Theodor Molien
Encyclopedia
Theodor Molien or Fedor Eduardovich Molin (September 10, 1861 - December 25, 1941) was a Baltic-German mathematician
. He was born in Riga
, Latvia
, which at that time was a part of Russian Empire
. Molien studied associative algebra
s and polynomial
invariant
s of finite groups
.
(in German
Kaiserliche Universität Dorpat) as a student of astronomy
. To support his studies his family also moved to Tartu. In October 1883 the council of the university gave him the degree of a candidate of astronomy. His thesis "Bahn des Cometen 1880 III" was published in Astronomische Nachrichten No. 2510. His further work was supervised by the head of the chair of applied mathematics
of the University of Tartu Anders Lindstedt
. In a report to the Faculty of Physics and Mathematics of the University of Tartu Lindstedt akcnowledges Molien as having unquestionably exceptional scientific talent (unzweifelhaft ungewöhnliche wissenschaftliche Begabung).
In the autumn of 1883, as part of his studies Molien was sent to Leipzig
for three semesters. There he attended lectures by Felix Klein
on different fields of mathematics and worked in his seminar. He also attended lectures of Carl Neumann
, Eduard Study
, Wilhelm Killing
and Georg Scheffers
. At that time Klein was dealing with deep problems of algebra
and theory of functions of a complex variable
. Following his suggestion, Molien started to study linear transformations of elliptic function
s. The obtained results he submitted to the Faculty of Physics and Mathematics of the University of Tartu as a master thesis titled "Ueber die lineare Transformation der elliptischen Functionen". In spring 1885 Molien passed the master's exams and after the defence in the autumn of 1885 he obtained the scientific degree of a Master of Mathematics. In November 1885 he became a docent at the University of Tartu. This position he held for 15 years.
Summers (that were free from teaching) of 1886, 1888 and 1889 Molien spent in scientific centers of Germany
. His interest concentrated on so-called higher complex numbers (nowadays called hypercomplex number
s). His studies resulted in his article "Über Systeme höherer komplexer Zahlen" ("On systems of higher complex numbers"), published in 1891 in Mathematische Annalen
.
On September 30, 1892, Molien defended his dissertation, also titled "Über Systeme höherer komplexer Zahlen". He got the degree of a doctor of pure mathematics. The importance of his work was acknowledged by Georg Frobenius, Sophus Lie
and other mathematicians. One of the main results of his dissertation sounds in modern terms as follows: every simple associative algebra
over the field
of complex number
s is isomorphic to the algebra of square matrices
of a suitable order over the same field.
For his scientific achievements, in 1892 Molien was elected a member of Moscow Mathematical Society
. In 1894 French mathematicians awarded him a golden medal dedicated to the seventieth birthday of Charles Hermite. During Tartu years, Molien had mathematical correspondence with Frobenius
and Hurwitz
.
Since the University of Tartu had only one professorship in pure mathematics, Molien had to stay for years at docent's position. Being a docent in Tartu, Molien prepared and gave different lecture courses: Theory of analytic
and elliptic function
s, modern geometry and algebra, theory of algebraic equations, number theory
, projective geometry
, theory of quaternion
s, history of mathematics
and others. Some of these courses were new for the university.
In 1887 Russian powers decided to change the language of secondary and higher education in Baltic governorates from German
to Russian
with the deadline January 1, 1895. With the purpose of improving his Russian language, Molien was sent to Moscow
for the year 1892.
, but in the starting Tomsk Technological Institute
in Siberia
. He became the first professor of mathematics in Siberia. His was given a task of organizing teaching mathematics at the institute. In Tomsk
, besides giving courses in mathematical analysis
and differential equation
s, he wrote textbooks and exercise books on these subjects, and also established a mathematical library at the institute.
Known for his oppositional political views, he had to retire in 1913. Since 1914, Molien was a professor at higher Siberian courses for women in Tomsk, and when in 1917 the faculty of physics and mathematics was opened at the Tomsk State University
, he got a professorship there, and stayed at that university until his death on December 25, 1941.
In Tomsk Molien spent 41 years of his life. These years were scientifically not as fruitful as earlier years.
He got the title of Honoured Worker of Science.
. In 1897-1898 he was in correspondence with a leading Russian chess player Mikhail Chigorin
. He was one of the strongest chess players in Dorpat and was particularly known for his blindfold play (Ken Whyld, personal communication, 1995). He was president of the Dorpat chess club, and several of his games were published in the chess journal Baltische Schachblätter (edited by Friedrich Amelung
). In 1898 Molien published four chess studies.
