# E. T. Whittaker

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**Edmund Taylor Whittaker** FRS^{[1]} FRSE (24 October 1873 – 24 March 1956)^{[1]}^{[2]}^{[3]} was an English mathematician who contributed widely to applied mathematics, mathematical physics and the theory of special functions. He had a particular interest in numerical analysis, but also worked on celestial mechanics and the history of physics. Near the end of his career he received the Copley Medal, the most prestigious honorary award in British science. The School of Mathematics of the University of Edinburgh holds The Whittaker Colloquium, a yearly lecture in his honour.^{[4]}^{[5]}

## Biography

Whittaker was born in Southport, in Lancashire. He was educated at Manchester Grammar School and Trinity College, Cambridge from 1892.^{[6]} He graduated as Second Wrangler in the examination in 1895 and also received the Tyson Medal for Mathematics and Astronomy. In 1896, Whittaker was elected as a fellow of Trinity College, Cambridge, and remained at Cambridge as a teacher until 1906. Between 1906 and 1911 he was the Royal Astronomer of Ireland and professor of astronomy at Trinity College Dublin where he taught mathematical physics. In 1911 Whittaker became professor at the University of Edinburgh and remained there for the rest of his career.

A classmate at Manchester Grammar School, Ernest Barker, with whom Edmund shared the office of prefect, later recalled his personality:

- He had a gay, lively, bubbling spirit: he was ready for every prank: he survives in my memory as a natural actor; and I think he could also, on occasion, produce a merry poem.
^{[7]}

Whittaker was a Christian and became a convert to the Roman Catholic Church (1930). In relation to that he was a member of the Pontifical Academy of Sciences from 1936 onward and was president of a Newman Society. Earlier at Cambridge in 1901 he married the daughter of a Presbyterian minister. They had five children, including the mathematician John Macnaghten Whittaker, (1905-1984) and his elder daughter, Beatrice, married E.T. Copson, who would later become Professor of Mathematics at St. Andrew's University.^{[8]}

Whittaker wrote the biography of a famous Italian mathematician, Vito Volterra for the Royal Society in 1941. In 1954, he was awarded the Copley Medal by the Royal Society, their highest award, *"for his distinguished contributions to both pure and applied mathematics and to theoretical physics"*. Back in 1931 Whittaker had received the Royal Society's Sylvester Medal *"for his original contributions to both pure and applied mathematics"*. Whittaker died in Edinburgh, Scotland.

*Whittaker & Watson*

Whittaker is remembered as the author of *A Course of Modern Analysis* (1902), which in its 1915 second edition in collaboration with George Neville Watson became *Whittaker and Watson*, one of the handful of mathematics texts of its era that was considered indispensable. This work has remained in print continuously for over a century.^{[8]}

## Special functions

Whittaker is the eponym of the Whittaker function or Whittaker integral, in the theory of confluent hypergeometric functions. This makes him also the eponym of the Whittaker model in the local theory of automorphic representations. He published also on algebraic functions and automorphic functions. He gave expressions for the Bessel functions as integrals involving Legendre functions.

## Partial differential equations

In the theory of partial differential equations, Whittaker developed a general solution of the Laplace equation in three dimensions and the solution of the wave equation. He developed the electrical potential field as a bi-directional flow of energy (sometimes referred to as alternating currents). Whittaker's pair of papers in 1903 and 1904 indicated that any potential can be analysed by a Fourier-like series of waves, such as a planet's gravitational field point-charge. The superpositions of inward and outward wave pairs produce the "static" fields (or scalar potential). These were harmonically-related. By this conception, the structure of electric potential is created from two opposite, though balanced, parts. Whittaker suggested that gravity possessed a wavelike "undulatory" character.

## History of science

In 1910, Whittaker wrote "A History of the Theories of Aether and Electricity", which gave a very detailed account of the aether theories from René Descartes to Hendrik Lorentz and Albert Einstein, including the contributions of Hermann Minkowski, and which made Whittaker a respected historian of science.

