Thomas Joannes Stieltjes was born on December 29, 1856 in Zwolle, capital of the province Overijssel, The Netherlands. He had two brothers and four sisters. He carried the same first names as his father, who was a civil engineer and member of parliament. The latter was rather well-known, mainly because of his achievements in the construction of harbours in Rotterdam. He was a doctor h.c. of Leiden University. To his memory a statue is erected by his friends and admirators on the Noordereiland, at the Burgemeester Hoffman Plein, in Rotterdam.

Thomas Jr. started his studies in 1873 at the Polytechnical School in Delft (now the Technical University). Instead of going to the lectures, he spent most of his time in the library studying the works of Gauss and Jacobi. As a consequence, he did not pass the propedeutical examination. Renewed attempts in 1875 and 1876 failed. His father, aware of the particular situation of his son, contacted his friend, Prof. H.G. van de Sande-Bakhuyzen, director of the Leiden Observatory. In April 1877 Thomas was appointed calculator at the Observatory, officially "assistant for astronomical calculations". Thomas devoted almost all free time to mathematics. Through his work on celestial mechanics he got in contact with Ch. Hermite in Paris. His first letter to Hermite was dated November 8, 1882. The letter was followed by a correspondence between Stieltjes and Hermite consisting of 432 letters. The last letter of Hermite to Stieltjes was written December 15, 1894, fourteen days before Stieltjes' death. It is to the credit of the director, H.G. van de Sande-Bakhuyzen, that he freed Stieltjes, on request, on January 1, 1883 from doing observation work. In May 1883 Thomas married Elizabeth (Lilly) Intveld, who was a tremendous stimulus for his mathematical work. From September till December of that year he substituted Prof. F.J. van den Berg in Delft, who had fallen seriously ill, and lectured analytical and descriptive geometry. On December 1, 1883 Thomas resigned from the Observatory to devote himself completely to mathematics.

On January 15, 1884 Stieltjes wrote to Hermite :

One has offered me, some days ago, a professorship in analysis (differential and integral calculus) at the University of Groningen. I have accepted this offer and I believe that this position will permit me to be more useful. I owe much, in this situation, to the extreme kindness of my old chief Mr. Bakhuyzen, the director of the observatory. One of these days, my nomination will become definitive. (translated from French)

On March 13, 1884 he wrote to Hermite :

The Groningen Faculty has indeed put me in first place for the vacancy, but the Minister has named one of the others. Probably the reason will have been that I having had no occasion to follow the ordinary route, I have not obtained any degree at the University. (translated from French)

From archives of the University of Groningen it appears, that the following nomination was made in 1883: 1. Prof. dr. D.J. Korteweg, 2. Mr. T.J. Stieltjes. When asked, Prof. Korteweg said he would not consider to move to Groningen. Stieltjes however declared that he would accept an appointment. A new nomination was then made: 1. T.J. Stieltjes, 2. F. (Floris) de Boer; the latter was appointed by Royal Decree of March 12, 1884.

In May 1884, Hermite met the Dutch professor in Mathematics, Bierens de Haan, at the celebration of the fifth centenary of the University of Edinburgh. A debate was devoted to the Stieltjes' poor circumstances. It is very likely that the wish to confer a doctorate honoris causa upon Stieltjes came into existence during this debate. On June, 1884 a doctorate in mathematics and astronomy, honoris causa, was conferred upon Stieltjes by Leiden University, following the nomination by D. Bierens de Haan and H.G. van de Sande-Bakhuyzen. In the archives of the Senate of Leiden University we found, dated May 27, 1884:

The rector reports that a request has been received from the Faculty of Mathematics and Physics to confer the degree of doctor honoris causa in Mathematics and Astronomy upon Mr. T.J. Stieltjes, a former employee of the Leiden Observatory. On behalf of the Faculty Mr. Lorentz explains the merits of Mr. Stieltjes and indicates the motives which have lead to the proposal. It is decided to form a conclusion in the next meeting of the Senate. (translated from Dutch)

Following is Stieltjes' reply to the official letter of the Senate of Leiden University (in translation):

To the Senate of Leiden University.

The undersigned wishes to thank you for the honourable distinction, conferred upon him by Your College, and to assure you that the distinction is highly appreciated. Due to a regrettable misunderstanding he was not aware of the intention of a public ceremony on last Tuesday June 17 at 3 o'clock.

Leiden, June 19, 1884

T.J. Stieltjes

In April 1885 Stieltjes' family settled in Paris. In 1889, Stieltjes was appointed professor of differential and integral calculus at the Faculty of Science of Toulouse. On June 18, 1894 a survey of his most important paper was published in the Comptes Rendus de l'Académie des Sciences: Recherches sur les fractions continues. An extended version of this paper was published in the Annales de la Faculté des Sciences de Toulouse, in 1894/95. This article, where he introduced the Stieltjes integral, was awarded a prize by the Académie des Sciences. On December 31, 1894 Stieltjes passed away in Toulouse, at the age of 38. The tomb of T.J. Stieltjes can be found at the cemetery of Terre Cabade in Toulouse (no. 828, section II, division 4). It has been restored by his family in 1990. The burial actually took place January 2, 1895.

Note:

A more extended text is included in the Stieltjes' Collected Papers, published by Springer Verlag on the occasion of the commemoration of the 100th anniversary of the death of Stieltjes.

For another short text, see this one.