripts of the ancient classics.

In 1447 he became professor of Greek in the newly foundedUniversity of Ferrara, to which students in great numbersfrom all parts of Italy were soon attracted by his fame as ateacher. 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 theobject of bringing about a reconciliation between the Greekand Latin Churches; and in 1450, at the invitation of PopeNicholas V, he went to Rome, where he was for some yearsemployed making Latin translations from Aristotle andother Greek authors. In Rome, he continued his teachingactivities.

After the death of Nicholas (1455), being unable to make aliving at Rome, Gaza removed to Naples. Shortly afterwardshe was appointed by Cardinal Bessarion to a benefice inCalabria, where the later years of his life were spent, andwhere 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 particularattention to the translation and exposition of Aristotle'sworks on natural science.

His Greek grammar (4 books), written in Greek, first printed atVenice in 1495, and partially translated by Erasmus in 1521,was for a long time the leading text‐book. His translationsinto Latin were very numerous.

Rodolphus AgricolaRodolphus Agricola (1443–1485) was a pre‐Erasmian humanist

of the northern Low Countries, famous for his supple Latinand 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 poetin Latin as well as the vernacular, a diplomat and asportsman of sorts (boxing). He is best known today as theauthor of De inventione dialectica, as the father of northernEuropean humanism and as a zealous anti‐scholastic in thelate fifteenth century.

De inventione dialectica was very influential in creating aproper place for logic in rhetorical studies, and was of greatsignificance in the education of early humanists. It is ahighly original, critical, and systematic treatment of all ideasand concepts related to dialectics.

Rodolphus AgricolaAgricola's De formando studio ‐ his long letter on a private

educational program ‐ was printed as a small booklet and thusinfluenced 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 haveactually met him through his own schoolmaster AlexanderHegius, one of Agricola's students, at Hegius's school inDeventer. Erasmus made it his personal mission to ensure thatseveral of Agricola's major works were printed posthumously.

Agricola's 'De inventione dialectica' has a huge impact on Deafcommunity. He felt that a person born deaf can expresshimself by putting down his thoughts in writing. The book wasnot published until 100 years later. The statement that deafpeople can be taught a language is one of the earliest positivestatements about deafness on records.

Alexander HegiusAlexander 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 distinguishedalumni. First and foremost of these was Erasmus; anotherfamous alumnus of Hegius was Pope Adrian VI.

His writings, consisting of short poems, philosophical essays,grammatical notes and letters, were published after hisdeath. They display considerable knowledge of Latin, butless of Greek, on the value of which he strongly insisted.

Alexander HegiusHegius's chief claim to be remembered rests not upon his

published works, but upon his services in the cause ofhumanism.

He succeeded in abolishing the old‐fashioned medievaltextbooks and methods of instruction, and led his pupils tothe study of the classical authors themselves.

His generosity in assisting poor students exhausted aconsiderable fortune, and at his death he left nothing buthis books and clothes.

ErasmusDesiderius 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 NewTestament. These raised questions that would be influentialin the Protestant Reformation and Catholic Counter‐Reformation. He also wrote The Praise of Folly, Handbookof a Christian Knight, On Civility in Children, and many otherworks.

ErasmusErasmus lived through the Reformation period and he

consistently criticized some contemporary popular Christianbeliefs.

In relation to clerical abuses in the Church, Erasmus remainedcommitted to reforming the Church from within. He alsoheld to Catholic doctrines such as that of free will, whichsome Protestant Reformers rejected in favor of thedoctrine of predestination.

His middle road disappointed and even angered manyProtestants, such as Martin Luther, as well as conservativeCatholics.

ErasmusOne of Erasmus’ best known works is Adagia, a collection of

4658 Greek and Latin adages. Many of which are commontoday!

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 submarineCause we are living in a material world and I’m a material girlTo dangle the bait To swallow the hook The bowels of the earth From heaven to earth 

ErasmusOne of Erasmus’ best known works is Adagia, a collection of

4658 Greek and Latin adages. Many of which are commontoday!

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 submarineCause we are living in a material world and I’m a material girlTo 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 

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Jacob Milich

Jacob Milich (1501–1559) was a disciple of Erasmus, Germanphysician, mathematician, and astronomer.