In 1951 (Vol. 1) and 1953 (Vol. 2), he published an extended and revised edition of his book in two volumes. The second volume contains some interesting historical remarks. For example, it contains a chapter named "The Relativity Theory of Poincaré and Lorentz", where Whittaker credited Henri Poincaré and Lorentz for developing special relativity, and he attributed to Albert Einstein's relativity paper only little importance. On Einstein's 1905 paper he states that it "set forth the relativity theory of Poincare and Lorentz with some amplifications, and which attracted much attention”, and he credited Einstein only with being the first to publish the correct relativistic formulas for aberration and the Doppler effect. He also attributed the formula to Poincaré. In 1984 Clifford Truesdell wrote that Whittaker "aroused colossal antagonism by trying to set the record straight on the basis of print and record rather than recollection and folklore and professional propaganda,..."^{[9]} On the other hand Abraham Pais wrote that "Whittaker's treatment of special relativity shows how well the author's lack of physical insight matches his ignorance of the literature".^{[10]} According to Roberto Torretti,^{[11]} "Whittaker's views on the origin of special relativity have been rejected by the great majority of scholars", and he cites Max Born (1956), Gerald Holton (1960,1964), Schribner (1964), Goldberg (1967), Zahar (1973), Hirosige (1976), Schaffner (1976), and Arthur I. Miller (1981).

## Applied mathematics and mathematical physics

Whittaker wrote *The Calculus of Observations: A Treatise on Numerical Mathematics* (1924)^{[12]} and *Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies* (1937).^{[13]}^{[14]} He was the editor of Eddington's *Fundamental Theory* (1946), and wrote
*From Euclid to Eddington, A Study of Conceptions of the External World* (1949), including a first scholarly account of some of the research between 1900 to 1925.

## References

- ↑
^{1.0}^{1.1}Template:Cite doi - ↑ Template:Cite pmid
- ↑ Template:Cite doi
- ↑ E. T. Whittaker at the Mathematics Genealogy Project
- ↑ Template:MacTutor Biography
- ↑ Template:Acad
- ↑ Ernest Barker (1953)
*Age and Youth*, p 280, Oxford University Press - ↑ Clifford Truesdell,
*An Idiot's Fugitive Essays on Science*, page 432, Springer ISBN 0-387-90703-3 - ↑ Pais, Abraham, "Subtle is the Lord", 1982
- ↑ Roberto Torretti, "Relativity and Geometry", 1983
- ↑ {{#invoke:Citation/CS1|citation |CitationClass=journal }}
- ↑ {{#invoke:Citation/CS1|citation |CitationClass=journal }}
- ↑ {{#invoke:Citation/CS1|citation |CitationClass=journal }}

## Further reading

*A Course of Modern Analysis*. 1902.- "On the partial differential equations of mathematical physics". Math. Ann., Vol. 57, 1903, p. 333–355.
- "On an expression of the electromagnetic field due to electrons by means of two scalar potential functions". Proc. Lond. Math. Soc. Series 2, Vol. 1, 1904, pp. 367–372.
*A Treatise on the Analytical Dynamics of Particles and Rigid Bodies*. First Edition, Cambridge 1904.*The Theory of Optical Instruments*(Cambridge Tracts in Mathematics and Mathematical Physics No. 7), Cambridge 1907.*Recent Researches on Space, Time, and Force*, MNRAS, Vol. 70, pp. 363–366.*A History of the theories of aether and electricity (1. edition)*, Dublin: Longman, Green and Co.- "On the functions which are represented by the expansions of the interpolation theory," Proc. Royal Soc. Edinburgh, Sec. A, vol.35, pp. 181–194, 1915.
*A Treatise on the Analytical Dynamics of Particles and Rigid Bodies*. Second Edition, Cambridge 1917.- "On the quantum mechanism in the atom". Proc. R. Soc. Edinb., Vol. 42, 1922, pp. 129–146
*A Short Course in Interpolation*. London 1923.*The Calculus of Observations: A treatise on numerical mathematics*. 1924.*Space and Spirit: Theories of the Universe and the Arguments for the Existence of God*. 1946.*The Beginning and End of the World*. Riddell Memorial Lectures, Fourteenth Series. Oxford 1942.*Eddington’s Principle in the Philosophy of Science*. Cambridge 1951.*A History of the Theories of Aether and Electricity*(2nd edition), vol. 1: The Classical Theories / vol. 2: The Modern Theories 1900–1926, London: Nelson, ISBN 0-486-26126-3*From Euclid to Eddington: A Study of Conceptions of the External World*. Dover 1958.- "
*Whittaker Memorial Volume*". Proceedings of the Edinburgh Mathematical Society, 1958. - Bearden, T. E., "
*Gravitobiology : Conception of Edmund Whittaker (papers of 1903-1904)*". Tesla Book Co., Chula Vista, CA, USA. - Whittaker and the Aether at MathPages

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