Thomas Joannes Stieltjes: Difference between revisions

Revision as of 19:16, 7 September 2006

Latest revision as of 20:22, 8 August 2025

(115 intermediate revisions by 81 users not shown)

Line 1:

{{Short description|Dutch mathematician (1856-1894)}}

:''This article is about Thomas Joannes Stieltjes, the mathematician. For his father, the Dutch engineer and politician, see [[Thomas Joannes Stieltjes Snr.]]''

{{Use dmy dates|date=April 2020}}

[[Image:ThomasStieltjes.jpeg|thumb|200px|Thomas Joannes Stieltjes, "the father of the analytic theory of [[continued fractions]]"]]

{{Infobox scientist

'''Thomas Joannes Stieltjes''' ([[December 29]], [[1856]] - [[December 31]], [[1894]]) was a [[Netherlands|Dutch]] [[mathematics|mathematician]]. He was born in [[Zwolle]] and died in [[Toulouse]], [[France]]. He was a pioneer in the field of [[moment problem]]s and contributed to the study of [[continued fraction]]s.

| name = Thomas Joannes Stieltjes

| image = Thomas Joannes Stieltjes.jpg

The Thomas Stieltjes Institute for Mathematics at the [[University of Leiden]] is named after him, as is the [[Riemann-Stieltjes integral]].

| image_size =

| caption =

| birth_date = {{birth date|1856|12|29|df=y}}

| birth_place = [[Zwolle]], Netherlands

| death_date = {{death date and age|1894|12|31|1856|12|29|df=y}}

| death_place = [[Toulouse]], France

| nationality = Dutch

| field = [[Mathematics]]

| work_institution = [[TU Delft]]<br>[[University of Leiden]]

| alma_mater = [[École Normale Supérieure]]

| doctoral_advisor = [[Charles Hermite]]<br>[[Jean Gaston Darboux]]

| doctoral_students =

| known_for =

* [[Lebesgue-StieltjesRiemann–Stieltjes integral]]

* [[Lebesgue–Stieltjes integration]]

* [[RiemannLebesgue-Stieltjes integralmeasure]]

* [[Laplace-Stieltjes transformconstants]]

* [[Stieltjes matrix]]

* [[Stieltjes transformation]]

* [[Stieltjes polynomials]]

* [[Laplace–Stieltjes transform]]

* [[Stieltjes–Wigert polynomials]]

* [[Chebyshev–Markov–Stieltjes inequalities]]

* [[Heine–Stieltjes polynomials]]

* [[Stieltjes moment problem]]

* [[Fourier-Stieltjes algebra]]

* [[Henstock-Kurzweil-Stieltjes integral]]

* [[Mertens conjecture]]

* [[Montel's theorem|Stieltjes–Osgood theorem]]

| prizes =

| footnotes =

}}

'''Thomas Joannes Stieltjes''' ({{IPAc-en|ˈ|s|t|iː|l|tʃ|ə|z}} {{respell|STEEL|chəz}},<ref>{{cite OED|Stieltjes integral|2321521871}}</ref> {{IPA|nl|ˈtoːmɑ ˈstiltɕəs|lang}}; 29 December 1856 – 31 December 1894) was a Dutch [[mathematician]]. He was a pioneer in the field of [[moment problem]]s and contributed to the study of [[continued fraction]]s. The Thomas Stieltjes Institute for Mathematics at [[Leiden University]], dissolved in 2011, was named after him, as is the [[Riemann–Stieltjes integral]].

==Biography==

Stieltjes was born in [[Zwolle]] on 29 December 29, 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]]s around [[Rotterdam]], and also satseated 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 [[Carl Friederich Gauss|Gauss]] and [[Carl Gustav Jakob Jacobi|Jacobi]] -— the consequence of this being he failed his examinations. There were 2two 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.<ref>{{Cite book |last1=Hermite |first1=Charles |url=http://archive.org/details/correspondancedh01hermuoft |title=Correspondance d'Hermite et de Stieltjes. Publiée par les soins de B. Baillaud [et] H. Bouget, avec une préf. de Émile Picard |last2=Baillaud |first2=Benjamin |last3=Bourget |first3=H. |last4=Stieltjes |first4=Thomas Jan |date=1905 |publisher=Paris Gauthier-Villars |others=Gerstein - University of Toronto}}</ref> 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.

Stieltjes was born in [[Zwolle]] on December 29, 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]]s around [[Rotterdam]], and also sat 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.

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 [[Delft University|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.

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.

In 1884, Stieltjes applied for a chair in [[Groningen (city)|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]] arranged for an honorary doctorate to be granted to Stieltjes by [[Leiden University]], enabling him to become a professor.<ref>{{Cite book |url=https://books.google.com/books?id=qj0vAAAAMAAJ |title=Mathematical Reviews |date=1994 |publisher=American Mathematical Society |pages=52–53 |language=en}}</ref> In 1885, he was appointed as member of the [[Royal Netherlands Academy of Arts and Sciences|Royal Dutch Academy of Sciences]] (Koninklijke Nederlandse Akademie van Wetenschappen, KNAW), and the next year he became a foreign member.<ref>{{cite web|url=http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00003151 |title=Thomas Jan Stieltjes Jr. (1856–1894) |publisher=Royal Netherlands Academy of Arts and Sciences |access-date=30 July 2015}}</ref> In 1889, he was appointed professor of differential and integral calculus at [[University of Toulouse|Toulouse University]].<ref>{{Cite book |url=https://books.google.com/books?id=u2nxAAAAMAAJ |title=Annales de la Faculté des Sciences de Toulouse: Mathématiques |date=1995 |publisher=Université Paul Sabatier |language=fr}}</ref>

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.

