**Ambrose Rogers** wrote extensively on Number Theory and on Sphere-packing problems.

- After the war ended, Rogers returned to his mathematical studies.
- It was a slightly disappointing start to Rogers publishing career for he published an Addendum in the same volume of the Journal explaining that the results of his first paper could be obtained more easily from a theorem of Stefan Banach and also reported that the first of his theorems was proved by the American mathematician Ralph Palmer Agnew (1900-1986) in 1939.
- However, this was only the first of a remarkable number of papers that Rogers published while a research student: A note on a theorem of Blichfeldt (1946); (with Harold Davenport) Hlawka's theorem in the geometry of numbers (1947); A note on a problem of Mahler (1947); A note on irreducible star bodies (1947); Existence theorems in the geometry of numbers (1947); (with J H H Chalk) The critical determinant of a convex cylinder (1948); A problem of Hirsch (1948); The product of the minima and the determinant of a set (1949); The product of n homogeneous linear forms (1949); The successive minima of measurable sets (1949); On the critical determinant of a certain nonconvex cylinder (1949); (with Harold Davenport) A note on the geometry of numbers (1949); and (with J H H Chalk) The successive minima of a convex cylinder (1949).
- Others such as The signatures of the errors of simultaneous Diophantine approximations and The asymptotic directions of n linear forms in n + 1 integral variables, were submitted by Rogers to the Proceedings of the London Mathematical Society on 6 September 1947 but did not appear in print until 1951.
- Rogers was awarded a Ph.D. in 1949 for his thesis The Transformation of Sequences by Matrices in which he studied divergent series.
- Before the award of his Ph.D., Rogers began working with Harold Davenport and, in addition to their joint papers given above, they published two joint papers On the critical determinants of cylinders and Diophantine inequalities with an infinity of solutions.
- Through Davenport, Rogers became interested in packing and covering.
- Returning to his position at University College London, Rogers was awarded a D.Sc. in 1952.
- After four years in Birmingham, Rogers returned to London, this time as the Astor Professor of Mathematics at University College.
- Ambrose had the largest desk piled high with totally incomprehensible research papers.
- Rogers held this post until he retired in 1986, when he became professor emeritus and remained at University College.
- Rogers produced a remarkable mathematical output having published around 180 papers and books.
- Rogers has written three important books, Packing and Covering in 1964, Hausdorff Measures in 1970, and (with John E Jayne) Selectors (2002).
- Much of Packing and Covering was written in 1961 while Rogers was spending a year in Canada at the University of British Columbia in Vancouver.
- Rogers wrote an obituary of Harold Davenport for the London Mathematical Society which was published in 1972, the year after Rogers wrote a survey of Davenport's work.
- Rogers was elected a fellow of the Royal Society in 1959 and served on the Council of the Royal Society for two spells, first from 1966 to 1968 and then again in 1983-84.
- Since about 1958, Professor Rogers' main research interests moved to the theory of Hausdorff measures, of analytic sets and of general convex bodies, to all of which he has made important contributions.

Born 1 November 1920, Cambridge, England. Died 5 December 2005, Islington, London, England.

View full biography at MacTutor

Origin England

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive