“Knowledge gained by experience”: Olaus Henrici—engineer,geometer and maker of mathematical models

The German mathematician Olaus Henrici,¹ who was born in Denmark in 1840, studied engineering and mathematics in Germany before making his career in London. Initially, and for only a short time, he worked in an engineering business. He subsequently took on academic positions, first at University College London and then, from 1884, at the newly formed Central Institution (later Central Technical College) where he established a Laboratory of Mechanics. While at University College he became an active promoter of pure geometry and a producer of models of surfaces. In this paper I explore the geometrical side of Henrici's work, setting it into the context of his career and arguing that his interdisciplinary background was a key factor in his success as a creator of models.     

Die Habilitation von John von Neumann an der Friedrich-Wilhelms-Universität in Berlin: Urteile über einen ungarisch-jüdischen Mathematiker in Deutschland im Jahr 1927

The mathematician John von Neumann was born in Hungary but principally received his scientific education and socialization in the German science system. He received his Habilitation from the Friedrich-Wilhelms–Universität in Berlin in 1927, where he lectured as a Privatdozent until his emigration to the USA. This article aims at making a contribution to this early part of Neumann’s scientific biography by analyzing in detail the procedure that led to his Habilitation as well as the beginnings of Neumann’s research on functional analysis. An analysis of the relevant sources shows that in Berlin in the year 1927 Neumann was not yet regarded as the outstanding mathematical genius of the 20th century. Furthermore it will be seen that Neumann had great difficulties in developing the fundamental concepts for his path breaking work in spectral theory and only managed to do so with the support of the Berlin mathematician Erhard Schmidt.     

Brian Hartley, 1939-94

Brian Hartley began his algebraic career as one of Philip Hall'sresearch students in Cambridge. He obtained his Ph.D. in 1964,spent two post-doctoral years in the USA and, on his returnto the United Kingdom, accepted a lectureship in the newly establishedMathematics Department at Warwick University; there he was promotedto a readership in 1973. He was appointed to a chair of puremathematics at the University of Manchester in 1977 and wasHead of the Mathematics Department there from 1982–4.He was elected to the London Mathematical Society in 1968 andserved on Council from 1987–9. He won an EPSRC SeniorResearch Fellowship, but died on 8 October 1994, a few daysafter taking it up. He travelled widely and took a lively interestin other cultures and languages. His intellectual energy, enthusiasmfor algebra, direct manner and dry sense of humour endearedhim to the many mathematical friends he made around the world.He was devoted to mathematics and gave generously of his timeand energy in support of younger colleagues.     

An interview with Laurens de Haan

Laurens de Haan was born January 15, 1937 in Rotterdam, The Netherlands. He graduated 1966 in mathematics and received a doctoral degree in 1970 from the University of Amsterdam, while working at the Mathematical center CWI in Amsterdam. Since 1973 he was Professor for probability and mathematical statistics at the Econometric Institute of the Economic Faculty at the Erasmus University Rotterdam, where he retired 1998. Since 2008 he is part-time professor at the Department of Econometrics and Operations Research of Tilburg University. Laurens de Haan has been active in research throughout his career. He has published more than 110 scientific papers. Among other distinctions, he was elected IMS fellow for his seminal contributions to extreme value theory in 1977, and he was appointed Honorary Doctor of the University of Lisbon in 2000.     

John von Neumann, the Mathematician

Imagine a poll to choose the best-known mathematician of the twentieth century. No doubt the winner would be John von Neumann. Reasons are seen, for instance, in the title of the excellent biography [M] by Macrae: John von Neumann. The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More. Indeed, he was a fundamental figure not only in designing modern computers but also in defining their place in society and envisioning their potential. His minimax theorem, the first theorem of game theory, and later his equilibrium model of economy, essentially inaugurated the new science of mathematical economics. He played an important role in the development of the atomic bomb. However, behind all these, he was a brilliant mathematician. My goal here is to concentrate on his development and achievements as a mathematician and the evolution of his mathematical interests.     

Shiing-Shen Chern��s Centenary

Shiing-Shen Chern was an editor of our journal Results in Mathematics from 1984 to 2004, the year he passed away at Tianjin. This article honors one of the greatest mathematicians of the twentieth century, in particular remembering his studies at Hamburg University during the years 1934?C1936. This period strongly influenced his mathematical work and was decisive for his later career. We survey the situation of the Department of Mathematics there, Chern??s studies, his visits to Germany in later years, his honours and awards from German institutions, and finally exemplarily his influence on the next generations of Chinese mathematicians studying in Germany.     

