Douglas Rayner Hartree PhD, FRS (March 27, 1897February 12, 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to atomic physics.

Early life

Douglas Hartree was born in Cambridge, United Kingdom. His father William was a lecturer in engineering at the University, and his mother Eva Rayner was president of the National Council of Women and mayor of the city. One of his great-grandfathers was Samuel Smiles.[1] He was the oldest of three sons, although his two younger brothers did not survive to adulthood. He attended St John's College, Cambridge but the first world war interrupted his studies. He joined a group working on anti-aircraft ballistics under A. V. Hill, where he gained considerable skill and an abiding interest in practical calculation and numerical methods, executing most of his own work with pencil and paper.

The Hartree-Fock method

After the end of World War I, Hartree returned to Cambridge. In 1921, a visit by Niels Bohr to Cambridge inspired Douglas to apply his knowledge of numerical analysis to the solution of differential equations for the calculation of atomic wavefunctions. Later that year, Douglas graduated with a Second Class degree in natural sciences. He later obtained his Ph.D. in 1926. Even at this stage, he was applying his numerical skill to problems in quantum mechanics and developing what came to be known as the Hartree-Fock method, making possible calculations that had previously been seen as intractable.

Manchester years

In 1929, he was appointed to the Beyer Chair of Applied Mathematics at the University of Manchester. In 1933, he visited Vannevar Bush at the Massachusetts Institute of Technology and learned at first hand about his differential analyser. Immediately on his return to Manchester, he set about building his own analyser from Meccano. Seeing the potential for further exploiting his numerical methods using the machine he prevailed on Sir Robert McDougall to fund a more robust machine which was built in collaboration with Metropolitan Vickers.

The first application of the machine reflected Hartree's enthusiasm for railways in calculating timetables for the London, Midland and Scottish Railway.[2] The machine was also applied in ballistics and other military calculations.

Later life and work

Hartree moved to theoretical physics in 1937 before returning to Cambridge to take up the post of Plummer professor of mathematical physics in 1946. He did further work in control systems and was involved in the early application of digital computers, advising the U.S. military on the use of ENIAC for calculating ballistics tables.

Hartree's last Ph.D. student at Cambridge, Charlotte Froese Fischer, would become world-famous for the development and implementation of the multi-configuration Hartree-Fock (MCHF) approach to atomic structure calculations and for her theoretical prediction concerning the existence of the negative calcium ion.

He died of heart failure in Addenbrooke's Hospital, Cambridge.


* Fellow of the Royal Society, (1932)

* The Hartee unit of energy is named after him.


1. ^ Darwin 1958, p103

2. ^ Hartree & Ingham (1938-9)


* Darwin, Charles [1958] (London). "Douglas Rayner Hartree", Biographical Memoirs of Fellows of the Royal Society, Volume 4. London: Royal Society.


* Hartree, D.R. & Ingham, J. (1938-9) "Note on the application of the differential analyser to the calculation of train running times", Memoirs and Proceedings of the Manchester Literary and Philosophical Society, vol.83, pp1-15

* Hartree, D.R. (1947) Calculating Machines: Recent and Prospective Developments and their Impact on Mathematical Physics

* - (1950) Calculating Instruments and Machines, reprinted 1984 ISBN 0-262-08147-4

* - (1952) Numerical Analysis ISBN 0-19-853111-7


* The Manchester differential analyser

* O'Connor, John J. & Robertson, Edmund F., "Douglas Hartree", MacTutor History of Mathematics archive

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