Douglas Rayner Hartree, FRS (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the construction of a differential analyser using Meccano.^{ [2] }^{ [3] }
Fellowship of the Royal Society is an award granted to individuals that the Royal Society of London judges to have made a 'substantial contribution to the improvement of natural knowledge, including mathematics, engineering science, and medical science'.
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: experimental physicists who specialize in the observation of physical phenomena and the analysis of experiments, and theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies.
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics ; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.
Douglas Hartree was born in Cambridge, England. His father, William, was a lecturer in engineering at Cambridge University and his mother, Eva Rayner, was president of the National Council of Women and mayor of the city of Cambridge. One of his great-grandfathers was Samuel Smiles;^{ [1] } another was the marine engineer William Hartree, partner of John Penn.^{ [4] } Douglas Hartree was the oldest of three sons that survived infancy. A brother and sister died in infancy when he was still a child, but his two brothers would later also die. Hartree's 7-year-old brother John Edwin died when Hartree was 17, and Hartree's 22-year-old brother Colin William died from meningitis in February 1920 when Hartree was 23.^{ [5] }
Cambridge is a university city and the county town of Cambridgeshire, England, on the River Cam approximately 50 miles (80 km) north of London. At the United Kingdom Census 2011, its population was 123,867 including 24,506 students. Cambridge became an important trading centre during the Roman and Viking ages, and there is archaeological evidence of settlement in the area as early as the Bronze Age. The first town charters were granted in the 12th century, although modern city status was not officially conferred until 1951.
Samuel Smiles was a Scottish author and government reformer. Although he campaigned on a Chartist platform, he concluded that more progress would come from new attitudes than from new laws. His masterpiece, Self-Help (1859), promoted thrift and claimed that poverty was caused largely by irresponsible habits, while also attacking materialism and laissez-faire government. It has been called "the bible of mid-Victorian liberalism" and raised Smiles to celebrity status almost overnight.
John Penn FRS (1805–1878) was an English marine engineer whose firm was pre-eminent in the middle of the 19th century due to his innovations in engine and propeller systems, which led his firm to be the major supplier to the Royal Navy as it made the transition from sail to steam power. He was also president of the Institution of Mechanical Engineers on two occasions.
Hartree attended St John's College, Cambridge but the first World War interrupted his studies. He (and his father and brother) 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 for differential equations, executing most of his own work with pencil and paper.^{ [6] }
St John's College is a constituent college of the University of Cambridge founded by the Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corporation established by a charter dated 9 April 1511. The aims of the college, as specified by its statutes, are the promotion of education, religion, learning and research. It is one of the larger Oxbridge colleges in terms of student numbers. For 2018, St. John’s was ranked 9th of 29 colleges in the Tompkins Table with over 30% of its students earning First-class honours.
World War I, also known as the First World War or the Great War, was a global war originating in Europe that lasted from 28 July 1914 to 11 November 1918. Contemporaneously described as "the war to end all wars", it led to the mobilisation of more than 70 million military personnel, including 60 million Europeans, making it one of the largest wars in history. It is also one of the deadliest conflicts in history, with an estimated nine million combatants and seven million civilian deaths as a direct result of the war, while resulting genocides and the resulting 1918 influenza pandemic caused another 50 to 100 million deaths worldwide.
Ballistics is the field of mechanics that concerns with the launching, flight behavior and impact effects of projectiles, especially ranged weapon munitions such as bullets, unguided bombs, rockets or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.
After the end of World War I, Hartree returned to Cambridge graduating in 1922 with a Second Class degree in natural sciences.
In 1921, a visit by Niels Bohr to Cambridge inspired Hartree to apply his numerical skills to Bohr's theory of the atom, for which he obtained his PhD in 1926 – his advisor was Ernest Rutherford. With the publication of Schrödinger's equation in the same year, Hartree was able to apply his knowledge of differential equations and numerical analysis to the new quantum theory. He derived the Hartree equations for the distribution of electrons in an atom and proposed the self-consistent field method for their solution. The wavefunctions from this theory did not satisfy the Pauli exclusion principle for which Slater showed that determinantal functions are required. V. Fock published the "equations with exchange" now known as Hartree–Fock equations. These are considerably more demanding computationally even with the efficient methods Hartree proposed for the calculation of exchange contributions.
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. Bohr was also a philosopher and a promoter of scientific research.
In atomic physics, the Rutherford–Bohr model or Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar System, but with attraction provided by electrostatic forces in place of gravity. After the cubic model (1902), the plum-pudding model (1904), the Saturnian model (1904), and the Rutherford model (1911) came the Rutherford–Bohr model or just Bohr model for short (1913). The improvement to the Rutherford model is mostly a quantum physical interpretation of it. The model's key success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reason for the structure of the Rydberg formula, it also provided a justification for its empirical results in terms of fundamental physical constants.
