Comments and explanations
The "recent" part of the information is from the
Project. For the older part, I have relied on biographies; here
"advising" needs to be interpreted more broadly than the supervision
of doctoral theses. Resources consulted include, among others,
and the Dictionary of Scientific Biography. The online catalogs of several
German university libraries, most notably Halle-Wittenberg, Tuebingen, and
Leipzig, were also helpful.
Goertler's name is often associated with Ludwig Prandtl. Indeed, he
under Prandtl during the period following his doctorate. The work
on Goertler vortices was done in Prandtl's lab.
There were two scientists named Robert Daublebsky von Sterneck, who
were father and son. The
one in the table is the son; he is known for computational work related to
the zeros of
the Riemann zeta function. The father was a surveying engineer in the
Petzval made important
contributions to optics and to the theory of the Laplace transform. The transform
might even have been named after Petzval, were it not for a disgruntled student named
Spitzer who claimed incorrectly that Petzval had plagiarized Laplace. For the full
story see M.A.B. Deakin, The development of the Laplace transform, 1737-1937 I : Euler
to Spitzer, 1737-1880, Arch. Hist. Exact Sci. 25 (1981), 343-390. The spelling of
Petzval's first name (s or z, f or ph) varies between sources.
Karl Weierstrass was awarded an honorary degree in 1854; he did not
seek a doctorate as a student. Gudermann was his principal mentor
during his student years and is generally regarded as his de facto advisor.
Kummer was not Kronecker's academic advisor, but he was his high
Kaestner was interested in poetry in addition to mathematics. His
teacher in that field was Gottsched. Gottsched's advisor Pietsch had a
doctorate in medicine, but his career turned towards poetry a few years
Hausen is known for work on electricity and has a crater on
the moon named after him. The mathematics genealogy project (and countless
other web sites as a consequence) has confused him with his father,
also named Christian August Hausen, who
got a doctorate in theology under Christian Siber in 1683. The son was
a mathematician from the beginning. His advisor was Johann
Wichmannshausen. My source for this is the catalog of the university
library at Halle-Wittenberg.
Wichmannshausen was primarily an orientalist, but his thesis was on a
topic in ethics. His advisor, Otto Mencke, founded the first academic
journal in Germany, titled Acta Eruditorum, jointly with Leibniz (the
journal existed 1682-1782). Otto Mencke should not be confused with his
grandson Friedrich Otto Mencke. Wichmannshausen was not only Mencke's
student, but also his son in law (this puts a twist on his thesis
title, Disputationem moralem de divortiis secundum ius naturae).
The Mathematics Genealogy Project lists Thomasius as Mencke's advisor.
This seems to make sense, but library catalog referenes for Mencke's
thesis do not mention any advisor.
The Mathematics Genealogy Project lists
Friedrich Leibniz (father of Gottfried Leibniz) as Thomasius' advisor, but
no thesis is referenced. The library in Erfurt has a thesis submitted in
Leipzig by "Jacob Thomae," under the direction of Andreas Schwartz. I
suspect that "Thomae" and Thomasius are the same person (it was common for
names to exist in several variants), but I am not sure.
Martin Ohm is
the brother of "the" Ohm. For an interesting piece of trivia, check
this web site, which discusses after which Ohm the Ohmstrasse in
Berlin is named.
Von Langsdorf is known for contributions to mechanical and
A town in Mecklenburg was named after him in 1816.
Encke is known as an astronomer. He had no doctorate, but studied under
Lichtenberg is known not only as a physicist, but also as a writer.
He is famous for quotes like the following: "When a book and a head
and there is a hollow sound, is it always from the book?"
The Mathematics Genealogy Project does not list any year for Poisson
and Fourier; the years I have listed for them and their predecessors are
years of "graduation." No
formal doctoral thesis seems to have been involved; this issue created
quite a stir when Dirichlet returned to Germany after studying in Paris
and was looking for a position. The year listed for Dirichlet is that of
an honorary degree from the University of Bonn which resolved the dilemma.
The Mathematics Genealogy Project lists Lagrange as advisor for Poisson
and Fourier; according to biographies, they were also taught by Laplace,
and Fourier also by Monge.
