# E. T. Whittaker

Edmund Taylor Whittaker
Born24 October 1873
Died24 March 1956 (aged 82)
NationalityEnglish
CitizenshipUnited Kingdom
Alma materTrinity College, Cambridge
Known for
Awards
Scientific career
FieldsMathematics
Institutions
Doctoral students
Other notable studentsW. V. D. Hodge
Marion Cameron Gray

Edmund Taylor Whittaker FRS[1] FRSE LLD (24 October 1873 – 24 March 1956)[1][3][4] was a British 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, the history of physics, and digital signal processing. 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.[2][5]

## Life

Whittaker was born in Southport, in Lancashire, the son of John Whittaker Esq. and his wife, Selina Septima Taylor.[6]

He was educated at Manchester Grammar School then studied Maths and Physics at Trinity College, Cambridge from 1892.[7] 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. He was elected a Fellow of the Royal Society of London in 1905. 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 of Mathematics at the University of Edinburgh and remained there for the rest of his career. In 1912 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Cargill Gilston Knott, Ralph Allan Sampson, James Gordon MacGregor and Sir William Turner. He served as Secretary to the Society from 1916 to 1922, He was twice Vice President, 1925-28 and 1937-39, and was President of the Society from 1939 to 1944, through the war years.[8]

Shortly after coming to Edinburgh, Whittaker established a Mathematical Laboratory, the first enterprise of this kind in Great Britain, and probably one of the first attempts to make numerical analysis an integral part of the university curriculum. It is probable that in starting this new venture, Whittaker was influenced by his work in astronomy, and by his friendship with the great actuaries of the period. To the knowledge of the present writer, he regarded the introduction of the Mathematical Laboratory course as his most notable contribution to mathematical education. He and his associates, among whom the most outstanding was A. C. Aitken, researched on curve fitting, numerical solution of integral equations, and similar topics. His thorough knowledge of the history and practice of numerical analysis found expression in his Calculus of Observations (written in collaboration with G. Robinson) which today, more than thirty years after its appearance, and after two revolutions in numerical computing, is still one of the most important works on the subject.

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.[9]

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.

Whittaker wrote the biography of a famous Italian mathematician, Vito Volterra for the Royal Society in 1941.

He was knighted by King George VI in 1945 for services to mathematics.

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 at his home, 48 George Square, Edinburgh on 24 March 1956.[10] His house was unceremoniously demolished by Edinburgh University in the 1960s to expand the campus and now holds the William Robertson Building.

## Family

At Cambridge in 1901 he married Mary Ferguson Macnaghten Boyd, the daughter of a Presbyterian minister (and grand-daughter of Thomas Jamieson Boyd). They had five children, including the mathematician John Macnaghten Whittaker (1905-1984). His elder daughter, Beatrice, married Edward Taylor Copson, who would later become Professor of Mathematics at St. Andrews University.[11]

## Whittaker & Watson

Whittaker is remembered as the author of the book A Course of Modern Analysis, first published in 1902. The book's later editions were in collaboration with George Neville Watson, and so the book became known as "Whittaker & Watson". The book is one of the handful of mathematics texts of its era that was considered indispensable. It has remained in print continuously for over a century.[11]

## 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.

## Special relativity

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 especially alluded to Lorentz's 1904 paper (dated by Whittaker as 1903), Poincaré's St. Louis speech (The Principles of Mathematical Physics) of September 1904, and Poincaré's June 1905 paper.[12] He attributed to Einstein's special relativity paper only little importance, which he said "set forth the relativity theory of Poincaré 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 relativistic aberration and the Doppler effect. He also attributed the formula ${\displaystyle E=mc^{2}}$ 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,..."[13] 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".[14] According to Roberto Torretti,[15] "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), Scribner (1964),[16] Goldberg (1967),[17] Zahar (1973), Hirosige (1976), Schaffner (1976), and Arthur I. Miller (1981).

Nevertheless, Whittaker gave a concise statement of relativity of simultaneity by referring to conjugate diameters of hyperbolas. He wrote, "[the] hyperbola is unaltered when any pair of conjugate diameters are taken as new axes, and a new unit of length is taken proportional to the length of either of these diameters."[18] His observation means that the simultaneous events for a worldline are hyperbolic-orthogonal to the worldline.