He was born in Freiburg im Breisgau, where he received hiseducation starting in 1513.

He taught at Wittenberg, where he became a professor ofmathematics.

His most important student there was Erasmus Reinhold. Hebecame Dean of the Wittenberg university's philosophicaland medical branches, then served as Rector of the schoolon several occasions.

The crater Milichius on the Moon is named after him.

Erasmus ReinholdErasmus Reinhold (1511 –1553) was a German astronomer and

mathematician, considered to be the most influentialastronomical pedagogue of his generation. He was bornand died in Saalfeld, Germany.

He was educated at the University of Wittenberg, where hebecame dean and later rector. In 1536 he was appointedprofessor of higher mathematics. In contrast to the limitedmodern definition, "mathematics" at the time also includedapplied 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 orPrussian Tables. These astronomical tables helped todisseminate calculation methods of Copernicus throughoutthe Empire.

Erasmus ReinholdBoth Reinholds's Prutenic Tables and Copernicus' studies were

the foundation for the Calendar Reform by Pope GregoryXIII in 1582.

However, Reinhold (like other astronomers before Kepler andGalileo) translated Copernicus' mathematical methods backinto a geocentric system, rejecting heliocentric cosmologyon physical and theological grounds.

Reinhold tutored many disciples amongst whom was ValentinNaboth.

Valentin NabothValentin Naboth was born in Niederlausitz to a Jewish family.

In 1544, Valentin immatriculated at the University ofWittenberg when Erasmus Reinhold taught there. In 1550he transferred to the University of Erfurt.

From 1553 Naboth taught mathematics at the University ofCologne. When he arrived at Cologne he began teachingmathematics as Privatdozent, since that discipline was notincluded in the university curriculum. He made such animpression that he was offered a University position,remunerated for his private lessons, and made ordinaryprofessor. Dutch mathematician Rudolph Snellius was oneof his students in Cologne.

Valentin NabothNaboth was the author of a general textbook on astrology

Enarratio elementorum astrologiae. Renowned forcalculating the mean annual motion of the Sun, his writingsare chiefly devoted to commenting upon Ptolemy and theArabian astrologers. Naboth teaches the calculation of themovement of the planets according to the Prutenic Tablesof Erasmus Reinhold.

He advocated a measure of time, by which 0°59'09" (the meandaily motion of the Sun in longitude) is equated to 1 year oflife in calculating primary directions. This was a refinementof Ptolemy’s value of exactly 1 degree per year. This bookwas banned by the Roman Catholic Church.

Ducunt volentem fata, nolentem trahunt!

In March 1564 Naboth resigned from his position at the Universityof 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 toenter a period of personal danger, so he stockpiled an adequatesupply of food and drink, closed his blinds, and locked his doorsand windows, intending to stay in hiding until the period ofdanger had passed.

Unfortunately, some thieves, seeing the house closed and theblinds drawn, decided that the resident was absent. Theytherefore broke into what they thought was an empty house,and, finding Naboth there, murdered him to conceal theiridentities. Thus he did not escape the fate predicted… by hisown astrological calculations.

Rudolph Snel van RoyenRudolph 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 ofMarburg.

In 1578, he was offered, and accepted, a position as professorof 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 andintellectual forces of the Dutch Golden Age. Finally, not theleast of Snel’s influence was cast upon his son, WillebrordSnellius, who would become the distinguished astronomerand mathematician.

Willebrord SnelliusWillebrord Snellius (1580–1626, Leiden) was a Dutch

astronomer and mathematician. His name is attached to thelaw of refraction of light (it is now known that this law wasdiscovered by Ibn Sahl in 984).

In 1613 he succeeded his father as professor of mathematics atthe University of Leiden. In 1615 he planned a new methodof finding the radius of the earth, by determining thedistance of one point on its surface from the parallel oflatitude of another, by means of triangulation. This workdescribes the method and gives as the result of hisoperations between Alkmaar and Bergen op Zoom whichhe measured to be equal to 107.395 km. The actual distanceis approximately 111 km. Snellius also produced a newmethod for calculating π, the first such improvement sinceancient 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 GoolJacob 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 andother Eastern languages. In 1622 he accompanied the Dutchembassy to Morocco. On his return he got a professorship. In thefollowing year he set out on a Syrian and Arabian tour from whichhe did not return until 1629. The remainder of his life was spent atLeiden where he held the chair of mathematics as well as that ofArabic.

