Thomas Jan Stieltjes born 29 Dec 1856 in Zwolle, Netherlands and he died 31 Dec 1894 in Toulouse, France.
Thomas Stieltjes was started his studies at the Polytechnical School of Delft in 1873 but spent his student years reading Gauss and Jacobi rather than attending lectures and failed his examinations. Two further failures in 1875 and 1876 had his father in despair, but having a friend as director of Leiden Observatory, Thomas's father was able to put in a good word for his son.
Thomas became assistant at Leiden Observatory in 1877 and began a correspondence with Hermite in 1882 which lasted the rest of his life. All his spare time was now devoted to mathematics and, in 1883 a few months after he married, he resigned his post at the observatory to make his career in mathematics.
Stieltjes applied for a chair in Groningen and in January 1884 wrote to Hermite:-
I have been offered, 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 become more useful. ... One of these days my nomination will become definite.
He was to be disappointed, however, for although he was placed first for a chair at Groningen he was not appointed because of his lack of qualifications. However, because of good work by Hermite behind the scenes, the University of Leiden conferred an honorary degree in mathematics and astronomy on Stieltjes in June 1884. However Stieltjes wrote:-
Due to a regrettable misunderstanding I was not aware of the intention of a public ceremony on last Tuesday June 17 at 3 o'clock.
Stieltjes went with his family to Paris in 1885 and he was appointed to a chair of differential and integral calculus in Toulouse in 1889.
Stieltjes worked on analysis, continued fractions and number theory. He is often called the father of the analytic theory of continued fractions . However, he is best remembered for the Stieltjes integral. In a 2 volume memoir Recherches sur les fractions continues , a beautifully written work of major importance, he introduces his integral. Volume 2 only appeared after his death. The memoir was awarded a prize by the Académie des Sciences.
Stieltjes also contributed to ordinary and partial differential equations, the gamma function, interpolation and elliptic functions. His work is an important first step towards Hilbert spaces. His work on divergent series is also important.