D'Alembert attended the
College des Quatre Nations, also known under the name College Mazarin
(the "four nations" refer to territories acquired by France in the Thirty
Caron taught mathematics there from lecture notes by Pierre Varignon,
who had been his predecessor in the position. Most sources
do not give Caron's
first name (some spell him with two rs). I found the name
Leonor in the abstract of an article. It seems a little odd,
since Leonor is usually a female name. Biographies
also mention that the mathematics classes d'Alembert took in
college were quite elementary, but d'Alembert took advantage of the
excellent library of the college. It appears that d'Alembert had no
Monge studied under Bossut while he was employed as a draftsman at
the military school in Mezieres. Before that, Monge did so well as a
student in Lyon that he was hired to teach the physics course. I have not
found much on Bossut's education; a biography says he was educated in Lyon
and then became a student of d'Alembert. No specifics of when, where and
how are given. Bossut collaborated extensively with d'Alembert later in
his life. 1752 is the year he started his position at Mezieres.
The Mathematics Genealogy project lists Euler as Lagrange's
advisor. Indeed, Euler did give substantial advice to Lagrange,
although all of it was by mail. Lagrange
studied Euler's work and corresponded extensively with him during the
time when he wrote his early papers. Euler was also
important in promoting Lagrange's career.
This is why Euler is often viewed as his
"advisor," even though Euler was in Berlin and Lagrange was in Torino.
Beccaria was Lagrange's most important teacher at the University of Torino.
Beccaria was a physicist known for his investigations on electricity;
he corresponded with Benjamin Franklin. The year listed for Lagrange is
that of his first mathematical paper. Beccaria's first name is an assumed name
as is the custom in Catholic orders; his original name was Francesco.
Jakob Bernoulli had a degree in theology, which he was made to
study by his father. His advisor in theology was Peter Werenfels. He
studied mathematics and astronomy on the
side, and he continued his mathematical studies
while traveling in France, the
Netherlands and England 1676-82. Malebranche, Hudde, Hooke and Boyle were
his most important teachers during this time. Johann Bernoulli got a
degree in medicine under Nikolaus Eglinger.
Malebranche studied theology at the Sorbonne and then continued his studies
at the Congregation of the Oratory (a school for priests), where he became a priest in
1664. Richard Simon is mentioned in biographies as his teacher at the Oratory.
Simon was later expelled from the Oratory because he questioned Moses' authorship
of the Pentateuch.
In 1664, Malebranche became interested in Descartes' work, which
led him to mathematics. Malebranche had no formal instruction in
mathematics, but he had many meetings with
Leibniz, who was in Paris as a diplomat
1672-76 (Leibniz invented the calculus during the later part of this
Malebranche is primarily remembered as a philosopher, but he also taught
mathematics beginning in 1674.
Leibniz studied philosophy and law in Leipzig. He applied for a
doctorate in law in 1666, but was refused because he was considered too
young (he was 20). He then went to Altdorf, where he immediately got his
doctorate and was offered a professorship as well (he did not accept).
His advisors in Leipzig were Schwendendoerffer for law and Thomasius
for philosophy. As a student, Leibniz
learned mathematics for a semester under Erhard Weigel in Jena. He
continued his mathematical studies under Huygens while he was in Paris
Pell's name is associated primarily with Pell's equation, which,
however, is misnamed. Pell mentioned the equation in a book after Fermat
wrote to him about it; he did no original work on the equation. Euler
cited Pell's book as a reference a century later. Pell's other claim to
fame is that he introduced one of the commonly used symbols for division
(the "obelus," which looks like a colon divided by a horizontal line);
the symbol was used both by Pell and by a Swiss mathematician named Rahn.
Pell and Rahn corresponded with each other; it is unknown whether Pell
or Rahn invented the symbol.
Wilhelm Schmuck was Leibniz' grandfather. The word "Schmuck" means
adornment or jewelry in German; it has nothing to do with a derogatory
term of American slang.
Georg Schwendendoerffer and his predecessors all have two theses,
usually separated by about two years. I do not know what the underlying
system was; where I found both theses, I used the later date.
Johann Hudde was mayor of Amsterdam for thirty years.
There are two Frans van Schootens, father and son, who were both
professors in Leiden. The one in the table is the
son. Van Schooten also taught Huygens during the early part of his
Jacob Gool (also known under the Latinized form Jacobus Golius) was
Professor of Oriental Studies, in addition to being Professor of
Mathematics. He studied both subjects in Leiden, where he also became a
professor. 1616 is the year he graduated in mathematics; he graduated in
oriental studies in 1621. Gool's advisor in oriental studies was Thomas
van Erpe. His mathematical advisor was Willebrord Snell.
