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# E. T. Whittaker

Edmund Taylor Whittaker FRS 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.

Biography

Whittaker was born in Southport, in Lancashire. He was educated at Manchester Grammar School and Trinity College, Cambridge from 1892.[4] 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 Edinburgh University and remained there for the rest of his career.

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 learned Presbyterian minister. They had five children, including the mathematician John Macnaghten Whittaker, (1905-1984) and his elder daughter, Beatrice, married the man later to become Professor of Maths at St. Andrew's University, ET Copson.[5]

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

Whittaker was, in 1954, selected by the Fellows of the Royal Society to receive the Copley Medal, the highest award granted by the scientific Royal Society of London, "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 to become indispensable. This work has remained in print continuously for over a century. [5]

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[disambiguation needed ]-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 which made Whittaker a respected historian of science. Though the book was a "History", apparently Whittaker innovated the use of the rapidity parameter in his exposition of relativity. Furthermore, he provided a rather succinct summary of relativity theory:

...the equation of the rectangular hyperbola \( x^2 - (ct)^2 = 1 \) in the plane of the variables (x, ct) is unaltered when any pair of conjugate diameters are taken as the new axis, and a new unit of length is taken proportional to the length of either of these diameters.[6]

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. He also attributed the formula \( E=mc^2 \) 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,..."[7]

Applied mathematics and mathematical physics

Whittaker wrote The Calculus of Observations: a treatise on numerical mathematics (1924) and Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies (1937). 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

^ Temple, G. (1956). "Edmund Taylor Whittaker. 1873-1956". Biographical Memoirs of Fellows of the Royal Society 2: 299–226. doi:10.1098/rsbm.1956.0021. edit

^ Dingle, H. (1956). "Edmund T. Whittaker, Mathematician and Historian". Science 124 (3214): 208–209. doi:10.1126/science.124.3214.208. PMID 17838072. edit

^ Aitken, A. C. (2009). "The Contributions of E. T. Whittaker to Algebra and Numerical Analysis". Proceedings of the Edinburgh Mathematical Society 11: 31. doi:10.1017/S001309150001436X. edit

^ Venn, J.; Venn, J. A., eds. (1922–1958). "Whittaker, Edmund Taylor". Alumni Cantabrigienses (10 vols) (online ed.). Cambridge University Press.

^ a b http://www.lms.ac.uk/newsletter/322/322_03.html

^ History of Aether (1910) p 441

^ Clifford Truesdell, An Idiot's Fugitive Essays on Science, page 432, Springer ISBN 0-387-90703-3

Further reading

Wikisource has original works written by or about:

Edmund Taylor Whittaker

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.

External links

O'Connor, John J.; Robertson, Edmund F., "E. T. Whittaker", MacTutor History of Mathematics archive, University of St Andrews.

Whittaker and the Aether at MathPages

E. T. Whittaker at the Mathematics Genealogy Project

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