Stieltjes died on 31 December 1894 in [[Toulouse]], France. He was buried in {{Interlanguage link|Terre-Cabade cemetery|fr|Cimetière de Terre-Cabade}} on 2 January 1895.

In 1884, Stieltjes applied for a chair in [[Groningen]]. He was, in the end, disappointed, as he was not appointed due to his lack of mathematical qualifications.

{{Expand section-stub|date=June 2008}}

==Research==

Stieltjes worked on almost all branches of [[Mathematical analysis|analysis]], [[continued fractions]] and [[number theory]],. and forFor his work, he is sometimes calledreferred to as "''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 function]]s and [[divergent series]], [[differential equation]]s, [[interpolation]], the [[gamma function]] and [[elliptic functions]]. He became known internationally because of the [[Riemann–Stieltjes integral]].

In 1886, [[Henri Poincaré]] and Stieltjes, simultaneously and independently, provided a definition of an asymptotic approximation and illustrated its use and practicality. Their papers were published in [[Acta Mathematica|Acta Math]] and [[Annales Scientifiques de l'École Normale Supérieure|Annales scientifiques de l'Ecole normale supérieure]], respectively.<ref>{{Cite book |last=O'Malley |first=Robert E. |title=Historical Developments in Singular Perturbations |date=2014 |publisher=Springer International Publishing : Imprint: Springer |isbn=978-3-319-11924-3 |edition=1st ed. 2014 |___location=Cham |pages=28–29}}</ref>

{{section-stub}}

{{Expand section|date=June 2008}}

==Awards==

==Awards and honours==

Stieltjes' work on continued fractions earned him the [[Ormoy Prize]] of the [[Académie des Sciences]].

Stieltjes' work on continued fractions earned him the Ormoy Prize (Prix Ormoy) of the [[Académie des Sciences]] in 1893. In 1884 the University of Leiden awarded him an honorary doctorate, and in 1885 he was elected to membership in the Royal Academy of Sciences of Amsterdam.<ref>

{{section-stub}}

{{Cite book |url=https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/stieltjes-thomas-jan |title=Encyclopaedia.com's Biography on Thomas Joannes Stieltjes}}

</ref>

In honour of Stieltjes, since 1996, the Stieltjes Prize (Stieltjesprijs) has been awarded annually for the best [[PhD]] [[thesis]] in mathematics to a student of any Dutch university. All mathematics institutes and departments of Dutch universities are asked for an overview of the PhDs that have taken place in the academic year. The list thus obtained forms the list of candidates for the prize.<ref>

==See also==

{{Cite book |url=https://platformwiskunde.nl/stieltjesprijs/ |title=Platform Wiskunde Nederland; stieltjesprijs - PWN}}

</ref> The award consists of a certificate and an amount of 1200 [[Euro]]s.<ref>

{{Cite book |url=https://stieltjes.org/stieltjes/stielprijs.php#:~:text=Each%20year%20a%20%22Stieltjes%20Prijs,an%20amount%20of%201200%20Euros |title=Thomas Stieltjes Institute for Mathematics; Stieltjes Prize}}

</ref>

==See also==

* [[Lebesgue-Stieltjes integral]]

* [[Annales de la Faculté des Sciences de Toulouse]] co-founded by Stieltjes

* [[Laplace-Stieltjes transform]]

* [[Chebyshev–Markov–Stieltjes inequalities]]

* [[Riemann-Stieltjes integral]]

* [[Heine–Stieltjes polynomials]]

* [[Laplace–Stieltjes transform]]

* [[Lebesgue–Stieltjes integral]]

* [[Montel's theorem]]

* [[Riemann–Stieltjes integral]]

* [[Stieltjes constants]]

* [[Stieltjes matrix]]

* [[Stieltjes moment problem]]

* [[Stieltjes polynomials]]

* [[Stieltjes transformation]] (and Stieltjes inversion formula)

* [[Stieltjes–Wigert polynomials]]

==References==

{{reflist}}

==External links==

*{{Commons category-inline}}

* {{MacTutor Biography|id=Stieltjes}}

* {{MathGenealogy |id=125366 }}

* ''Œuvres complètes de Thomas Jan Stieltjes, pub. par les soins de la Société mathématique d'Amsterdam.'' (Groningen: P. Noordhoff, 1914–18) ([http://name.umdl.umich.edu/AAS8082.0001.001 PDF copy at UMDL], text in Dutch, French and German)

{{Authority control}}

[[de:Thomas Jean Stieltjes]]

[[Category{{DEFAULTSORT:1856 births|Stieltjes, Thomas Joannes]]}}

[[Category:18941856 deaths|Stieltjes, Thomas Joannesbirths]]

[[Category:Dutch1894 mathematicians|Stieltjes, Thomas Joannesdeaths]]

[[Category:19th centuryFrench mathematicians|Stieltjes, Thomas Joannes]]

[[Category:Academic staff of the Delft University of Technology]]

[[Category:Members of the Royal Netherlands Academy of Arts and Sciences]]

[[Category:People from Zwolle]]

[[Category:19th-century Dutch mathematicians]]