His most important work is the Lexicon Arabico‐Latinum (1653) whichwas only superseded in 1837. Among his earlier publications maybe mentioned editions of various Arabic texts.

After his death, there was found among his papers a DictionariumPersico‐Latinum which was published in 1669. Golius also edited,translated and annotated the astronomical treatise of Alfragan in1669.

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 SchootenFranciscus 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 tounderstand, he went to France to study the works of otherimportant mathematicians of his time, such as François Viète andPierre 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 broadermathematical community, and thus was responsible for the spreadof analytic geometry to the world. Over the next decade heexpanded the commentaries to two volumes, published in 1659and 1661. This edition and its extensive commentaries was farmore influential than the 1649 edition. It was this edition thatGottfried Leibniz and Isaac Newton knew.

Franciscus van SchootenSchooten 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 HuygensChristiaan Huygens (1629–1695) was a prominent Dutch

mathematician, astronomer, physicist, horologist, and writer ofearly science fiction. His work included early telescopic studieselucidating the nature of the rings of Saturn and the discoveryof its moon Titan, investigations and inventions related to timekeeping and the pendulum clock, and studies of both opticsand the centrifugal force.

Huygens achieved note for his argument that light consists ofwaves, now known as the Huygens–Fresnel principle, whichbecame instrumental in the understanding of wave‐particleduality. He generally receives credit for his discovery of thecentrifugal force, the laws for collision of bodies, for his role inthe development of modern calculus and his originalobservations on sound perception.

Huygens is seen as the first theoretical physicist as he was the firstto use formulae in physics.

• 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 thestudies Mathematics and Computer Science at the DelftUniversity of Technology

• Huygens Laboratory: Home of the Physics department atLeiden University, The Netherlands

• Huygens Supercomputer: National Supercomputer facilityof The Netherlands, located at SARA in Amsterdam

• The Huygens‐building in Noordwijk, The Netherlands, firstbuilding 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 sciencedepartment at the university of Nijmegen.

• etc…

Named After Christiaan Huygens

Huygens: Mechanics

Huygens formulated what is now known as the second law of motionof Isaac Newton in a quadratic form. Newton reformulated andgeneralized that law. In 1659 Huygens derived the now well‐knownformula for the centrifugal force, exerted by an object describing acircular motion, for instance on the string to which it is attached, inmodern notation:

with m the mass of the object, v the velocity and r the radius.

Furthermore, Huygens concluded that Descartes' laws for the elasticcollision of two bodies must be wrong and formulated the correctlaws.

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‐Fresnelprinciple).

The later theory of light by Isaac Newton in his Opticks proposed adifferent explanation for reflection, refraction and interferenceof light assuming the existence of light particles.

The interference experiments of Thomas Young vindicatedHuygens' wave theory in 1801, as the results could no longer beexplained with light particles.

Huygens experimented with double refraction in Icelandic crystal(calcite) and explained it with his wavetheory and polarisedlight.

Huygens: Clocks

He also worked on the construction of accurate clocks, suitable fornaval navigation. In 1658 he published a book on this topic calledHorologium. His invention of the pendulum clock, patented in1657, was a breakthrough in timekeeping.

Huygens discovered that the cycloid was an isochronous curveand, applied to pendulum clocks in the form of cycloidal cheeksguiding a flexible pendulum suspension, would ensure a regular(i.e isochronous) swing of the pendulum irrespective of itsamplitude, i.e. irrespective of how it moved side to side. Themathematical and practical details of this finding were publishedin "Horologium Oscillatorium" of 1673.

Huygens: ClocksHuygens was the first to derive the formula for the period of the

mathematical pendulum (with massless rod or cable), in modernnotation:

with T the period, l the length of the pendulum and g thegravitational acceleration.

In 1675, Christiaan Huygens patented a pocket watch.