Scaliger is known primarily as a philologist. He studied law under
Cujas after learning Greek in self-study a decade earlier (he "could not
benefit" from Turnebe's lectures at the Sorbonne; I think that means he
flunked out). Cujas' advisor, Arnaud du Ferrier, became a high ranking
French diplomat. Scaliger is
also known for introducing the Julian date, a calendar counting days from
January 1, 4713 BC. The idea is that a single number, just counting the
number of days, removes the ambiguities posed by different calendars
used in various places at various times. In 1849, Scaliger's calendar was
John Herschel (the son of William Herschel who discovered Uranus) to date
Snell is known for the law of refraction in optics. His
degree in 1607 was in law. He studied and taught mathematics even
while he was a law student. His father Rudolph Snell was also his predecessor
of Mathematics at Leiden. Snell studied with Brahe and Kepler
while he visited Prague beginning in
1600. In Leiden, he studied with Ludolph van Ceulen,
who was the engineering professor.
Van Ceulen is known for calculating pi to 35 digits.
The record was surpassed soon after the calculus was invented, but in
Germany the name
"Ludolphische Zahl" survived into the twentieth century. Van Ceulen had
no university education. He was 60 when he became a professor; prior to that,
he ran a fencing school and also offered private tutoring in mathematics.
Tycho Brahe studied at a number of universities during the period
1559-1570 in a variety of subjects. He never obtained a degree.
Schultz is listed here because he is generally credited with having introduced
Brahe to astronomy. Schultz was actually Brahe's fellow student in
Brahe studied 1562-1565. Schultz studied mathematics in Leipzig under Hommel.
He obtained a degree in 1564, but in Wittenberg, not in Leipzig. I do not know
who his advisor was there.
Beeckman's doctorate in 1618 was in the field of medicine.
He did not practice as a doctor and is known for his work in
physics and mathematics. As a student, Beeckman took some
mathematics classes from Rudolph Snell, father of Willebrord
worked briefly with Beeckman before he enlisted to fight in the Thirty
Year War. According to Descartes' statements, the basis of his
philosophical ideas took shape after a dream he had while he was
a soldier in 1619. Whether he also began to develop his
mathematics at that point is a matter of speculation. Descartes
also had a long relationship with Marin Mersenne, which I would not
characterize as a student-teacher relation.
Perhaps a more accurate description is that Mersenne was
Boyle's education was in the hands of a private tutor from
Geneva named Isaac Marcombes. Boyle had no university education,
but he was awarded honorary degrees later.
Boyle and Marcombes visited Florence in 1642, where Boyle
studied Galilei's work; biographies emphasize this as a crucial
event for his future scientific career. He apparently
did not get to meet Galilei himself, who died during Boyle's visit.
According to the Dictionary of Scientific Biography, it is
conjectured but uncertain
that Tartaglia was Ricci's teacher. Tartaglia himself had no formal
instruction beyond the alphabet.
Maestlin studied mathematics and astronomy in Tuebingen under Apian; he completed
these studies in 1571. Subsequently, he also obtained a degree in theology
in 1574 under Heerbrand. Several web sites incorrectly identify Peter Apian
instead of his son Philipp as Maestlin's teacher.
Philipp Apian seems to owe
much of his mathematical education to his father, but also spent three years
traveling and studying in France. The Mathematics Genealogy Project lists
Johannes Sturm and Michael Beuther as "advisors" for this period. He
succeeded his father in Ingolstadt in 1552.
The University of Ingolstadt in the 15th/16th century is not connected to any
institution now in Ingolstadt. It was the state university of Bavaria, a
predecessor of the current University of Munich.
Philipp Apian eventually had to leave
Ingolstadt because he was a Protestant, and he was later fired from Tuebingen
because he refused to sign a document taking
sides in the arguments between Lutherans and Calvinists (the chancellor
of the university, Jacob Andreae, had contributed to determining the
"truth" in this
dispute, and he expected his faculty to support
the efforts of their administrators). Maestlin then became Apian's
successor. Jacob Andreae appears in Jacob
Bernoulli's theological ancestry.
Bebel studied Latin under Corvinus (a.k.a. Korwin, Rab) in Cracow and
finished his studies under Brant in Basel. Bebel brought Corvinus' works
with him to Basel and had them printed there. Corvinus obtained a masters degree
in 1488. His subsequent studies were strongly influenced by
Celtis, who was in Cracow 1489-91.
