Thomas Joannes Stieltjes
Encyclopedia
Thomas Joannes Stieltjes (ˈstiltʃəs, 29 December 1856 – 31 December 1894) was a Dutch
mathematician
. He was born in Zwolle
and died in Toulouse
, France
. He was a pioneer in the field of moment problems and contributed to the study of continued fraction
s.
The Thomas Stieltjes Institute for Mathematics at the University of Leiden is named after him, as is the Riemann–Stieltjes integral.
on 29 December 1856. His father (who had the same first names) was a civil engineer
and politician
. Stieltjes Sr. was responsible for the construction of various harbours around Rotterdam
, and also seated in the Dutch parliament. Stieltjes Jr. went to university at the Polytechnical School in Delft
in 1873. Instead of attending lectures, he spent his student years reading the works of Gauss and Jacobi
— the consequence of this being he failed his examinations. There were 2 further failures (in 1875 and 1876), and his father despaired. His father was friends with H. G. van de Sande Bakhuyzen
(who was the director of Leiden University
), and Stieltjes Jr. was able to get a job as an assistant at Leiden Observatory.
Soon afterwards, Stieltjes began a correspondence with Charles Hermite
which lasted for the rest of his life. Stieltjes originally wrote to Hermite concerning celestial mechanics
, but the subject quickly turned to mathematics and he began to devote his spare time to mathematical research.
The director of Leiden Observatory, van de Sande-Bakhuyzen, responded quickly to Stieltjes' request on 1 January 1883 to stop his observational work to allow him to work more on mathematical topics. In 1883, he also married his Elizabeth Intveld in May. She also encouraged him to move from astronomy to mathematics. And in September, Stieltjes was asked to substitute at University of Delft for F J van den Berg. From then until December of that year, he lectured on analytical geometry and on descriptive geometry
. He resigned his post at the observatory at the end of that year.
In 1884, Stieltjes applied for a chair in Groningen. He was initially accepted, but in the end turned down by the Department of Education, since he lacked the required diplomas. In 1884, Hermite and professor Bierens de Haan arranged for an honorary doctorate to be granted to Stieltjes by Leiden University
, enabling him to become a professor. In 1885, he was honorably appointed as member of the Royal Dutch Academy of Sciences (Koninklijke Nederlandse Akademie van Wetenschappen, KNAW), and in 1889, he was appointed professor of differential and integral calculus at Toulouse University.
, continued fractions and number theory
, and for his work, he is sometimes called "the father of the analytic theory of continued fractions".
His work is also seen as important as a first step towards the theory of Hilbert space
s. Other important contributions to mathematics that he made involved discontinuous functions and divergent series
, differential equation
s, interpolation
, the gamma function
and elliptic functions.
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
mathematician
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. He was born in Zwolle
Zwolle
Zwolle is a municipality and the capital city of the province of Overijssel, Netherlands, 120 kilometers northeast of Amsterdam. Zwolle has about 120,000 citizens.-History:...
and died in Toulouse
Toulouse
Toulouse is a city in the Haute-Garonne department in southwestern FranceIt lies on the banks of the River Garonne, 590 km away from Paris and half-way between the Atlantic Ocean and the Mediterranean Sea...
, France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
. He was a pioneer in the field of moment problems and contributed to the study of continued fraction
Continued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...
s.
The Thomas Stieltjes Institute for Mathematics at the University of Leiden is named after him, as is the Riemann–Stieltjes integral.
Biography
Stieltjes was born in ZwolleZwolle
Zwolle is a municipality and the capital city of the province of Overijssel, Netherlands, 120 kilometers northeast of Amsterdam. Zwolle has about 120,000 citizens.-History:...
on 29 December 1856. His father (who had the same first names) was a civil engineer
Civil engineer
A civil engineer is a person who practices civil engineering; the application of planning, designing, constructing, maintaining, and operating infrastructures while protecting the public and environmental health, as well as improving existing infrastructures that have been neglected.Originally, a...
and politician
Politician
A politician, political leader, or political figure is an individual who is involved in influencing public policy and decision making...
. Stieltjes Sr. was responsible for the construction of various harbours around Rotterdam
Rotterdam
Rotterdam is the second-largest city in the Netherlands and one of the largest ports in the world. Starting as a dam on the Rotte river, Rotterdam has grown into a major international commercial centre...
