Thomas Joannes Stieltjes (, 29 December 1856 – 31 December 1894) was a Dutch mathematician. He was a pioneer in the field of
moment problems and contributed to the study of
continued fractions. The Thomas Stieltjes Institute for Mathematics at
Leiden University
Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a Public university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince o ...
, dissolved in 2011, was named after him, as is the
Riemann–Stieltjes integral.
Biography
Stieltjes was born in
Zwolle 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
harbour
A harbor (American English), harbour (British English; see spelling differences), or haven is a sheltered body of water where ships, boats, and barges can be docked. The term ''harbor'' is often used interchangeably with ''port'', which is a ...
s around
Rotterdam, and also seated in the
Dutch parliament. Stieltjes Jr. went to university at the Polytechnical School in
Delft
Delft () is a List of cities in the Netherlands by province, city and Municipalities of the Netherlands, municipality in the Provinces of the Netherlands, province of South Holland, Netherlands. It is located between Rotterdam, to the southeast, ...
in 1873. Instead of attending lectures, he spent his student years reading the works of
Gauss and
Jacobi Jacobi may refer to:
* People with the surname Jacobi (surname), Jacobi
Mathematics:
* Jacobi sum, a type of character sum
* Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations
* Jacobi eigenva ...
— 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
Hendricus Gerardus van de Sande Bakhuyzen (April 2, 1838, The Hague – January 8, 1923, Leiden) was a Dutch astronomer. His surname, van de Sande Bakhuyzen, is sometimes erroneously given as Backhuyzen or Bakhuysen. His first name is somet ...
(who was the director of
Leiden University
Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a Public university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince o ...
), 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. He 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 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
F, or f, is the sixth Letter (alphabet), letter in the Latin alphabet, used in the English alphabet, modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is English alphabet#Let ...
. From then until December of that year, he lectured on
analytical geometry and on
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 ...
. He resigned his post at the observatory at the end of that year.
In 1884, Stieltjes applied for a chair in
Groningen
Groningen (; gos, Grunn or ) is the capital city and main municipality of Groningen province in the Netherlands. The ''capital of the north'', Groningen is the largest place as well as the economic and cultural centre of the northern part of t ...
. 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
David Bierens de Haan
David Bierens de Haan (3 May 1822, in Amsterdam – 12 August 1895, in Leiden) was a Dutch mathematician and historian of science.
Biography
Bierens de Haan was a son of the rich merchant Abraham Pieterszoon de Haan (1795–1880) and Catharina Ja ...
arranged for an honorary doctorate to be granted to Stieltjes by
Leiden University
Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a Public university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince o ...
, enabling him to become a professor. In 1885, he was appointed as member of the
Royal Dutch Academy of Sciences (Koninklijke Nederlandse Akademie van Wetenschappen, KNAW), the next year he became foreign member.
In 1889, he was appointed professor of differential and integral calculus at Toulouse University.
Research
Stieltjes worked on almost all branches of
analysis,
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
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...
s. Other important contributions to mathematics that he made involved
discontinuous function
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in val ...
s and
divergent series,
differential equations,
interpolation
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points.
In engineering and science, one often has a n ...
, the
gamma function
In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except ...
and
elliptic functions
In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those i ...
. He became known internationally because of the
Riemann–Stieltjes integral.
Awards
Stieltjes' work on continued fractions earned him the
Ormoy Prize Ormoy is the name of four communes in France:
* Ormoy, Eure-et-Loir
* Ormoy, Haute-Saône
* Ormoy, Yonne
* Ormoy, Essonne
Ormoy () is a commune in the Essonne department in Île-de-France in northern France.
Population
Inhabitants of Ormoy ar ...
of the
Académie des Sciences.
See also
*
Chebyshev–Markov–Stieltjes inequalities In mathematical analysis, the Chebyshev–Markov–Stieltjes inequalities are inequalities related to the problem of moments that were formulated in the 1880s by Pafnuty Chebyshev and proved independently by Andrey Markov and (somewhat late ...
*
Lebesgue–Stieltjes integral
*
Laplace–Stieltjes transform
*
Riemann–Stieltjes integral
*
Heine–Stieltjes polynomials
In mathematics, the Heine–Stieltjes polynomials or Stieltjes polynomials, introduced by , are polynomial solutions of a second-order Fuchsian equation, a differential equation all of whose singularities are regular singularity, regular. The Fuc ...
*
Stieltjes–Wigert polynomials
In mathematics, Stieltjes–Wigert polynomials (named after Thomas Jan Stieltjes and Carl Severin Wigert) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, for the weight function
: w(x) = \frac x^ \exp(-k^2\l ...
*
Stieltjes polynomials
In mathematics, the Stieltjes polynomials ''E'n'' are polynomials associated to a family of orthogonal polynomials ''P'n''. They are unrelated to the Stieltjes polynomial solutions of differential equations. Stieltjes originally considered ...
*
Stieltjes constants
In mathematics, the Stieltjes constants are the numbers \gamma_k that occur in the Laurent series expansion of the Riemann zeta function:
:\zeta(s)=\frac+\sum_^\infty \frac \gamma_n (s-1)^n.
The constant \gamma_0 = \gamma = 0.577\dots is known a ...
*
Stieltjes matrix
*
Stieltjes moment problem In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (''m''0, ''m''1, ''m''2, ...) to be of the form
:m_n = \int_0^\infty x^n\,d\mu(x)
for some measure ''μ ...
*
Stieltjes transformation In mathematics, the Stieltjes transformation of a measure of density on a real interval is the function of the complex variable defined outside by the formula
S_(z)=\int_I\frac, \qquad z \in \mathbb \setminus I.
Under certain conditions we c ...
(and Stieltjes inversion formula)
*
Annales de la Faculté des Sciences de Toulouse co-founded by Stieltjes
*
Montel's theorem
References
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)
{{DEFAULTSORT:Stieltjes, Thomas Joannes
1856 births
1894 deaths
French mathematicians
Delft University of Technology faculty
Members of the Royal Netherlands Academy of Arts and Sciences
People from Zwolle
19th-century Dutch scientists
19th-century Dutch mathematicians