To 1895 dates his manuscript "On theory of assigning prizes in tournaments".
Molien had also talent for languages. He knew German
, Estonian
, French
, Swedish
already before he entered gymnasium where he learned Greek
, Hebrew
, Latin
, English
, Italian
. Later he learned Spanish
, Portuguese
, Dutch
, Norwegian
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He was born in Riga
Riga
Riga is the capital and largest city of Latvia. With 702,891 inhabitants Riga is the largest city of the Baltic states, one of the largest cities in Northern Europe and home to more than one third of Latvia's population. The city is an important seaport and a major industrial, commercial,...
, Latvia
Latvia
Latvia , officially the Republic of Latvia , is a country in the Baltic region of Northern Europe. It is bordered to the north by Estonia , to the south by Lithuania , to the east by the Russian Federation , to the southeast by Belarus and shares maritime borders to the west with Sweden...
, which at that time was a part of Russian Empire
Russian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...
. Molien studied associative algebra
Associative algebra
In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R...
s and polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
invariant
Invariant (mathematics)
In mathematics, an invariant is a property of a class of mathematical objects that remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually indicated by the context in which the term is used...
s of finite groups
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...
.
Youth in Riga
Theodor Molien's father Eduard Molien was a teacher at the Riga Governorate Gymnasium. Theodor entered that gymnasium in 1872 and graduated in 1879.Studies and work in Tartu
In January 1880 Molien entered the Faculty of Physics and Mathematics of the University of TartuUniversity of Tartu
The University of Tartu is a classical university in the city of Tartu, Estonia. University of Tartu is the national university of Estonia; it is the biggest and highest-ranked university in Estonia...
(in German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
Kaiserliche Universität Dorpat) as a student of astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
. To support his studies his family also moved to Tartu. In October 1883 the council of the university gave him the degree of a candidate of astronomy. His thesis "Bahn des Cometen 1880 III" was published in Astronomische Nachrichten No. 2510. His further work was supervised by the head of the chair of applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
of the University of Tartu Anders Lindstedt
Anders Lindstedt
Anders Lindstedt was a Swedish mathematician, astronomer, and actuarial scientist, known for the Lindstedt-Poincaré method.- Life and work :...
. In a report to the Faculty of Physics and Mathematics of the University of Tartu Lindstedt akcnowledges Molien as having unquestionably exceptional scientific talent (unzweifelhaft ungewöhnliche wissenschaftliche Begabung).
In the autumn of 1883, as part of his studies Molien was sent to Leipzig
Leipzig
Leipzig Leipzig has always been a trade city, situated during the time of the Holy Roman Empire at the intersection of the Via Regia and Via Imperii, two important trade routes. At one time, Leipzig was one of the major European centres of learning and culture in fields such as music and publishing...
for three semesters. There he attended lectures by Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
on different fields of mathematics and worked in his seminar. He also attended lectures of Carl Neumann
Carl Neumann
Carl Gottfried Neumann was a German mathematician.Neumann was born in Königsberg, Prussia, as the son of the mineralogist, physicist and mathematician Franz Ernst Neumann , who was professor of mineralogy and physics at Königsberg University...
, Eduard Study
Eduard Study
Eduard Study was a German mathematician known for work on invariant theory of ternary forms and for the study of spherical trigonometry. He is also known for contributions to space geometry, hypercomplex numbers, and criticism of early physical chemistry.Study was born in Coburg in the Duchy of...
, Wilhelm Killing
Wilhelm Killing
Wilhelm Karl Joseph Killing was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry....
and Georg Scheffers
Georg Scheffers
Georg Scheffers was a German mathematician specializing in differential geometry. He was born on November 21, 1899 in the village of Altendorf near Holzminden . Scheffers began his university career at the University of Leipzig where he studied with Felix Klein and Sophus Lie...
. At that time Klein was dealing with deep problems of algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
and theory of functions of a complex variable
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
. Following his suggestion, Molien started to study linear transformations of elliptic function
Elliptic function
In complex analysis, an elliptic function is a function defined on the complex plane that is periodic in two directions and at the same time is meromorphic...
s. The obtained results he submitted to the Faculty of Physics and Mathematics of the University of Tartu as a master thesis titled "Ueber die lineare Transformation der elliptischen Functionen". In spring 1885 Molien passed the master's exams and after the defence in the autumn of 1885 he obtained the scientific degree of a Master of Mathematics. In November 1885 he became a docent at the University of Tartu. This position he held for 15 years.