Sebastian Brant is best known for his satirical poem "Das
ship of fools). 1489 is the year of a doctorate in law.
Gabriel Biel is referred to as Luther's "teacher" by some sources.
Biel, however, was professor in Tuebingen until 1495 when he died; Luther
was 12 years old at this time. Luther was thoroughly familiar with Biel's
work. It is likely that Biel taught von Staupitz during the early part of
his studies. In addition to his work in theology, Biel is also known as an
economist (he was an early proponent of a market based economy).
Biel obtained a masters degree in Heidelberg in 1438 under Gummeringen.
More than a decade later, he was a student in Erfurt and another decade later in
Cologne. It is not known what degrees he obtained there. Becker was his
most important teacher in Erfurt.
Tannstetter obtained a masters degree in Ingolstadt in 1501. In 1503
he joined a group of scholars in Vienna led by Konrad Celtis. It
is likely that Tannstetter's
advisor in Ingolstadt was Stoeberer, who, according to some sources,
taught mathematics in Ingolstadt 1498-1502.
Celtis himself was in Ingolstadt 1491-97, and he was a strong influence on
Stoeberer (I do not know if he was his advisor in
a formal sense). Eventually, Celtis brought both Stoeberer
and Tannstetter to Vienna. Tannstetter pursued medicine in addition to
mathematics and became the emperor's personal physician. He obtained a
doctorate in medicine in 1513; I have found no information on who his
teacher was in that field. Tannstetter may have been drawn to medicine
because he saw it as a field of applications for astrology (scientists
still took astrology seriously a century after Tannstetter). In addition
to Stoeberer, Tannstetter also
referred to Andreas Stoeberl (Stiborius) as his teacher. Stoeberl seems to
have left Ingolstadt before Tannstetter was a student there, but he
was his colleague and collaborator in Vienna.
Celtis is known primarily as a poet. He obtained his master of arts
in Heidelberg under Agricola in 1485. Like many scholars of his era,
he subsequently became a lecturer, but at the same time also continued to
be a student. He studied Greek under Pomponius Laetus in Rome
and mathematics under Brudzewski in Cracow 1489-91.
Wojciech Brudzewski (who is also known under the name Albert Blar)
also taught Copernicus. Brudzewski continued
the work of Regiomontanus and his teacher Peurbach, but I have found no
evidence suggesting that Regiomontanus was ever Brudzewski's teacher.
Wikipedia says he was educated in Prague, and Regiomontanus did not teach
Rudolph Agricola was a leader of the humanist movement, known for his
expertise in Latin and Greek literature. His real name was Roelof Huysmann.
Agricola obtained a masters degree in Louvain (I found a reference which
claims Thomas a Kempis was his teacher there, but biographies of
Thomas a Kempis,
who was a monk, say nothing about him ever teaching at a university).
studied with Heynlin in Paris and then spent several years in
Italy, primarily in Ferrara. Some biographies of Agricola say that
he studied Greek under Theodorus Gaza there, but more recent sources
say his principal teacher of Greek in Ferrara was Battista Guarini, son
of Guarino da Verona. Biographies of Gaza contradict each other when it
comes to the final years of his life. According to some, he was in Ferrara
1476-78 and would have overlapped there with Agricola, according to others,
he died in Calabria in 1475.
1479 is the year Agricola left Italy and returned to the Netherlands.
The name Agricola was used by a number of other scholars of the 15th
and 16th centuries including the composer Alexander Agricola, the
geologist Georg Agricola, and the Protestant reformer Johannes
Agricola. It was customary at the time for scholars to use Latin or Greek
names which either referred to their place of origin or were attempts to
translate their names. For instance, Celtis' real name was Pickel and
Apian's was Bienewitz.
Biene is bee in German and apis is bee in Latin; I do not really believe,
however, that the origin of the name Bienewitz has anything to do with
bees. Celtis' Latin name is even more far-fetched.
He bases his choice on a passage from
the Book of Job (19:24): stilo ferreo et plumbi lammina vel certe
sculpantur in silice. Apparently, he had a version in which certe was
misspelled as celte, and he translates this (actually nonexistent) word as
chisel. A "Pickel" actually is not a chisel anyway, but a pickax.
