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Harry Bateman attended Manchester Grammar School, then won a scholarship to Trinity College Cambridge. He went up to Cambridge in 1900 and was awarded a Smith's prize in 1905 for an essay on differential equations. That year he became a Fellow of Trinity College.
During the years 1905 and 1906 Bateman travelled on the continent visiting Göttingen and Paris. On his return to England in 1906 he was appointed a lecturer at Liverpool University, becoming a Reader in mathematical physics at the University of Manchester the following year.
Bateman emigrated to the USA in 1910. The years 1910 1912 were spent at Bryn Mawr College, the years 1912  1917 being spent at Johns Hopkins University in Baltimore. He spent the rest of his life at Pasadena holding a variety of different chairs at the California Institute of Technology.
There is one strange aspect to his career which is not evident from the above description. In 1913, while at Johns Hopkins University, he was awarded a Ph.D. At this time he was an extremely eminent mathematician with over 60 publications, some of great importance. He didn't have the usual CV of a Ph.D. student!
Some of his early work was on geometry and the influence of geometry on all his work is evident. In 1905 he studied certain quartic surfaces studied earlier by Cayley and Chasles. In particular he constructed the tangent plane and exhibited the surface as an envelope of planes.
Bateman worked on special functions and partial differential equations. In 1904 he extended Whittaker's solution of the potential and wave equation by definite integrals to more general partial differential equations
Bateman was one of the first to apply Laplace transforms to integral equations in 1906. In 1910 he solved systems of differential equations discovered by Rutherford which describe radioactive decay. Bateman's method was the now familiar one of applying the complex inversion formula of the Laplace transform.
The finest contribution Bateman made to mathematics was his work on transformations of partial differential equations, in particular his general solutions containing arbitrary functions. In particular he applied his methods to equations resulting from electromagnetics, then later to those arising from hydrodynamics.
He accumulated a vast store of information on all the familiar special functions and on his death the publication of his manuscript was undertaken by Erdélyi and his associates in the form of the wellknown series Higher Transcendental Functions and Tables of Integral Transforms . In all Bateman published around 200 papers in a period of 40 years. He only published five joint papers, one of those in 1924 being with Ehrenfest.
His interests outside mathematics were few (publishing 5 papers a year for 40 years doesn't leave much time over!). He was a top class chess player, good enough to represent Britain in a match against the USA when he was an undergraduate at Cambridge. He played in other chess tournaments too with some notable victories over leading players.
He is described in [3] as
a charmingly modest and unassuming person, very quite, almost of retiring disposition, but always helpful and ready to put his time and extensive knowledge at the disposal of others.References (4 books/articles)
References elsewhere in this archive:
Harry Bateman was elected to the Royal Society of London in 1928. You can see a history of the Royal Society and a list of the members among the mathematicians in our archive.