**Thomas Stieltjes** worked on almost all branches of analysis, continued fractions and number theory.

- Stieltjes started his studies at the Polytechnical School of Delft in 1873 but spent his student years reading Gauss and Jacobi in the library rather than attending lectures.
- It may have been enjoyable to Stieltjes to read the works of these great mathematicians rather than study the coursework but the consequence was that he failed his examinations.
- Perhaps the most significant event in Stieltjes' life, as far as mathematics was concerned, occurred on 8 November 1882 when he began a correspondence with Hermite which was to last the rest of his life (which would only be 12 more years during which time they exchanged 432 letters).
- The original reason that Stieltjes wrote to Hermite concerned his work on celestial mechanics.
- However the correspondence turned quickly to mathematics and Stieltjes began to devote all his spare time to mathematical research.
- It is a great credit to van de Sande-Bakhuyzen, the director of Leiden Observatory, that he responded quickly to Stieltjes' request on 1 January 1883 to stop his observational work to allow him to work more on mathematical topics.
- In September Stieltjes was asked to substitute at the University of Delft for F J van den Berg who had taken ill.
- From September to December 1883 Stieltjes lectured on analytical geometry and on descriptive geometry.
- This confirmed what must have been becoming increasing clear in Stieltjes' mind, that mathematics was the only p[ossible career for him.
- Although this gives the complete facts that Stieltjes was aware of, the events surrounding this appointment were a little more complex than he realised.
- Top of the list had been Korteweg with Stieltjes in second place and indeed the position was offered to Korteweg who was a professor at the University of Amsterdam.
- At this stage the appointing committee at Groningen drew up a new list putting Stieltjes in first place with Floris de Boer second.
- However, despite Stieltjes accepting the position at this stage, a Royal Decree was issued on 12 March 1884 appointing de Boer to the chair.
- As one might imagine Hermite was very disturbed to learn that Stieltjes had been ruled out after an offer had been made to him because of his lack of a degree.
- There he talked to Bierens de Haan, a professor of mathematics from the Netherlands, and they devised a plan to help Stieltjes by having him proposed for an honorary degree at Leiden University.
- After de Haan returned, he and van de Sande-Bakhuyzen proposed Stieltjes for an honorary degree in mathematics and astronomy.
- On behalf of the Faculty, Mr Lorentz explained the merits of Mr Stieltjes and indicated the reasons which led to the proposal.
- The Senate wrote to Stieltjes regarding the award of the honorary degree but somehow it failed to reach him in time.
- In the same year Stieltjes was appointed to the University of Toulouse, being appointed to a chair of differential and integral calculus in Toulouse in 1889.
- Stieltjes worked on almost all branches of analysis, continued fractions and number theory.
- He is best remembered for the Stieltjes integral which he introduced in Recherches sur les fractions continues Ⓣ(Research on continued fractions) while solving the moment problem, that is, given the moments of all orders of a body, find the distribution of its mass.
- The first part of Stieltjes' article in the Annales de la Faculté des Sciences de Toulouse covers 120 pages and appeared in 1894.
- The second part is a forty page article which appeared after Stieltjes' death in 1895.
- Stieltjes' work is also seen as an important first step towards the theory of Hilbert spaces.
- Stieltjes also contributed to ordinary and partial differential equations, the gamma function, interpolation, and elliptic functions.
- Stieltjes died on 31 December 1894 and was buried in the cemetery of Terre Cabade in Toulouse on 2 January 1895.

Born 29 December 1856, Zwolle, Overijssel, The Netherlands. Died 31 December 1894, Toulouse, France.

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Astronomy, Origin Netherlands

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive