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HENRY FREDERICK BAKER, Fellow 1914-1936, was born on 1866 July 3, and was educated at the Perse School and St Johns College, Cambridge. He was bracketed Senior Wrangler with three others in 1887 and was a Smiths Prizeman two years later. He became Fellow, Lecturer and Director of Studies in Mathematics in St Johns College.
He worked in most fields of pure mathematics. His principal undergraduate lectures were on the theory of functions, geometry, differential equations, and analysis (which meant what is now usually called special functions); but he was quite capable of giving one on dynamics or elementary electricity in an emergency. His speed was amazing. A contemporary of mine took notes in shorthand and made a fair copy afterwards, which was in great demand. But if anyone confessed to being bewildered, Baker would explain every detail at extreme length.
He had written books on Abelian functions (1897) and Multiply-periodic functions (1907); ideas from these generalizations of elliptic functions permeated much of his work on geometry, and later, on figures of rotating fluids. He is best known for his book Principles of Geometry (6 vols, 1922–33). The first four volumes deal with projective geometry of two, three, and four dimensions In these he makes much use of synthetic (or, as we should now say, axiomatic) methods, without the use of coordinates. To those trained in the tradition of C. Smith and Askwith it was astonishing that so much could be done in this way. In the last years of his tenure of the chair his lectures were mainly on the birational theory of curves and surfaces, and the last two volumes of the Principles deal with this subject. The modern tendency is closer to his later methods than his earlier ones; coordinates are introduced as early as possible, and the distinction between geometry and algebra has almost disappeared.
He became a Fellow of the Royal Society in 1898 and received the Sylvester Medal in 1910. For a time he was a Senior Fellow of the Royal Society.
He was elected to the Lowndean Professorship of Astronomy and Geometry on January 5, 1914, in succession to Sir Robert Ball. The appointment surprised most people not actively concerned in it, and it is believed that the electors were equally divided and that the decision was made by the Chancellor, Lord Rayleigh. The chair had been held by astronomers throughout the 19th century, and Baker had written no specifically astronomical work. One consideration that probably influenced the electors was that there was only one chair in the whole of pure mathematics, while astronomy had three. Another was that geometry was mentioned in the title of the chair; but to this astronomers had the reply that geometry had often been used in a very broad sense. Laplace, Leverrier, and Adams had been referred to as geometers. In any case, Baker's own diffidence would have prevented him from being a candidate unless he had been encouraged to enter by some of the electors.
Having been elected, Baker proceeded to make himself a Professor of both astronomy and geometry A fortnight before his election, he began a course of lectures on periodic orbits, in addition to three regular college courses. In these, he showed familiarity with all treatments of the subject, which must have been among his interests for some time. In a paper in the Philosophical Transactions for 1916, he studied certain differential equations with periodic and what would now be called almost-periodic coefficients, introduced some new methods of solution, and proved the existence of convergent solutions. In one respect, he amended a result of Poincaré. He returned to the subject in the Proceedings of the Cambridge Philosophical Society for 1920. He also lectured on planetary, lunar, and satellite theory, and on figures of rotating liquids. A paper on the derivation of the equations of motion is in Monthly Notices, 87, 93, 1927. He was for some time skeptical about Jeans's proof of the instability of the pear-shaped figure, doubting the accuracy of the first few terms as an approximation to the sum of a certain series; but he managed to obtain a copy of Liapounoff's works and found that Liapounoff had actually got a result that amounted to a justification of Jeans's method. Baker was the first Englishman to understand Liapounoff.
Besides his own work, he gave valuable help to younger workers, notably Greaves.
He published many papers on a range of subjects comparable to that of Poincaré. One, in the Cambridge Proceedings for 1920, discusses the Lorentz transformation of the electromagnetic equations and incidentally includes the Pauli and Eddington matrices.
His contribution to pure mathematics with the widest application was possibly to notice that the bisection method used by Goursat in his proof of Cauchy's theorem could be adapted to give general proofs of the Heine-Borel theorem and the so-called modified Heine-Borel theorem
He retired in 1936 and died on March 17, 1956. He was mentally active until the last.