Ernest Rutherford, 1st Baron Rutherford of Nelson,, HFRSE, was a New Zealand-born British physicist who came to be known as the father of nuclear physics. Encyclopædia Britannica considers him to be the greatest experimentalist since Michael Faraday (1791–1867).
In 1929, Hartree 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 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 persuaded Sir Robert McDougall to fund a more robust machine, which was built in collaboration with Metropolitan-Vickers.
The School of Mathematics at the University of Manchester is one of the largest mathematics departments in the United Kingdom, with around 80 academic staff and an undergraduate intake of roughly 400 a year and another 200 postgraduate students. The school was formed in 2004 by the merger of the mathematics departments of University of Manchester Institute of Science and Technology (UMIST) and the Victoria University of Manchester (VUM). In July 2007 the school moved from the Mathematics Tower into a purpose-designed building – the first three floors of the Alan Turing Building – on Upper Brook Street.
Vannevar Bush was an American engineer, inventor and science administrator, who during World War II headed the U.S. Office of Scientific Research and Development (OSRD), through which almost all wartime military R&D was carried out, including important developments in radar and the initiation and early administration of the Manhattan Project. He emphasized the importance of scientific research to national security and economic well-being, and was chiefly responsible for the movement that led to the creation of the National Science Foundation.
The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts. The Institute is a land-grant, sea-grant, and space-grant university, with an urban campus that extends more than a mile (1.6 km) alongside the Charles River. The Institute also encompasses a number of major off-campus facilities such as the MIT Lincoln Laboratory, the Bates Center, and the Haystack Observatory, as well as affiliated laboratories such as the Broad and Whitehead Institutes. Founded in 1861 in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. It has since played a key role in the development of many aspects of modern science, engineering, mathematics, and technology, and is widely known for its innovation and academic strength, making it one of the most prestigious institutions of higher learning in the world.
The first application of the machine, reflecting Hartree's enthusiasm for railways, was calculating timetables for the London, Midland and Scottish Railway. ^{ [7] } He spent the rest of the decade applying the differential analyser to find solutions of differential equations arising in physics. These included control theory and laminar boundary layer theory in fluid dynamics making significant contributions to each of the fields.
The differential analyser was not suitable for the solution of equations with exchange. When Fock's publication pre-empted Hartree's work on equations with exchange, Hartree turned his research to radio-wave propagation that led to the Appleton–Hartree equation. In 1935, his father, William Hartree, offered to do calculations for him. Results with exchange soon followed. Douglas recognised the importance of configuration interaction that he referred to as "superposition of configurations". The first multiconfiguration Hartree–Fock results were published by father, son, and Bertha Swirles (later Lady Jeffreys) in 1939.
At Hartree's suggestion, Bertha Swirles proceeded to derive equations with exchange for atoms using the Dirac equation in 1935. With Hartree's advice, the first relativistic calculations (without exchange) were reported in 1940 by A. O. Williams, a student of R. B. Lindsay.
During the Second World War Hartree supervised two computing groups. The first group, for the Ministry of Supply, has been described by Jack Howlett ^{ [8] } as a "job shop" for the solution of differential equations. At the outbreak of World War II, the differential analyser at the University of Manchester was the only full-size (eight integrator) differential analyser in the country. Arrangements were made to have the machine available for work in support of the national war effort. In time, the group consisted of four members^{ [9] } (front to back: Jack Howlett, Nicholas R. Eyres, J. G. L. Michel; center, Douglas Hartree; right Phyllis Lockett Nicolson). Problems were submitted to the group without information about the source but included the automatic tracking of targets, radio propagation, underwater explosions, heat flow in steel, and the diffusion equation later found to be for isotope separation. The second group was the magnetron research group of Phyllis Lockett Nicolson, David Copely, and Oscar Buneman. The work was done for the Committee for the Co-ordination of the Valve Development assisting the development of radar. A differential analyser could have been used if more integrators had been available, so Hartree set up his group as three "CPUs" to work on mechanical desk calculators in parallel. For a method of solution he selected what is now a classical particle simulation.^{ [10] } Hartree never published any of his magnetron research findings in journals though he wrote numerous highly technical secret reports during the war.
In April 1944 a committee which included Hartree recommended that a mathematical section be set up within the National Physical Laboratory (NPL). In October this recommendation was put into effect with its first two objectives being the investigation of the possible adaptation of automatic telephone equipment to scientific equipment and the development of electronic computing devices suitable for rapid computing. One suspects that some members already knew of the Colossus computer. John R. Womersley (Turing's bête noire) was the first Director. In February 1945 he went on a two-month tour of computing installations in the USA, including visiting ENIAC (still not complete). He became acquainted with drafts of von Neumann's famous June 1945 EDVAC report. About two months later Hartree also went over to see ENIAC, not then publicly known.
