Harry Bateman

Harry Bateman first grew to love mathematics at Manchester Grammar School, and in his final year, won a scholarship to Trinity College, Cambridge. Bateman studied with coach Robert Alfred Herman preparing for Cambridge Mathematical Tripos. He distinguished himself in 1903 as Senior Wrangler (tied with P.E. Marrack) and by winning the Smith's Prize (1905).[5] He published his first paper when he was still an undergraduate student on "The determination of curves satisfying given conditions".[6] He studied in Göttingen and Paris, taught at the University of Liverpool and University of Manchester before moving to the US in 1910. First he taught at Bryn Mawr College and then Johns Hopkins University. There, working with Frank Morley in geometry, he achieved the PhD, but he had already published more than sixty papers including some of his celebrated papers before getting his PhD. In 1917 he took up his permanent position at California Institute of Technology, then still called Throop Polytechnic Institute.

Eric Temple Bell says, "Like his contemporaries and immediate predecessors among Cambridge mathematicians of the first decade of this century [1901–1910]... Bateman was thoroughly trained in both pure analysis and mathematical physics, and retained an equal interest in both throughout his scientific career."[7]

Theodore von Kármán was called in as an advisor for a projected aeronautics laboratory at Caltech and later gave this appraisal of Bateman.[8]

In 1926 Cal Tech [sic] had only a minor interest in aeronautics. The professorship that came nearest to aeronautics was occupied by a shy, meticulous Englishman, Dr. Harry Bateman. He was an applied mathematician from Cambridge who worked in the field of fluid mechanics. He seemed to know everything but did nothing important. I liked him.

Harry Bateman married Ethel Horner in 1912 and had a son named Harry Graham, who died as a child, later the couple adopted a daughter named Joan Margaret. He died on his way to New York in 1946 of Coronary thrombosis.

In 1907 Harry Bateman was lecturing at the University of Liverpool together with another senior wrangler, Ebenezer Cunningham. Together they came up in 1908 with the idea of a conformal group of spacetime (now usually denoted as C(1,3))[9] which involved an extension of the method of images.[10] For his part, in 1910 Bateman published The Transformation of the Electrodynamical Equations.[11] He showed that the Jacobian matrix of a spacetime diffeomorphism which preserves the Maxwell equations is proportional to an orthogonal matrix, hence conformal. The transformation group of such transformations has 15 parameters and extends both the Poincaré group and the Lorentz group. Bateman called the elements of this group spherical wave transformations.[12]

In evaluating this paper, one of his students, Clifford Truesdell, wrote

The importance of Bateman's paper lies not in its specific details but in its general approach. Bateman, perhaps influenced by Hilbert's point of view in mathematical physics as a whole, was the first to see that the basic ideas of electromagnetism were equivalent to statements regarding integrals of differential forms, statements for which Grassmann's calculus of extension on differentiable manifolds, Poincaré's theories of Stokesian transformations and integral invariants, and Lie's theory of continuous groups could be fruitfully applied.[13]

Bateman was the first to apply Laplace transform to integral equation in 1906. He submitted a detailed report on integral equation in 1911 in the British association for the advancement of science.[14] Horace Lamb in his 1910 paper[15] solved an integral equation

${\displaystyle 2\int _{0}^{\infty }f(y-\zeta ^{2})\,d\zeta =F(y)}$

as a double integral, but in his footnote he says, "Mr. H. Bateman, to whom I submitted the question, has obtained a simpler solution in the form"

${\displaystyle f(y)={\frac {1}{\pi }}\int _{-y}^{\infty }{\frac {F'(-z)}{\sqrt {z+x}}}dz}$.

In 1914 Bateman published The Mathematical Analysis of Electrical and Optical Wave-motion. As Murnaghan says, this book "is unique and characteristic of the man. Into less than 160 small pages is crowded a wealth of information which would take an expert years to digest."[4] The following year he published a textbook Differential Equations, and sometime later Partial differential equations of mathematical physics. Bateman is also author of Hydrodynamics and Numerical integration of differential equations. Bateman studied the Burgers' equation[16] long before Jan Burgers started to study.

Harry Bateman wrote two significant articles on the history of applied mathematics:

• "The influence of tidal theory upon the development of mathematics"[17]
• "Hamilton's work in dynamics and its influence on modern thought"[18]

In his Mathematical Analysis of Electrical and Optical Wave-motion (p. 131) he describes the charged-corpuscle trajectory as follows:

a corpuscle has a kind of tube or thread attached to it. When the motion of the corpuscle changes a wave or kink runs along the thread; the energy radiated from the corpuscle spreads out in all directions but is concentrated round the thread so that the thread acts as a guiding wire.

This figure of speech is not to be confused with a string in physics, for the universes in string theory have dimensions inflated beyond four, something not found in Bateman's work. Bateman went on to study the luminiferous aether with an article "The structure of the Aether".[19] His starting point is the bivector form of an electromagnetic field E + iB. He recalled Alfred-Marie Liénard's electromagnetic fields, and then distinguished another type he calls "aethereal fields":

When a large number of "aethereal fields" are superposed their singular curves indicate the structure of an "aether" which is capable of supporting a certain type of electromagnetic field.

Bateman received many honours for his contributions, including election to the Royal Society of London in 1928, election to the National Academy of Sciences in 1930. He was elected as vice-president of the American Mathematical Society in 1935 and was the Society's Gibbs Lecturer for 1943.[4][20] He was on his way to New York to receive an award from the Institute of Aeronautical Science when he died of coronary thrombosis. The Harry Bateman Research Instructorships at the California Institute of Technology are named in his honour.[21]

After his death, his notes on higher transcendental functions were edited by A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, and published in 1954.[22]

In a review of Bateman's book Partial Differential Equations of Mathematical Physics, Richard Courant says that "there is no other work which presents the analytical tools and the results achieved by means of them equally completely and with as many original contributions" and also "advanced students and research workers alike will read it with great benefit".

• Bateman Manuscript Project

Wikisource has original works written by or about: Harry Bateman

• Academy of Sciences Biographical Memoir
• Harry Bateman at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Harry Bateman", MacTutor History of Mathematics archive, University of St Andrews.