Thomas Joannes Stieltjes (, 29 December 1856 – 31 December 1894) was a Dutch mathematician. He was a pioneer in the field of
moment problem
In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure ''μ'' to the sequences of moments
:m_n = \int_^\infty x^n \,d\mu(x)\,.
More generally, one may consider
:m_n = \int_^\infty M_n(x) ...
s and contributed to the study of
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 ...
s. The Thomas Stieltjes Institute for Mathematics at
Leiden University, dissolved in 2011, was named after him, as is the
Riemann–Stieltjes integral
In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was first published in 1894 by Stieltjes. It serves as an inst ...
.
Biography
Stieltjes was born in
Zwolle
Zwolle () is a city and municipality in the Northeastern Netherlands. It is the capital of the province of Overijssel and the province's second-largest municipality after Enschede with a population of 130,592 as of 1 December 2021. Zwolle is on ...
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
Rotterdam ( , , , lit. ''The Dam on the River Rotte'') is the second largest city and municipality in the Netherlands. It is in the province of South Holland, part of the North Sea mouth of the Rhine–Meuse–Scheldt delta, via the ''"Ne ...
, and also seated in the
Dutch parliament
The States General of the Netherlands ( nl, Staten-Generaal ) is the supreme bicameral legislature of the Netherlands consisting of the Senate () and the House of Representatives (). Both chambers meet at the Binnenhof in The Hague.
The States ...
. 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
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
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
Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
Hermi ...
which lasted for the rest of his life. He originally wrote to Hermite concerning
celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
, but the subject quickly turned to mathematics and he began to devote his spare time to mathematical research.
The director of
Leiden
Leiden (; in English and archaic Dutch also Leyden) is a city and municipality in the province of South Holland, Netherlands. The municipality of Leiden has a population of 119,713, but the city forms one densely connected agglomeration wi ...
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. From then until December of that year, he lectured on
analytical geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and engineer ...
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
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, enabling him to become a professor. In 1885, he was appointed as member of the
Royal Dutch Academy of Sciences
The Royal Netherlands Academy of Arts and Sciences ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed ...
(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
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...
,
continued fractions
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 ...
and
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...
, 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 spaces. 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
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 finite limit.
If a series converges, the individual terms of the series mus ...
,
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s,
interpolation, 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. He became known internationally because of the
Riemann–Stieltjes integral
In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was first published in 1894 by Stieltjes. It serves as an inst ...
.
Awards
Stieltjes' work on continued fractions earned him the
Ormoy Prize of the
Académie des Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...
.
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 The Laplace–Stieltjes transform, named for Pierre-Simon Laplace and Thomas Joannes Stieltjes, is an integral transform similar to the Laplace transform. For real-valued functions, it is the Laplace transform of a Stieltjes measure, however it is ...
*
Riemann–Stieltjes integral
In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was first published in 1894 by Stieltjes. It serves as an inst ...
*
Heine–Stieltjes polynomials
*
Stieltjes–Wigert polynomials
*
Stieltjes polynomials
*
Stieltjes constants
*
Stieltjes matrix In 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. Every ''n× ...
*
Stieltjes moment problem
*
Stieltjes transformation (and Stieltjes inversion formula)
*
Annales de la Faculté des Sciences de Toulouse
The ''Annales de la Faculté des Sciences de Toulouse'' is a peer-reviewed scientific journal covering all fields of mathematics. Articles are written in English or French. It is published by the Institut de Mathématiques de Toulouse and edited wi ...
co-founded by Stieltjes
*
Montel's theorem
In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after French mathematician Paul Montel, and give conditions under which a family of holomorphic ...
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