Heynlin was the first German who was awarded a doctorate by the
Sorbonne, in 1472. They made him rector before that, in 1469. Jointly with
Guillaume Fichet, he started the first printing press in France. 1455 is
the year of a master of arts degree. A biography lists Lucas Desmoulin,
Thomas de Courcelles and Petrus de Vancello as Heynlin's most important
teachers in Paris. Thomas de Courcelles is the only one of the three on
whom I found further information. He was a well known theologian and
rector of the Sorbonne; he is primarily remembered, however, because he
was one of the judges at Joan of Arc's trial in 1431.
Battista Guarini seems to have been educated primarily by his father.
He should not be confused with his great-grandson who shares the same
Guarino da Verona studied Latin under Conversini and then
Chrysoloras in Constantinople; 1408 is the year he returned from there.
Lorenzo Valla is known for exposing the donation of Constantine,
which allegedly established the Vatican state, as a forgery.
Aurispa became professor of astrology in Bologna in 1392. He later
went to Constantinople to study Greek. His main contribution to posterity
is bringing back 238 manuscripts when he returned in 1423.
There seem to be three different people known as Giovanni da Ravenna.
Giovanni Conversini was the teacher of Guarino da Verona.
Giovanni Malpaghini, also from Ravenna, was a student of Petrarca, and a
third Giovanni was Petrarca's secretary.
Some sources in the literature have merged two or more of these into one.
site for a discussion. 1368 is the year Conversini is first mentioned
as a professor in Florence, his education must be prior to that.
say that Chrysoloras was a "pupil" of Plethon. I found no precise
explanation of what
that means; they were actually about the same age. Another source
mentions Kydones as Chrysoloras' teacher. Plethon (who named himself
after his favorite philosopher Plato) is said to have
studied at the Ottoman court in Adrianopolis (Edirne) under a Jewish teacher
named Helisseus (I also found the spelling Elisaius), about whom nothing else
seems to be known. Kydones was a Greek theologian who argued in favor
of Thomas Aquinas and closer ties between the Greek Orthodox and Roman
Catholic churches. This brought him in conflict with his former teacher
Petrarca was made to study law by his father. He had little interest
for the subject and instead concentrated on poetry and the classics. He
last studied in Bologna 1323-25. Biographies single out Cino da Pistoia
and Giovanni d'Andrea
as his most influential teachers. Barlaam di Seminara later taught
Petrarca Greek. Barlaam is known primarily as a theologian (he lost a
dispute in the Orthodox church and became a Catholic), but he also
contributed to mathematics and astronomy.
Cino da Pistoia had studied and practiced law, but he
was also a poet. The award of a doctorate in 1314 marks the beginning
of a university career, not the conclusion of his education. Cino was in his
forties and his teachers were dead at this time.
The elder Francesco d'Accorso is by far the more famous one as a law
scholar. It is
the son, however, who appears in Dante's hell. The conventional
explanation is for
sodomy, but I also found the explanations that he collected
too much interest from students whom he loaned money, that he improperly
benefited from his father's reputation or that he was a political
opportunist. The year 1215 is the year when the elder Francesco d'Accorso
began to teach as a law professor.
Guido de Baysio is infamous for his arguments why women cannot be
ordained as priests:
"Moreover, woman was the effective cause of damnation since she was the
origin of transgression and Adam was deceived through
her, and thus she cannot be the effective cause of salvation,
because holy orders causes grace in others and so salvation."
Guido da Suzzara was the defense lawyer at the trial of Conradin,
the last of the Hohenstaufen. Conradin was executed in 1268 after losing
a struggle for power against the pope.
Irnerius established a law school at Bologna in 1088; this date is
usually regarded as the beginning of the University of Bologna, the first
university of medieval Europe. Irnerius was a German whose
original name was Werner or Warner; Guarnerius is another variant
of his name. Irnerius and a certain Pepo who taught
law in Bologna before him are responsible for a revival of the study of
Roman law. It does not seem to be known if Pepo was in any way Irnerius'
teacher. Irnerius and his followers are known as the "glossators," because
of their comments or "glosses" on Roman law. These glosses were originally
inserted between the lines or in the margin of the text (in contrast to poor
Fermat, the glossators seem to have found enough space).
Major boo-boos: Not always does science progress from success to
success, and even famous people make mistakes. Some famous examples from
folks included in the table:
Scaliger claimed to have squared the circle.
Beccaria believed that earthquakes were an electrical phenomenon.
D'Alembert argued that the tides were the cause of the wind.
When Kepler derived his second law of planetary motion (the one about equal
areas), he made two errors which cancelled each other. He later realized this
and tried to explain why they cancelled. This explanation was also erroneous.