Huygens: Astronomy

In 1655, Huygens proposed that Saturn was surrounded by a solidring, "a thin, flat ring, nowhere touching, and inclined to theecliptic." Using a 50 power refracting telescope that he designedhimself, Huygens also discovered the first of Saturn's moons,Titan. In the same year he observed and sketched the OrionNebula. His drawing, the first such known of the Orion nebula,was published in Systema Saturnium in 1659. Using his moderntelescope he succeeded in subdividing the nebula into differentstars. He also discovered several interstellar nebulae and somedouble stars.

In 1661, he observed planet Mercury transit over the Sun.

Gottfried Wilhelm Leibniz 

It is impossible to present Leibniz’ (1646‐1716) contribution tohumanity without devoting to it at least an entire workshop.

He is remembered for work in infinitesimal calculus, calculus, a newformula for π, Leibniz’ harmonic triangle, Leibniz formula fordeterminants, Leibniz integral rule, Leibniz differential, Notationfor differentiation, Differential calculus, Proof of Fermat's littletheorem and Kinetic energy.

Other contributions, in the fields of humanity or philosophy, areless known to the mathematical community. These nonethelessinclude: Monadology, Theodicy, Optimism, Principle of sufficientreason, 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 linesto 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 thegoodness of God, and that notwithstanding its many evils, theworld we know is the best of all possible worlds.

Leibniz wrote his Théodicée as a criticism of Pierre Bayle'sDictionnaire Historique et Critique, that argued that the sufferingsexperienced in this earthly life prove that God could not be goodand 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 andastronomy.

He traveled throughout Europe from 1676 to 1682, learning aboutthe latest discoveries in mathematics and the sciences.

He published papers on transcendental curves (1696) andisoperimetry (1700, 1701). In 1690, Jacob became the firstperson to develop the technique for solving separabledifferential equations.

Jacob Bernoulli 

Upon returning to Basel in 1682, he founded a school formathematics and the sciences. He was appointed professor ofmathematics at the University of Basel in 1687, remaining inthis position for the rest of his life.

He is the author as the law of large numbers. The terms Bernoullitrial and Bernoulli numbers result from this work. The lunarcrater Bernoulli is also named after him jointly with his brotherJohann.

Bernoulli chose a figure of a logarithmic spiral and the mottoEadem mutata resurgo for his gravestone; the spiral executedby 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 Bernoullibrothers worked together spending much of their timestudying the newly discovered calculus.

After graduating from Basel University Johann Bernoulli moved toteach differential equations and in 1694, became a professor ofmathematics at the University of Groningen. As a student ofLeibniz’s calculus, Johann Bernoulli sided with him in 1713 in theNewton–Leibniz debate over who deserved credit for thediscovery of calculus. Johann Bernoulli defended Leibniz byshowing that he had solved certain problems with his methodsthat 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 twoyears he received five answers, one of which was from hisolder brother, Jakob.

Johann Bernoulli 

Johann Bernoulli 

Johann was hired by Guillaume François Antoine de L'Hôpital totutor him in mathematics. Bernoulli and L'Hôpital signed acontract which gave L'Hôpital the right to use Bernoulli’sdiscoveries as he pleased. L'Hôpital authored the first textbookon 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 hisyouth

Leonhard Paul Euler 

Leonhard Paul Euler (1707–1783) was a pioneering Swissmathematician and physicist who spent most of his life inRussia and Germany.

Euler made important discoveries in fields as diverse as calculusand graph theory. He also introduced much of the modernmathematical terminology and notation, particularly formathematical analysis, such as the notion of a mathematicalfunction. He is also renowned for his work in mechanics, fluiddynamics, optics, and astronomy.

Euler is considered to be the preeminent mathematician of the18th century and one of the greatest of all times. He is also oneof the most prolific; his collected works fill 60–80 quartovolumes.

The city of Kaliningrad (Russia) was set on both sides of thePregel River, and included two large islands which wereconnected to each other and the mainland by seven bridges.The problem was to find a walk through the city that would crosseach bridge once and only once. The islands could not bereached by any route other than the bridges, and every bridgemust have been crossed completely every time (one could notwalk halfway onto the bridge and then turn around to come at itfrom another side).