## References

1. ^ a b c Temple, G. (1956). "Edmund Taylor Whittaker. 1873-1956" (PDF). Biographical Memoirs of Fellows of the Royal Society. 2: 299–325. doi:10.1098/rsbm.1956.0021.
2. ^ a b c
3. ^ Dingle, H. (1956). "Edmund T. Whittaker, Mathematician and Historian". Science. 124 (3214): 208–209. doi:10.1126/science.124.3214.208. PMID 17838072.
4. ^ Aitken, A. C. (2009). "The Contributions of E. T. Whittaker to Algebra and Numerical Analysis". Proceedings of the Edinburgh Mathematical Society. 11: 31–38. doi:10.1017/S001309150001436X.
5. ^
6. ^ Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 978-0-902198-84-5.
7. ^ "Whittaker, Edmund Taylor (WHTR892ET)". A Cambridge Alumni Database. University of Cambridge.
8. ^ Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 978-0-902198-84-5.
9. ^ Ernest Barker (1953) Age and Youth, p 280, Oxford University Press
10. ^ http://www-history.mcs.st-andrews.ac.uk/DNB/Whittaker.html
11. ^ a b "Archived copy". Archived from the original on 15 February 2005. Retrieved 22 February 2010.CS1 maint: archived copy as title (link)
12. ^
13. ^ Clifford Truesdell, An Idiot's Fugitive Essays on Science, page 432, Springer ISBN 0-387-90703-3
14. ^ Pais, Abraham, "Subtle is the Lord", 1982
15. ^ Roberto Torretti, "Relativity and Geometry", 1983; 1996 Dover reprint
16. ^ Scribner Jr, Charles (1964). "Henri Poincaré and the principle of relativity". American Journal of Physics. 32 (9): 672–678. doi:10.1119/1.1970936.
17. ^ Goldberg, Stanley (1967). "Henri Poincaré and Einstein's theory of relativity". American Journal of Physics. 35 (10): 934–944. doi:10.1119/1.1973643.
18. ^ E. T. Whittaker (1910) A History of the theories of aether and electricity Dublin: Longmans, Green and Co. (see page 441)
19. ^ Bôcher, Maxime (1904). "Book Review: A Course of Modern Analysis". Bulletin of the American Mathematical Society. 10 (7): 351–355. doi:10.1090/s0002-9904-1904-01123-4.
20. ^ Wilson, Edwin Bidwell (1906). "Book Review: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies; with an Introduction to the Problem of Three Bodies". Bulletin of the American Mathematical Society. 12 (9): 451–459. doi:10.1090/s0002-9904-1906-01372-6.
21. ^ Wilson, Edwin Bidwell (1913). "Book Review: A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century". Bulletin of the American Mathematical Society. 19 (8): 423–428. doi:10.1090/s0002-9904-1913-02381-4.
22. ^ Birkhoff, G. D. (1920). "Book Review: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies; with an Introduction to the Problem of Three Bodies". Bulletin of the American Mathematical Society. 26 (4): 183–184. doi:10.1090/s0002-9904-1920-03290-8.
23. ^ Lehmer, D. N. (1925). "Review: The calculus of observations: a treatise on numerical mathematics, by E. T. Whittaker and G. Robinson". Bull. Amer. Math. Soc. 31 (3): 181–182. doi:10.1090/s0002-9904-1925-04014-8.
24. ^ Hille, Einar (1936). "Book Review: Interpolatory Function Theory". Bulletin of the American Mathematical Society. 42 (5): 305–307. doi:10.1090/s0002-9904-1936-06294-4.
25. ^ Buchanan, Herbert Earle (1938). "Review: Treatise on the Analytical Dynamics of Particles and Rigid Bodies, by E. T. Whittaker". Bull. Amer. Math. Soc. 44 (5): 316. doi:10.1090/s0002-9904-1938-06728-6.
26. ^ Wilson, E. B. (1906). "Treatise on the Analytical Dynamics of Particles and Rigid Bodies, by E. T. Whittaker". Bull. Amer. Math. Soc. 12 (9): 451–458. doi:10.1090/s0002-9904-1906-01372-6.
27. ^ E.T. Whittaker (1943). "Chance, freewill and necessity, in the scientific conception of the universe". Proceedings of the Physical Society. 55 (6): 459–471. doi:10.1088/0959-5309/55/6/303.
28. ^ Lenzen, V. F. (1952). "A History of the Theories of Aether and Electricity. Edmund Whittaker". Isis. 43 (3): 293–294. doi:10.1086/348142. ISSN 0021-1753. p. 294