In February 1946, Max Newman (who had been involved in the Colossus computer) submitted an application to the Royal Society for funds to start the task of building a general purpose computer at the University of Manchester. The Royal Society referred the request to Hartree and C.G. Darwin, Director of the NPL, to advise them. Hartree recommended the grant but Darwin opposed it on the grounds that Turing's ACE at NPL would be sufficient to serve the needs of the country. But Hartree's view won the day and the Manchester developments in computing were started.
Hartree did further work in control systems and was involved in the early application of digital computers, advising the US military on the use of ENIAC for calculating ballistics tables. In the summer of 1946 Hartree made his second trip to ENIAC as an evaluation of its applicability to a broad range of science, when he became the first civilian to program it. For this he selected a problem involving the flow of a compressible fluid over a surface, such as air over the surface of a wing travelling faster than the speed of sound.^{ [11] }
At the end of 1945 or very early in 1946 Hartree briefed Maurice Wilkes of the University of Cambridge on the developments in computing in the USA which he had seen. Wilkes, then received an invitation from the Moore School of Electrical Engineering (the builders of ENIAC) to attend a course on electronic computers. Before leaving for this, Hartree was able to brief him more fully on ENIAC. It was on the boat home that Wilkes planned the original design of EDSAC, which was to become operational in May 1949. Hartree worked closely with Wilkes in developing use of the machine for a wide range of problems and, most importantly, showed users from a number of areas in the university how they could use it in their research work.
Hartree returned to Cambridge to take up the post of Plummer professor of mathematical physics in 1946. In October he gave an inaugural lecture entitled "Calculating Machines: Recent and Prospective Developments and their impact on Mathematical Physics”. This described ENIAC and the work that Hartree had done on it. Even in 1946, two years before stored programming electronic computing became a reality, Hartree saw the need for the use of sub-routines. His inaugural lecture ended with a look at what computers might do. He said: "..there are, I understand many problems of economic, medical and sociological interest and importance awaiting study which at present cannot be undertaken because of the formidable load of computing involved."
On 7 November 1946 the Daily Telegraph, having interviewed Hartree, quoted him as saying: "The implications of the machine are so vast that we cannot conceive how they will affect our civilisation. Here you have something which is making one field of human activity 1,000 times faster. In the field of transportation, the equivalent to ACE would be the ability to travel from London to Cambridge ... in five seconds as a regular thing. It is almost unimaginable."^{ [12] }
Hartree's fourth and final major contribution to British computing started in early 1947 when the catering firm of J. Lyons & Co. in London heard of the ENIAC and sent a small team in the summer of that year to study what was happening in the USA, because they felt that these new computers might be of assistance in the huge amount of administrative and accounting work which the firm had to do. The team met with Col. Herman Goldstine at the Institute for Advanced Study in Princeton who wrote to Hartree telling him of their search. As soon as he received this letter, Hartree wrote and invited representatives of Lyons to come to Cambridge for a meeting with him and Wilkes. This led to the development of a commercial version of EDSAC developed by Lyons, called LEO, the first computer used for commercial business applications. After Hartree's death, the headquarters of LEO Computers was renamed Hartree House. This illustrates the extent to which Lyons felt that Hartree had contributed to their new venture.
Hartree's last famous contribution to computing was an estimate in 1950 of the potential demand for computers, which was much lower than turned out to be the case: "We have a computer here in Cambridge, one in Manchester and one at the [NPL]. I suppose there ought to be one in Scotland, but that's about all." Such underestimates of the number of computers that would be required were common at the time.^{ [13] }
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, on 12 February 1958.
(1950) Cambridge University Press)
The Atanasoff–Berry computer (ABC) was the first automatic electronic digital computer, an early electronic digital computing device that has remained somewhat obscure. The ABC's priority is debated among historians of computer technology, because it was neither programmable, nor Turing-complete.
Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids. It is necessary because, apart from relatively recent results concerning the hydrogen molecular ion, the quantum many-body problem cannot be solved analytically, much less in closed form. While computational results normally complement the information obtained by chemical experiments, it can in some cases predict hitherto unobserved chemical phenomena. It is widely used in the design of new drugs and materials.
The Electronic delay storage automatic calculator (EDSAC) was an early British computer. Inspired by John von Neumann's seminal First Draft of a Report on the EDVAC, the machine was constructed by Maurice Wilkes and his team at the University of Cambridge Mathematical Laboratory in England. EDSAC was the second electronic digital stored-program computer to go into regular service.
John William Mauchly was an American physicist who, along with J. Presper Eckert, designed ENIAC, the first general purpose electronic digital computer, as well as EDVAC, BINAC and UNIVAC I, the first commercial computer made in the United States.