V − E + F = 2 relates the number of vertices, edges, and faces ofa convex polyhedron

The asteroid 2002 Euler was named in his honor. He is alsocommemorated by the Lutheran Church on their Calendar of Saintson 24 May ‐ he was a devout Christian (and believer in biblicalinerrancy) who wrote apologetics and argued forcefully against theprominent atheists of his time.

Joseph LagrangeJoseph‐Louis Lagrange, born Giuseppe Lodovico Lagrangia (1736–

1813) was an Italian‐born mathematician and astronomer, wholived most of his life in Prussia and France, making significantcontributions to all fields of analysis, to number theory, and toclassical and celestial mechanics. On the recommendation ofEuler and D'Alembert, in 1766 Lagrange succeeded Euler as thedirector of mathematics at the Prussian Academy of Sciences inBerlin, where he stayed for over twenty years, producing alarge body of work and winning several prizes of the FrenchAcademy of Sciences.

Lagrange's treatise on analytical mechanics (MécaniqueAnalytique, 1888), written in Berlin and first published in 1788,offered the most comprehensive treatment of classicalmechanics since Newton and formed a basis for thedevelopment of mathematical physics in the nineteenthcentury.

French or Italian?Born Giuseppe Lodovico Lagrangia in Turin of Italian parents,

Lagrange had French ancestors on his father's side. In 1787 hebecame a member of the French Academy, and he remained inFrance until the end of his life. Therefore, Lagrange isalternatively considered a French and an Italian scientist.

Lagrange survived the French Revolution and became the firstprofessor of analysis at the École Polytechnique upon itsopening in 1794. Napoleon named Lagrange to the Legion ofHonour and made him a Count of the Empire in 1808. He isburied 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 isalways a multiple of n, 1771.

His papers of 1773, 1775, and 1777 gave demonstrations of severalresults enunciated by Fermat, and not previously proved.

His Recherches d'Arithmétique of 1775 developed a general theoryof binary quadratic forms to handle the general problem ofwhen an integer is representable by the form ax2 + by2 + cxy.

Joseph Lagrange

Siméon PoissonSiméon 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 onthe number of integrals of a finite difference equation.

The latter was examined by Legendre, who recommended that itshould be published in the Recueil des savants étrangers, anunprecedented honor for a youth of eighteen. This success atonce procured entry for Poisson into scientific circles.

Lagrange, who lectured at the École Polytechnique, recognizedPoisson’s talent, and also became his friend. Laplace, in whosefootsteps Poisson followed, regarded him almost as his son.Poisson was made deputy professor in 1802, and, in 1806 fullprofessor succeeding Fourier. In 1808 he became astronomerto the Bureau des Longitudes; and professor of rationalmechanics in 1809.

Siméon PoissonHe became a member of the Institute in 1812, examiner at the

military school of Saint‐Cyr in 1815, graduation examiner at theÉcole Polytechnique in 1816, councillor of the university in 1820,and geometer to the Bureau des Longitudes succeeding Laplacein 1827.

His father, whose early experiences had led him to hate aristocrats,bred him in the creed of the First Republic. Throughout theRevolution, the Empire, and the following restoration, Poissonwas not interested in politics, concentrating on mathematics.

He was appointed to the dignity of baron in 1821; but he neithertook out the diploma or used the title.

Siméon PoissonThe 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, whilehis "revocation" was being plotted by the council ofministers, procured him an invitation to dine at the PalaisRoyal, where he was openly and effusively received by thecitizen king, who "remembered" him. After this, of course,his degradation was impossible, and seven years later he wasmade a peer of France, not for political reasons, but as arepresentative of French science.

Notwithstanding his many official duties, he found time topublish more than three hundred works, several of themextensive treatises.

Siméon Poisson’s WorksMemoirs 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 lesinégalités séculaires des moyens mouvements des planètes,Sur la variation des constantes arbitraires dans les questionsde mécanique, (1809); Sur la libration de la lune, (1821), andSur le mouvement de la terre autour de son centre de gravité(1827).

Poisson Distribution

In probability the Poisson distribution is a discrete probabilitydistribution that expresses the probability of a number ofevents occurring in a fixed period of time if these events occurwith a known average rate and independently of the time sincethe last event. The Poisson distribution can also be used forthe number of events in other specified intervals such asdistance, area or volume.

