Harold Jeffries attended school at Fatfield then, in 1903, he was awarded a scholarship to attend Rutherford College in Newcastle- upon- Tyne. In 1907 he went to Armstrong College, also in Newcastle, which later became Newcastle University. At the time Jeffreys entered the College it was a part of Durham University. There he studied mathematics, physics, chemistry and geology, graduating in 1910 with distinction in mathematics.
He went to St John's College, Cambridge after leaving Newcastle, having obtained one of four mathematics scholarships. Among his teachers at Cambridge to exert a strong influence on him were H F Baker, T J I'A Bromwich, R Webb, A Berry and E Cunningham. He became a fellow of St John's College, Cambridge in 1914 and remained a fellow all his life.
Jeffreys worked in the Cavendish Laboratories on war related work from 1915 until 1917. He joined the Meteorological Office from 1917 to 1922 where he worked on hydrodynamical problems. He returned to Cambridge and he lectured there in mathematics until 1932. Jeffreys was to remain on the staff at Cambridge, but not as a mathematician. From 1932 to 1946 he taught geophysics there, then he became Plumian Professor of Astronomy.
As a lecturer Jeffreys had a poor reputation. A former student D J Finney recalls:-
In 1937-8 .. Lawley and I were two young graduate mathematicians in Cambridge ... We began by attending a lecture course given by Professor Harold Jeffreys on 'Probability'. He was not the clearest of lecturers, and we were soon very confused ... . Jeffreys's personal charm and enthusiasm did not prevent a steady decline in attendance until Lawley and I found ourselves the only survivors of an initial 15. ... There came a week when we were both prevented from attending, and the following week we found to our embarrassment that the lecturer had abandoned the course.Jeffreys's work in diverse areas of science had mathematical applications as their link. In geophysics he studied earthquakes, and the circulation of the atmosphere. As a result of his study of earthquake waves, Jeffreys became the first to claim that the core of the Earth is liquid.
In astronomy he studied the outer planets proposing models for their structures. He also studied the origin of the solar system.
He was awarded honours from the Royal Astronomical Society (1937), from the Royal Society of London (1948) and was knighted in 1953. The 1948 award from the Royal Society of London was their Royal Medal which they awarded:-
... for distinguished work in geophysics and his important contributions to the astronomy of the solar system.The Royal Society awarded him their Copley Medal in 1960:-
... in recognition of his distinguished work in many branches of geophysics, and also in the theory of probability and astronomy.Among Jeffreys's works are The Earth: Its Origin, History and Physical Constitution (1924), Earthquakes and Mountains (1935) and he wrote Methods of Mathematical Physics (1946) jointly with his wife Bertha Jeffreys. They state clearly in the preface that their aims are
to provide an account of those parts of pure mathematics that are most frequently needed in physics.In pure mathematics he studied operational methods (where he improved on Heaviside's operational calculus and Laplace transforms), cartesian tensors and asymptotic approximations. In addition to Methods of Mathematical Physics other contributions of his to pure mathematics are contained in Theory of Probability (1939). His work in probability is developed along Bayesian lines and again aimed at application in the physical sciences.
Jeffreys's character is well illustrated in  and the following quotes give a picture:-
For many years he smoked intensely and in Cambridge he bicycled everywhere until over 90, even after he had broken his wrist in an accident. ... Although uncommunicative, Harold could be a good talker ... though shy, [he] was at heart a sociable man ...Jeffreys's life is summed up in  as follows:-
Harold was held in respect, indeed reverence, in many countries, but in those who knew him well it was more than respect or reverence that he inspired, it was affection, affection for a man who for all his impressive abilities as a mathematician, for all his wide and deep knowledge, for all he had done to develop geophysics, was at heart a very friendly, unassuming person, quite free of pride or pretension.
Article by: J J O'Connor and E F Robertson