| | | Carl-Gustav Esseen |
Professor Carl-Gustav Esseen grew up in Linköping, where he finished high school with top grades. In the fall of 1936 he came to Uppsala to study mathematics, astronomy, physics and chemistry. His main interest since his early days, however, was mathematics, in particular the calculus of probabilities. He obtained his PhD degree in the fall of 1944 with an extensive and deep thesis titled Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law. His thesis was published in Acta Mathematica, one of the most prestigious mathematics journals.
The normal distribution, or the Gauss distribution, is a classical concept in probability theory. The distribution originates from the fact that the cumulative effect of independent trials can be approximated by the normal distribution -- this is the Central Limit Theorem. Inspired by the works of Harald Cramér and the legendary Uppsala mathematician Arne Beurling, Carl-Gustav Esseen investigated the accuracy of the approximation. By ingenious Fourier analytic computations he obtained the sharpest possible estimates of the approximation error; he solved the simplest case, that of when all the summands are independent and have the same distribution, as early as the fall of 1940 when he was only 22 years old. The key step in his proof is now known as the Esseen Lemma, and it is an inequality in which the difference between two distribution functions is estimated via an integral based on the difference between the corresponding characteristic functions. The method and technique established by Esseen, and epitomized by this renowned lemma, have been exploited by researchers throughout the world ever since.
Carl-Gustav Esseen
After a few years as Assistant Professor in Uppsala, Carl-Gustav Esseen was appointed Full Professor of Applied Mathematics at the Royal Institute of Technology in Stockholm. In those days a full professor, also known as `The Chair', was responsible for all kinds of mathematics. As a consequence of the rapid development of Mathematical Foundations as well as the technical applications, however, the professorship was split into two: one in Information Technology, and in particular numerical analysis; and one in Mathematical Statistics. In 1962 Esseen moved to a Chair in Mathematical Statistics. He was subsequently elected a member of the Royal Swedish Academy of Engineering Sciences in 1963.
In 1967, after 18 years at the Royal Institute of Technology, Carl-Gustav Esseen became the first holder of the Chair in Mathematical Statistics at Uppsala University, a position he held until his retirement at the end of 1984.
During his many years as a professor Carl-Gustav Esseen guided several PhD students to their degrees. Throughout the years he was also known for his meticulously prepared and perfectly delivered lectures on a wide variety of topics. His lecture notes in several areas have been influential for innovations in Swedish industry, for example in Control Theory and in Telecommunications.
The wide scope of knowledge Carl-Gustav Esseen demonstrated was impressive. On several occasions the problems he presented from books and papers had been insufficiently investigated, on other occasions proofs were missing or incorrect. In his modest manner he would comment on this with phrases such as "I had to fix that" or "there was no proof, but it turned out that it was possible to prove the result as follows", which typically was not at all an easy task, but rather a contribution to the field. Had he wanted, many learned books and papers could have been written by him. But rather his passion was simply to discover for its own sake, and to teach. In addition, an internal aesthetic that required perfection to his own standards, kept his list of publications short, but always of the highest quality.
He remained faithful to his department after his retirement, until health and eyesight began to fail. During this period he returned to one of his first intellectual loves, that of number theory, where he investigated problems concerning the factorization of large numbers, a topic that has become important in cryptology.
Carl-Gustav Esseen was by no means a man of gestures and ceremonies. There is a Swedish saying to the effect that great achievements are accomplished quietly. A great master, one of our important scientists has left us. We shall miss him.
Allan Gut, Uppsala University,
and
Lars Holst, The Royal Institute of Technology
| | | Carl-Gustav Esseen |