HAROLD JEFFREYS
He worked in most fields of pure mathematics. His principal undergraduate lectures were on the theory of functions, geometry, differential equations, and analysis (which meant what is now usually called special functions); but he was quite capable of giving one on dynamics or elementary electricity in an emergency. His speed was amazing. A contemporary of mine took notes in shorthand and made a fair copy afterwards, which was in great demand. But if anyone confessed to being bewildered, Baker would explain every detail at extreme length.
He had written books on Abelian functions (1897) and Multiply-periodic functions (1907); ideas from these generalizations of elliptic functions permeated much of his work on geometry, and later, on figures of rotating fluids. He is best known for his book Principles of Geometry (6 vols, 1922–33). The first four volumes deal with projective geometry of two, three, and four dimensions In these he makes much use of synthetic (or, as we should now say, axiomatic) methods, without the use of coordinates. To those trained in the tradition of C. Smith and Askwith it was astonishing that so much could be done in this way. In the last years of his tenure of the chair his lectures were mainly on the birational theory of curves and surfaces, and the last two volumes of the Principles deal with this subject. The modern tendency is closer to his later methods than his earlier ones; coordinates are introduced as early as possible, and the distinction between geometry and algebra has almost disappeared.
He became a Fellow of the Royal Society in 1898 and received the Sylvester Medal in 1910. For a time he was a Senior Fellow of the Royal Society.
He was elected to the Lowndean Professorship of Astronomy and Geometry on January 5, 1914, in succession to Sir Robert Ball. The appointment surprised most people not actively concerned in it, and it is believed that the electors were equally divided and that the decision was made by the Chancellor, Lord Rayleigh. The chair had been held by astronomers throughout the 19th century, and Baker had written no specifically astronomical work. One consideration that probably influenced the electors was that there was only one chair in the whole of pure mathematics, while astronomy had three. Another was that geometry was mentioned in the title of the chair; but to this astronomers had the reply that geometry had often been used in a very broad sense. Laplace, Leverrier, and Adams had been referred to as geometers. In any case, Baker's own diffidence would have prevented him from being a candidate unless he had been encouraged to enter by some of the electors.
Having been elected, Baker proceeded to make himself a Professor of both astronomy and geometry A fortnight before his election, he began a course of lectures on periodic orbits, in addition to three regular college courses. In these, he showed familiarity with all treatments of the subject, which must have been among his interests for some time. In a paper in the Philosophical Transactions for 1916, he studied certain differential equations with periodic and what would now be called almost-periodic coefficients, introduced some new methods of solution, and proved the existence of convergent solutions. In one respect, he amended a result of Poincaré. He returned to the subject in the Proceedings of the Cambridge Philosophical Society for 1920. He also lectured on planetary, lunar, and satellite theory, and on figures of rotating liquids. A paper on the derivation of the equations of motion is in Monthly Notices, 87, 93, 1927. He was for some time skeptical about Jeans's proof of the instability of the pear-shaped figure, doubting the accuracy of the first few terms as an approximation to the sum of a certain series; but he managed to obtain a copy of Liapounoff's works and found that Liapounoff had actually got a result that amounted to a justification of Jeans's method. Baker was the first Englishman to understand Liapounoff.
Besides his own work, he gave valuable help to younger workers, notably Greaves.
He published many papers on a range of subjects comparable to that of Poincaré. One, in the Cambridge Proceedings for 1920, discusses the Lorentz transformation of the electromagnetic equations and incidentally includes the Pauli and Eddington matrices.
His contribution to pure mathematics with the widest application was possibly to notice that the bisection method used by Goursat in his proof of Cauchy's theorem could be adapted to give general proofs of the Heine-Borel theorem and the so-called modified Heine-Borel theorem
He retired in 1936 and died on March 17, 1956. He was mentally active until the last.
HAROLD JEFFREYS
Henry Frederick Baker's obituary appeared in Monthly Notices of the Royal Astronomical Society 117:3 (1957), 248-250.