The distribution was discovered by Poisson and published,together with his probability theory, in 1838 in his workRecherches sur la probabilité des jugements en matièrescriminelles et matière civile. The work focused on certainrandom variables N that count, among other things, thenumber of discrete occurrences (sometimes called "arrivals")that take place during a time‐interval of given length.

Poisson DistributionIf the expected number of occurrences in this interval is λ,

then the probability that there are exactly k occurrences isequal to

λ is a positive real number, equal to the expected number ofoccurrences that occur during the given interval. Forinstance, if the events occur on average 4 times per minute,and you are interested in the number of events occurring ina 10 minute interval, you would use as your model a Poissondistribution with λ = 10×4 = 40.

As a function of k, this is the probability mass function. ThePoisson distribution can be derived as a limiting case of thebinomial distribution.

The Poisson distribution can be applied to systems with alarge number of possible events, each of which is rare. Aclassic example is the nuclear decay of atoms.

Siméon Poisson

Michel Floréal Chasles (1793–1880) studied at the ÉcolePolytechnique under Poisson. In the War of the Sixth Coalitionhe was drafted to fight in the defence of Paris in 1814. After thewar, he gave up on a career as an engineer or stockbroker inorder to pursue his mathematical studies.

In 1837 he published his Historical view of the origin anddevelopment of methods in geometry, a study of the method ofreciprocal polars in projective geometry. The work gained himconsiderable fame and respect and he was appointed Professorat the École Polytechnique in 1841, then he was awarded a chairat the Sorbonne in 1846.

Jakob Steiner had proposed the problem of enumerating thenumber of conic sections tangent to each of five given conics,and had answered it incorrectly. Chasles developed a theory ofcharacteristics that enabled the correct enumeration of theconics (there are 3264).

Michel Chasles 

He established several important theorems (all called Chasles'theorem). That on solid body kinematics was seminal forunderstanding their motions, and hence to the development ofthe 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 forgedletters from Frenchman Vrain‐Denis Lucas. Included in this trove— all apparently written in modern French — were letters fromAlexander the Great to Aristotle, from Cleopatra to Julius Caesar(written in French!), and from Mary Magdalene to a revivedLazarus.

Chasles' name is one of 72 that appears on the Eiffel Tower.

Michel Chasles 

« Ce grand mathématicien collectionnait les documents anciens et futune victime un peu naïve et complaisante d’un faussaire qui lui venditdes fausses lettres de Pascal prouvant soi‐disant que Pascal avaitdécouvert la gravitation universelle avant Newton. L’histoire de cettefraude scientifique a fait l’objet d’un téléfilm très réussi en 1998, avecMichel Piccoli.

A partir de juillet 1867, le mathématicien présenta à l'Académie dessciences une série de lettres inédites prétendument de Pascal, que lefaussaire Vrain‐Lucas venait de fabriquer. Elles voulaient établirqu'avant Newton, l'auteur des Pensées avait découvert le principe del'attraction universelle. Un savant anglais fit observer qu'on ytrouvait des mesures astronomiques bien postérieures à la mort dePascal. Approvisionné une nouvelle fois par Vrain‐Lucas, Chaslesmontra alors des lettres où Galilée communiquait à Pascal lesrésultats 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 étaitcomplètement aveugle depuis près de quatre ans. Surgit alors unenouvelle lettre, postérieure à la précédente et datée de décembre1641, dans laquelle un autre savant italien apprenait à Pascal queGalilée, dont la vue n'avait cessé de baisser, avait fini par la perdreentièrement.

Ses collègues de l'Institut prirent la chose avec bonne humeur, mais àl'étranger — à Londres en particulier — on fit des gorges chaudesdu manque d'esprit critique des scientifiques français. Quant àChasles, 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 JulesCésar à Vercingétorix, de César à Cléopâtre, toutes rédigées dans unfaux vieux français. Chasles légua à sa mort sa collection à l'Institut,y compris les faux fabriqués par Vrain‐Lucas. »

The Gullible Chasles 

Michel Chasles 

Michel Chasles 

AB + BC = AC

Jean‐Gaston DarbouxJean‐Gaston Darboux (1842‐1917) was a French mathematician

who made important contributions to geometry andmathematical analysis. He was a biographer of Henri Poincaréand edited the Selected Works of Joseph Fourier.