, and also seated in the Dutch parliament. Stieltjes Jr. went to university at the Polytechnical School in Delft
Delft
Delft is a city and municipality in the province of South Holland , the Netherlands. It is located between Rotterdam and The Hague....
in 1873. Instead of attending lectures, he spent his student years reading the works of Gauss and Jacobi
Carl Gustav Jakob Jacobi
Carl Gustav Jacob Jacobi was a German mathematician, widely considered to be the most inspiring teacher of his time and is considered one of the greatest mathematicians of his generation.-Biography:...
— the consequence of this being he failed his examinations. There were 2 further failures (in 1875 and 1876), and his father despaired. His father was friends with H. G. van de Sande Bakhuyzen
H. G. van de Sande Bakhuyzen
Hendricus Gerardus van de Sande Bakhuyzen was a Dutch astronomer. His surname, van de Sande Bakhuyzen, is sometimes erroneously given as Backhuyzen or Bakhuysen. His first name is sometimes given as Hendrik Gerard...
(who was the director of Leiden University
Leiden University
Leiden University , located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, leader of the Dutch Revolt in the Eighty Years' War. The royal Dutch House of Orange-Nassau and Leiden University still have a close...
), and Stieltjes Jr. was able to get a job as an assistant at Leiden Observatory.
Soon afterwards, Stieltjes began a correspondence with Charles Hermite
Charles Hermite
Charles Hermite was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra....
which lasted for the rest of his life. Stieltjes originally wrote to Hermite concerning celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
, but the subject quickly turned to mathematics and he began to devote his spare time to mathematical research.
The director of Leiden Observatory, van de Sande-Bakhuyzen, responded quickly to Stieltjes' request on 1 January 1883 to stop his observational work to allow him to work more on mathematical topics. In 1883, he also married his Elizabeth Intveld in May. She also encouraged him to move from astronomy to mathematics. And in September, Stieltjes was asked to substitute at University of Delft for F J van den Berg. From then until December of that year, he lectured on analytical geometry and on descriptive geometry
Descriptive geometry
Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art...
. He resigned his post at the observatory at the end of that year.
In 1884, Stieltjes applied for a chair in Groningen. He was initially accepted, but in the end turned down by the Department of Education, since he lacked the required diplomas. In 1884, Hermite and professor Bierens de Haan arranged for an honorary doctorate to be granted to Stieltjes by Leiden University
Leiden University
Leiden University , located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, leader of the Dutch Revolt in the Eighty Years' War. The royal Dutch House of Orange-Nassau and Leiden University still have a close...
, enabling him to become a professor. In 1885, he was honorably appointed as member of the Royal Dutch Academy of Sciences (Koninklijke Nederlandse Akademie van Wetenschappen, KNAW), and in 1889, he was appointed professor of differential and integral calculus at Toulouse University.
Research
Stieltjes worked on almost all branches of analysisMathematical 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...
, continued fractions and 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...
, and for his work, he is sometimes called "the father of the analytic theory of continued fractions".
His work is also seen as important as a first step towards the theory of Hilbert space
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
s. Other important contributions to mathematics that he made involved discontinuous functions and divergent series
Divergent series
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a limit....
, 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, interpolation
Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
, the gamma function
Gamma function
In mathematics, the gamma function is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers...
and elliptic functions.
Awards
Stieltjes' work on continued fractions earned him the Ormoy Prize of the Académie des Sciences.See also
- Lebesgue–Stieltjes integral
- Laplace–Stieltjes transform
- Riemann–Stieltjes integral
- Stieltjes matrixStieltjes matrixIn mathematics, particularly matrix theory, a Stieltjes matrix, named after Thomas Joannes Stieltjes, is a real symmetric positive definite matrix with nonpositive off-diagonal entries. A Stieltjes matrix is necessarily an M-matrix...
- Stieltjes moment problem
- Stieltjes–Wigert polynomials
- Chebyshev–Markov–Stieltjes inequalities
- Annales de la Faculté des Sciences de ToulouseAnnales de la Faculté des Sciences de ToulouseThe Annales de la Faculté des Sciences de Toulouse is aninternational peer reviewed scientific journal, in the domain of mathematics research. Its ISSN is 0240-2963....
co-founded by Stieltjes
External links
- Œuvres complètes de Thomas Jan Stieltjes, pub. par les soins de la Société mathématique d'Amsterdam. (Groningen: P. Noordhoff, 1914–18) (PDF copy at UMDL, text in Dutch, French and German)