Sir Maurice Vincent Wilkes was a British computer scientist who designed and helped build the Electronic delay storage automatic calculator (EDSAC), one of the earliest stored program computers and invented microprogramming, a method for using stored-program logic to operate the control unit of a central processing unit's circuits. At the time of his death, Wilkes was an Emeritus Professor of the University of Cambridge.
In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operationally. The original machines could not add, but then it was noticed that if the two wheels of a rear differential are turned, the drive shaft will compute the average of the left and right wheels. A simple gear ratio of 1:2 then enables multiplication by two, so addition are achieved. Multiplication is just a special case of integration, namely integrating a constant function.
Herman Heine Goldstine was a mathematician and computer scientist, who worked as the director of the IAS machine at Princeton University's Institute for Advanced Study, and helped to develop ENIAC, the first of the modern electronic digital computers. He subsequently worked for many years at IBM as an IBM Fellow, the company's most prestigious technical position.
Kathleen "Kay" McNulty Mauchly Antonelli was an Irish-American computer programmer and one of the six original programmers of the ENIAC, one of the first general-purpose electronic digital computers.
Ruth Teitelbaum (1924–1986) was one of the first computer programmers in the world. Teitelbaum was one of the original programmers for the ENIAC computer.
Theory and Techniques for Design of Electronic Digital Computers was a course in the construction of electronic digital computers held at the University of Pennsylvania's Moore School of Electrical Engineering between July 8, 1946, and August 30, 1946, and was the first time any computer topics had ever been taught to an assemblage of people. The course disseminated the ideas developed for the EDVAC and initiated an explosion of computer construction activity in the United States and internationally, especially in the United Kingdom.
Phyllis Nicolson was a British mathematician most known for her work on the Crank–Nicolson method together with John Crank.
Differential equations, in particular Euler equations, rose in prominence during World War II in calculating the accurate trajectory of ballistics, both rocket-propelled and gun or cannon type projectiles. Originally, mathematicians used the simpler calculus of earlier centuries to determine velocity, thrust, elevation, curve, distance, and other parameters.
The Mallock machine is an electrical analog computer built in 1933 to solve simultaneous linear differential equations. It uses coupled transformers, with numbers of turns digitally set up to +/-1000 and solved sets of up to 10 linear differential equations. It was built by Rawlyn Richard Manconchy Mallock of Cambridge University. The Mallock machine was contemporary with the mechanical differential analyser, which was also used at Cambridge during the late 1930s and 1940s.
In 1927, a year after the publication of the Schrödinger equation, Hartree formulated what are now known as the Hartree equations for atoms, using the concept of self-consistency that Lindsay had introduced in his study of many electron systems in the context of Bohr theory. Hartree assumed that the nucleus together with the electrons formed a spherically symmetric field. The charge distribution of each electron was the solution of the Schrödinger equation for an electron in a potential , derived from the field. Self-consistency required that the final field, computed from the solutions was self-consistent with the initial field and he called his method the self-consistent field method.
Jack Howlett CBE was a British mathematician and computer scientist who was head of the Atlas Computer Laboratory for the duration of its existence.
John Ronald Womersley was a British mathematician and computer scientist who made important contributions to computer development, and hemodynamics. Nowadays he is principally remembered for his contribution to blood flow, fluid dynamics and the eponymous Womersley number, a dimensionless parameter characterising unsteady flow.
Adolfas Pranaitis Jucys was a Lithuanian theoretical physicist and mathematician, and inducted member of the Lithuanian Academy of Sciences in 1953. He graduated from Kaunas University in 1931 and later worked with both creators of the self-consistent field method – Douglas Hartree in Manchester and Vladimir Fock in Leningrad (1949–1951). Adolfas Jucys created the scientific school of theoretical physics in Vilnius, was the head of the Department of Theoretical Physics at Vilnius University (1944–1971). He organized the first Institute of Physics and Mathematics in Lithuania and was its first director (1956–1963), and later (1971–1974) the head of the Institute's Department of Quantum Mechanical Calculations.
Beatrice "Trixie" Helen Worsley was the first female computer scientist in Canada. She received her Ph.D. degree from the University of Cambridge with Alan Turing and Douglas Hartree as advisers, the first Ph.D granted in what would today be known as computer science. She wrote the first program to run on EDSAC, co-wrote the first compiler for Toronto's Ferranti Mark 1, wrote numerous papers in computer science, and taught computers and engineering at Queen's University and the University of Toronto for over 20 years before her untimely death at the age of 50.
The following is a timeline of scientific computing, also known as computational science.
Preceded by Edward Arthur Milne | Beyer Chair of Applied Mathematics at University of Manchester 1929–1937 | Succeeded by Sydney Goldstein |