Darboux received his Ph.D. from ENS in 1866. His thesis, writtenunder the direction of Chasles, was titled Sur les surfacesorthogonales. In 1884, Darboux was elected to the Académiedes Sciences. In 1900, he was appointed the Academy'spermanent secretary of its Mathematics section.

Among his students were Charles‐Emile Picard, Emile Borel andÉlie Cartan.

In 1902, he was elected to the Royal Society; in 1916, he receivedthe Sylvester Medal from the Society.

Jean‐Gaston DarbouxMany mathematical objects are named after Darboux:

Darboux’s equation, frame, integral, function, net invariants,formula, vector, problem, cubic, transformation, theorem insymplectic geometry, theorem in real analysis (related toIntermediate 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 PicardCharles Émile Picard (1856‐1941) was a French mathematician. He was

elected the fifteenth member to occupy seat 1 of the AcadémieFrançaise in 1924.

Picard's mathematical papers, textbooks, and many popular writingsexhibit an extraordinary range of interests, as well as an impressivemastery of the mathematics of his time. Modern students ofcomplex variables are probably familiar with two of his namedtheorems. His lesser theorem states that every nonconstant entirefunction takes every value in the complex plane, with perhaps oneexception. His greater theorem states that an analytic functionwith an essential singularity takes every value infinitely often, withperhaps one exception, in any neighborhood of the singularity.

Charles‐Emile PicardPicard also made important contributions in the theory of differential

equations, including work on Painlevé transcendents and hisintroduction of a kind of symmetry group for a linear differentialequation, the Picard group. In connection with his work onfunction theory, he was one of the first mathematicians to use theemerging ideas of algebraic topology. In addition to his path‐breaking theoretical work, Picard made important contributions toapplied mathematics, including the theories of telegraphy andelasticity. His collected papers run to four volumes.

Like his contemporary, Henri Poincaré, Picard was much concernedwith the training of mathematics, physics, and engineeringstudents. He wrote a classic textbook on analysis, one of the firsttextbooks on the theory of relativity. Picard's popular writingsinclude biographies of many leading French mathematicians,including his father in law, Charles Hermite.

Charles‐Emile Picard

Jacques Salomon HadamardJacques 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, andClaire Marie Jeanne Picard, Hadamard attended the LycéeCharlemagne and Lycée Louis‐le‐Grand, where his fathertaught.

In 1884 Hadamard entered the ENS, having been placed first in theentrance examinations both there and at the ÉcolePolytechnique. His teachers included Hermite, Darboux andPicard. He obtained his doctorate in 1892 and in the same yearwas awarded the Grand Prix des Sciences Mathématiques for hisprize essay on the Riemann zeta function.

Jacques Salomon HadamardIn 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 equalityholds. In 1896 he made two important contributions: he provedthe prime number theorem, using complex function theory andhe was awarded the Bordin Prize of the French Academy ofSciences for his work on geodesics in the differential geometryof surfaces and dynamical systems. In the same year he wasappointed Professor of Astronomy and Rational Mechanics inBordeaux. For his cumulative work, he was awarded the PrixPoncelet in 1898.

After the Dreyfus affair, which involved him personally becausehis wife was related to Dreyfus, Hadamard became politicallyactive and a supporter of Jewish causes though he professed tobe an atheist in his religion.

Jacques Salomon HadamardIn 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 Polytechniquein 1912 and at the École Centrale in 1920, succeeding Jordan. InParis Hadamard concentrated on the problems of mathematicalphysics, in particular partial differential equations, the calculus ofvariations and the foundations of functional analysis.

He introduced the idea of well‐posed problem and the method ofdescent in the theory of partial differential equations, culminatingin his book on the subject, based on lectures given at Yale in 1922.He was elected to the French Academy of Sciences in 1916, insuccession to Poincaré. He was awarded the CNRS Gold medal forlifetime achievements in 1956.

His students included Maurice Fréchet, Szolem Mandelbrojt andAndré Weil.

Jacques Salomon Hadamard

Szolem MandelbrojtSzolem Mandelbrojt (1899–1983) was a Jewish‐Polish mathematician.

