John Nicholson was Mathematics Tutor at Balliol from 19191931. Around 1912 Nicholson had been the first to realise that in quantum theory the angular momentum of particles must be quantised, and that this fact should make it possible to explain the spectra of atoms. Unfortunately, Rutherford's work on the structure of atoms was not yet complete, so Nicholson was forced to work with an incorrect model of the atom, and his results were correspondingly modest. When in the following year Bohr coupled Nicholson's idea of quantised angular momentum with Rutherford's planetary model of the atom everything fitted perfectly and provided the first theoretical understanding of Balmer's empirical spectral formulae. Nicholson felt that he never received the proper recognition for his contribution and increasingly consoled himself with the contents of the College cellar. By 1930 he was no longer capable of carrying out his tutorial duties, and he spent the last twentyfive years of his life, practically forgotten, in the Warneford Hospital.
Edward Titchmarsh matriculated in 1917, and crowned a glittering undergraduate career by winning the Senior Mathematical Prize. In 1931 he succeeded G.H. Hardy as Savilian Professor of Geometry. Titchmarsh is best known for his work in analysis, particularly his books on Fourier integrals, The Theory of functions, The Riemann Zeta function, and the twovolume Eigenfunction expansions. In this last mentioned treatise he expounded his mathematically rigorous treatment of several quantum mechanical sytems. For example, it was Titchmarsh who first proved that the spectrum of a hydrogen atom in a uniform electric field is continuous.
Further information about TitchmarshAfter leaving at Balliol, Bosanquet moved to London where he became in succession, a Reader and then a Professor. He worked mainly on analysis, making important contributions to integration theory, harmonic analysis, Tauberian theorems, inequalities, and convexity theory.
Further information about BosanquetAfter graduating from Balliol Alexander Oppenheim worked first with G.H. Hardy in Oxford, and then with Dickson in Chicago. Oppenheim's conjectures stimulated enormous interest over more than half a century, and were eventually settled by Gel'fand. They had further strong influence on the work of Gregory Margulis for which he received the Fields Medal in 1978. After lecturing at Edinburgh, Oppenheim became Professor of Mathematics at Raffles College, Singapore, where he was taking prisoner by the advancing Japanese army in 1942. He taught and gave chess displays in the prison camps in Thailand, and attributed his survival to his ability to immerse himself in mathematics. After the war, and he held chairs successively at the Universities of Malaysia, Reading, Ghana and Benin.
Henry Whitehead studied at Balliol and, after two years in finance and a research visit to Princeton, returned in 1933 to become Mathematics Tutor, a post he held until his election to the Waynflete Professorship in 1947. (During the war, like many other mathematicians, he worked on cryptography at Bletchley Park.) His treatise with Veblen on The Foundations of Differential Geometry contained the first precise definition of a differential manifold. He is best known for his contributions to algebraic topology and to homological algebra, being one of the founders of each subject. He was well known for his high spirits, and once insisted on being lowered in a laundry basket on the end of a rope out of a fourth floor window at Balliol, in order to avoid disturbing the porter. The Whitehead Prizes of the London Mathematical Society are named after Henry Whitehead.
Further information about WhiteheadJohn Hicks took a first in Mathematics Mods before changing to the new school of Philosophy, Politics and Economics. He became Professor of Political Economy in 1952, and shared the 1972 Nobel Prize in Economics with Kenneth Arrow for contributions to economic equilibrium theory and welfare theory.
Geoffrey Walker came to Balliol as a Mathematics Scholar in 1928. In 1930 he won the Junior Mathematical Exhibition and then graduated with First Class Honours and a distinction in Differential Geometry the following year. He worked on the borders of Differential Geometry and General Relativity and is known particularly for his part in the discovery of the FriedmannRobertsonWalker metrics, and FermiWalker transport in Relativity. He was the first recipient of the London Mathematical Society's Junior Berwick Prize, and was later President of the Society.
Further information about WalkerJack de Wet came to Balliol as a South African Rhodes scholar in 1935. After graduating he studied with Eugene Wigner at Princeton, and his doctoral thesis represented a major step towards the first mathematical proof of the SpinStatistics Theorem in Quantum Field Theory. He continued to work on mathematical problems in physics, and in 1946 returned to Balliol to become a widely admired tutor, held in great affection by his pupils. In 1971 he returned to South Africa as Dean of Sciences at Cape Town. It was whilst he served on the South African Rhodes Scholarship Selection Panel that the first coloured and black Scholars were elected, in each case mathematicians.
Amongst the many distinguished Balliol mathematicians of the last century, Graham Higman is one of two to have been an undergraduate, a graduate student, a Fellow, and an Honorary Fellow of the College. His main contributions to mathematics are in the field of group theory and its connections with logic and combinatorics. A joint paper with Philip Hall provided the basic tools with which Feit and Thompson were able to settle Burnside's conjecture that groups of odd order are solvable. He succeeded his former tutor and supervisor Henry Whitehead as Waynflete Professor of Pure Mathematics in 1960. The following year his new proof of Novikov's theorem opened up a whole new area at the frontier of algebra and logic. Higman is also known for his major contributions to the classification of finite simple groups. he won both the Senior Berwick Prize (1962) and the de Morgan medal (1974) of the London Mathematical Society.
Further information about HigmanDavid Kendall came to Balliol as a Skynner Senior Student in 1939 after graduating from Queen's College. After the war he became tutor at Magdalen College before and moving to the Chair in Mathematical Statistics at Cambridge in 1962. He made numerous contributions to Applied Probability and Statistics, in particular, to stochastic geometry. In addition to his research distinction he was renowned as an excellent lecturer.
Further information about KendallChristopher LonguetHiggins was also an undergraduate, graduate, Fellow and Honorary Fellow of the College. Whilst still an undergraduate (reading chemistry) he proposed the correct structure for diborane, which had until then posed a major problem for valency theory. After distinguished work in theoretical chemistry, he became one of the pioneers of computer programming and artificial intelligence, and was Director of the Institute of Cognitive and Information Sciences at Sussex. He is a foreign associate of the United States National Academy of Sciences. LonguetHiggins was awarded the Naylor Prize and Lecturership of the London Mathematical Society in 1981.

