Lindeberg was son of a teacher at the
Helsinki Polytechnical Institute and at an early age showed mathematical talent and interest. The family was well off and later Jarl Waldemar would prefer to be a reader than a full professor. Lindeberg's career centred on the
University of Helsinki. His early interests were in
partial differential equations and the
calculus of variations but from 1920 he worked in
probability and
statistics. In 1920 he published his first paper on the
central limit theorem. His result was similar to that obtained earlier by
Lyapunov whose work he did not then know. However, their approaches were quite different; Lindeberg's was based on a
convolution argument while Lyapunov used the
characteristic function. Two years later Lindeberg used his method to obtain a stronger result: the so-called
Lindeberg condition. His work on probability led to him becoming involved in applied fields. He developed what we know as
Kendall's τ and he found the first two moments of its sampling distribution. Lindeberg used
line transect methods in
forestry, and when in 1926 determining the necessary number of transects to obtain a sufficiently precise
confidence interval, he seems to have rediscovered
Student's t-distribution. The Swedish mathematician
Harald Cramér met Lindeberg in 1922. He later recalled this story about Lindeberg and the beautiful farm he owned. "When he was reproached for not being sufficiently active in his scientific work, he said 'Well, I am really a farmer.' And if somebody happened to say that his farm was not properly cultivated, his answer was 'Of course my real job is to be a professor.' I was very fond of him and saw him often during the following years." Lindeberg's work was unknown to
Alan Turing, who proved the central limit theorem in his dissertation in 1935. ==Writing available on the web==