He worked mainly in classical analysis; he was a student of JacquesHadamard, and became Hadamard's successor as Professor at theCollège de France.

He was an early member of the Bourbaki group. In fact his directionwas very different, as his publications show, with an interest inDirichlet series, lacunary series, entire functions and other majortopics in complex analysis and harmonic analysis.

During World War II he was in Houston, USA at the Rice Institutefrom 1940, being one of many French scientists helped by theprogram of Louis Rapkine after the fall of France in June.

Benoît Mandelbrot is his nephew, and Jean‐Pierre Kahane one of hisstudents.

Jean‐Pierre Kahane

Jean Pierre Kahane (born in 1926) is a french mathematician. Heattended ENS and obtained his mathematics agrégation in1949. He then worked for the CNRS from 1949 to 1954, anddefended his PhD in 1954; his advisor was SzolemMandelbrojt.

He was assistant professor and professor of mathematics inMontpellier from 1954 to 1961 and a professor from 1961 untilhis retirement (1994) at Université de Paris‐Sud in Orsay.

He was elected corresponding member of the French Academy ofSciences in 1982 and full member in 1998. In 2002 he becamecommander in the order of the Légion d'Honneur.

Jean‐Pierre Kahane

Jean‐Louis Krivine

Jean‐Louis Krivine

Jacques!

Demetrios KydonesManuel Chrysoloras Guarino da VeronaVittorino da FeltreTheodorus Gaza Rodolphus AgricolaAlexander HegiusErasmusJacob MilichErasmus ReinholdValentin NabothRudolph Snel van RoyenWillebrord SnelliusJacob van GoolFranciscus van SchootenChristiaan HuygensGottfried Wilhelm Leibniz

Jacob Bernoulli Johann Bernoulli Leonhard Paul Euler Joseph LagrangeSiméon PoissonMichel Chasles Jean‐Gaston DarbouxCharles‐Emile PicardJacques Salomon HadamardSzolem MandelbrojtJean‐Pierre KahaneJean‐Louis KrivineJacques Stern 

Jacques’ studentswith no descendents as yet

Jacques’ studentswith descendents

Industry: 32

VeriSignNagra (2)EADSCryptolog (2)Clipperton FidequityHSBC (2)AppleCryptoExpertsBNP ParibasSAGEMGemalto

Orange (7)SwissSignSiemensOberthurGoogle Irisresearch, Norway.Thales (2)Ingénico (2)plus two unspecified occupations.

State Services: 11

CELARDéfense (5)DCSSI (3)DGAMinistère des Affaires Etrangères

Full‐Time Researchers : 7

DR CNRS ‐ LRIDR CNRS ‐ CaenDR CNRS – ENS DR INRIA ‐ ENSCR CNRS ‐ LRICR CNRS ‐ LIXCR CNRS ‐ Caen

Full Time Researchers, Abroad: 1CONICET (CNRS Argentina), Buenos Aires

Educators, France : 24

Pr. Caen (2)Pr. UVSQ  Pr. Paris IIPr. 3iL LimogesPr. Paris 7Pr. UVSQPr. Univ. DauphinePr. LIF Marseilles

MC Paris 6MC Telecom ParisTechMC ENSMC Paris 8MC GREYC, Caen (4)MC LIF, Marseilles (2)MC LATP, MarseilleMC LINA, Nantes

plus two classe prépatoire professors.

Educators, Abroad: 5

Pr. EPFL   Pr. MoroccoPr. LuxembourgPr. HES‐SO: Haute école Pr. spécialisée de Suisse occidentalePr. UCL, London

Postdocs and other humanitarian volunteers: 7

Humanitarian mission at Burkina FassoPost‐doc at Univ. ReimsPost‐doc at ENS (2)Post‐doc at Univ. Catholique de Louvain‐la‐NeuvePost‐doc at Univ. GrenoblePost‐doc at LORIA

A Variety of Contributions

I asked each of the descendents to send me his/her most importantscientific contribution.

Not all responded but all answers I got were compiled in a « full list »,available upon request.

As This Presentation EndsI 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 upto this heritage, transmit it and enrich it by writing the book’s nextpages!

A Small Token of Recognition…