Summers (that were free from teaching) of 1886, 1888 and 1889 Molien spent in scientific centers of Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
. His interest concentrated on so-called higher complex numbers (nowadays called hypercomplex number
Hypercomplex number
In mathematics, a hypercomplex number is a traditional term for an element of an algebra over a field where the field is the real numbers or the complex numbers. In the nineteenth century number systems called quaternions, tessarines, coquaternions, biquaternions, and octonions became established...
s). His studies resulted in his article "Über Systeme höherer komplexer Zahlen" ("On systems of higher complex numbers"), published in 1891 in Mathematische Annalen
Mathematische Annalen
Mathematische Annalen is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann...
.
On September 30, 1892, Molien defended his dissertation, also titled "Über Systeme höherer komplexer Zahlen". He got the degree of a doctor of pure mathematics. The importance of his work was acknowledged by Georg Frobenius, Sophus Lie
Sophus Lie
Marius Sophus Lie was a Norwegian mathematician. He largely created the theory of continuous symmetry, and applied it to the study of geometry and differential equations.- Biography :...
and other mathematicians. One of the main results of his dissertation sounds in modern terms as follows: every simple associative algebra
Associative algebra
In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R...
over the field
Field (mathematics)
In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms...
of complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s is isomorphic to the algebra of square matrices
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
of a suitable order over the same field.
For his scientific achievements, in 1892 Molien was elected a member of Moscow Mathematical Society
Moscow Mathematical Society
The Moscow Mathematical Society is a society of Moscow mathematicians aimed at the development of mathematics in Russia.The first meeting of the society was . Nikolai Brashman was the first president of MMO. Victor Vassiliev is the current president of MMO....
. In 1894 French mathematicians awarded him a golden medal dedicated to the seventieth birthday of Charles Hermite. During Tartu years, Molien had mathematical correspondence with Frobenius
Ferdinand Georg Frobenius
Ferdinand Georg Frobenius was a German mathematician, best known for his contributions to the theory of differential equations and to group theory...
and Hurwitz
Adolf Hurwitz
Adolf Hurwitz was a German mathematician.-Early life:He was born to a Jewish family in Hildesheim, former Kingdom of Hannover, now Lower Saxony, Germany, and died in Zürich, in Switzerland. Family records indicate that he had siblings and cousins, but their names have yet to be confirmed...
.
Since the University of Tartu had only one professorship in pure mathematics, Molien had to stay for years at docent's position. Being a docent in Tartu, Molien prepared and gave different lecture courses: Theory of analytic
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others...
and elliptic function
Elliptic function
In complex analysis, an elliptic function is a function defined on the complex plane that is periodic in two directions and at the same time is meromorphic...
s, modern geometry and algebra, theory of algebraic equations, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, projective geometry
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
, theory of quaternion
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...
s, history of mathematics
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
and others. Some of these courses were new for the university.
In 1887 Russian powers decided to change the language of secondary and higher education in Baltic governorates from German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
to Russian
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
with the deadline January 1, 1895. With the purpose of improving his Russian language, Molien was sent to Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
for the year 1892.
Career in Tomsk
Only in December 1900 Molien was given a professor's position, but not in TartuTartu
Tartu is the second largest city of Estonia. In contrast to Estonia's political and financial capital Tallinn, Tartu is often considered the intellectual and cultural hub, especially since it is home to Estonia's oldest and most renowned university. Situated 186 km southeast of Tallinn, the...
, but in the starting Tomsk Technological Institute
Tomsk Polytechnic University
Tomsk Polytechnic University in Tomsk, Russia, is the oldest technical university in Russia east of the Urals. The university was founded in 1896 and opened in 1900 as the Tomsk Technological Institute. In 1923, the school was renamed the Siberian Technological Institute and in 1930, the institute...
in Siberia
Siberia
Siberia is an extensive region constituting almost all of Northern Asia. Comprising the central and eastern portion of the Russian Federation, it was part of the Soviet Union from its beginning, as its predecessor states, the Tsardom of Russia and the Russian Empire, conquered it during the 16th...
. He became the first professor of mathematics in Siberia. His was given a task of organizing teaching mathematics at the institute. In Tomsk
Tomsk
Tomsk is a city and the administrative center of Tomsk Oblast, Russia, located on the Tom River. One of the oldest towns in Siberia, Tomsk celebrated its 400th anniversary in 2004...
, besides giving courses in mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
and differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s, he wrote textbooks and exercise books on these subjects, and also established a mathematical library at the institute.
Known for his oppositional political views, he had to retire in 1913. Since 1914, Molien was a professor at higher Siberian courses for women in Tomsk, and when in 1917 the faculty of physics and mathematics was opened at the Tomsk State University
Tomsk State University
Tomsk State University , formerly Imperial Tomsk University, is the first university in Siberia—it was founded in 1878 in Tomsk, Russia. TSU opened in 1888 with only one department, the medical school...
, he got a professorship there, and stayed at that university until his death on December 25, 1941.
In Tomsk Molien spent 41 years of his life. These years were scientifically not as fruitful as earlier years.
He got the title of Honoured Worker of Science.
Works
- Bahn des Cometen 1880 III (candidates thesis), Astron. Nachr. Bd. 105, No. 2519.
- Ueber Systeme höherer complexer Zahlen: eine behufs Erlangung des Grades eines Doctors der reinen Mathematik der physico-mathematischen Fakultät der Kaiserl. Universität Dorpat (dissertation), Tartu, 1892. (full text)
- Ueber die lineare Transformation der elliptischen Functionen: eine zur Erlangung des Grades eines Magisters der Mathematik der physico-mathematischen Facultät der Kaiserlichen Universität Dorpat (master's thesis), Tartu, 1885, 23 pp.
Other interests
Molien was interested in chessChess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
. In 1897-1898 he was in correspondence with a leading Russian chess player Mikhail Chigorin
Mikhail Chigorin
Mikhail Ivanovich Chigorin also was a leading Russian chess player...
. He was one of the strongest chess players in Dorpat and was particularly known for his blindfold play (Ken Whyld, personal communication, 1995). He was president of the Dorpat chess club, and several of his games were published in the chess journal Baltische Schachblätter (edited by Friedrich Amelung
Friedrich Amelung
Friedrich Ludwig Balthasar Amelung was a Baltic German chess player, endgame composer, and journalist.Amelung was born at Võisiku manor in Governorate of Livonia of the Russian Empire . He played a few games with Adolf Anderssen, Gustav Neumann, Carl Mayet, Emil Schallopp, Andreas Ascharin,...
). In 1898 Molien published four chess studies.
To 1895 dates his manuscript "On theory of assigning prizes in tournaments".
Molien had also talent for languages. He knew German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
, Estonian
Estonian language
Estonian is the official language of Estonia, spoken by about 1.1 million people in Estonia and tens of thousands in various émigré communities...
, French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
, Swedish
Swedish language
Swedish is a North Germanic language, spoken by approximately 10 million people, predominantly in Sweden and parts of Finland, especially along its coast and on the Åland islands. It is largely mutually intelligible with Norwegian and Danish...
already before he entered gymnasium where he learned Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
, Hebrew
Hebrew language
Hebrew is a Semitic language of the Afroasiatic language family. Culturally, is it considered by Jews and other religious groups as the language of the Jewish people, though other Jewish languages had originated among diaspora Jews, and the Hebrew language is also used by non-Jewish groups, such...
, Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
, English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
, Italian
Italian language
Italian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
. Later he learned Spanish
Spanish language
Spanish , also known as Castilian , is a Romance language in the Ibero-Romance group that evolved from several languages and dialects in central-northern Iberia around the 9th century and gradually spread with the expansion of the Kingdom of Castile into central and southern Iberia during the...
, Portuguese
Portuguese language
Portuguese is a Romance language that arose in the medieval Kingdom of Galicia, nowadays Galicia and Northern Portugal. The southern part of the Kingdom of Galicia became independent as the County of Portugal in 1095...
, Dutch
Dutch language
Dutch is a West Germanic language and the native language of the majority of the population of the Netherlands, Belgium, and Suriname, the three member states of the Dutch Language Union. Most speakers live in the European Union, where it is a first language for about 23 million and a second...
, Norwegian
Norwegian language
Norwegian is a North Germanic language spoken primarily in Norway, where it is the official language. Together with Swedish and Danish, Norwegian forms a continuum of more or less mutually intelligible local and regional variants .These Scandinavian languages together with the Faroese language...
.