John Hawkes (1944-2001)

In his curriculum vitae, John Hawkes lists his research interestsas geometric measure theory, probability (Lévy processes),and potential theory (probabilistic). In fact, he made significantcontributions to all three areas, and there are strong relationshipsbetween them. He used both geometric measure theory and potentialtheory as tools for his study of the trajectories of particularLévy processes, but in many cases he needed to developthe tool before it was ready to be used. We will summarise hisresearch later, but first we discuss what is known of his lifehistory.     

E.W. Chittenden and the early history of general topology

E.W. Chittenden's work and its influence on the early history of general topology are examined. Particular attention is given to his work in metrization theory and its role in the background of the Aleksandrov-Uryson Metrization Theorem. A recounting of Professor Chittenden's career, a list of his students and his publications and a chronology in the early history of General Topology are also included.     

Scientific contributions of Leo Khachiyan (a short overview)

On April 29, 2005, Leo Khachiyan passed away with tragic suddenness in the middle of his scientific career. He became famous for his polynomial time algorithm for linear programming (LP)[L. Khachiyan, A polynomial algorithm in linear programming, Soviet Math. Doklady 20 (1) (1979) 191-194; L. Khachiyan, Polynomial algorithms for linear programming, USSR Comp. Math. and Math. Phys. 20 (2) (1980) 51-68]. However, he contributed fundamentally to several other areas, as well. In this introductory paper, we would like to recall briefly his main contributions, and provide a complete (up to our best knowledge) list of his publications.     

Philip Holgate (1934-1993)

Philip Holgate was born in Chesterfield on 8 December 1934.His family moved from Derbyshire to Devon in 1945, and he waseducated at Newton Abbot Grammar School from 1945 to 1952, andthe University College of the South-West (now Exeter University,but which then awarded London degrees) from 1952 to 1955. Hequalified as both a teacher (King's College, London, 1955–56)and a statistician (University College, London, 1956–57). After teaching mathematics and physics at Burgess Hill School,in Hampstead and then in Borehamwood, Philip joined the StatisticsSection at Rothamsted Experimental Station (1961–62).He then spent five years in the Biometrics Section of the NatureConservancy. His first publications date from this period, andthe interests he acquired then were to develop into what becamehis most enduring, and distinctive, scientific interests. Philip joined the Department of Statistics, Birkbeck College,University of London, in 1967, and remained at Birkbeck forthe rest of his career, until his death from a heart attackon 13 April 1993.     

The mathematics of F. J. Almgren, Jr.

Frederick Justin Almgren, Jr, one of the world’s leading geometric analysts and a pioneer in the geometric calculus of variations, died on February 5, 1997 at the age of 63 as a result of myelodysplasia. Throughout his career, Almgren brought great geometric insight, technical power, and relentless determination to bear on a series of the most important and difficult problems in his field. He solved many of them and, in the process, discovered ideas which turned out to be useful for many other problems. This article is a more-or-less chronological survey of Almgren’s mathematical research. (Excerpts from this article appeared in the December 1997 issue of theNotices of the American Mathematical Society.) Almgren was also an outstanding educator, and he supervised the thesis work of nineteen PhD students; the 1997 volume 6 issue of the journalExperimental Mathematics is dedicated to Almgren and contains reminiscences by two of his PhD students and by various colleagues. A general article about Almgren’s life appeared in the October 1997Notices of the American Mathematical Society [MD]. See [T3]for a brief biography.     

Kenneth O. May, 1915–1977 : His early life to 1946

Kenneth Ownsworth May graduated from the University of California at Berkeley in 1936 with highest honors in mathematics. The following year he received his Masters degree and became a fellow of the Institute of Current World Affairs, and during the next two years he traveled to England, Europe, and Russia. On his return to the United States he became active in the Communist Party, the consequences of which would plague him for years. He joined the United States Army in 1942, serving with distinction, and after the war returned to Berkeley, where he obtained his Ph.D. in 1946. He immediately accepted an assistant professorship at Carleton College in Northfield, Minnesota, later moving to the University of Toronto.This part of May's biography focuses on the events up to his accepting a position at Carleton College. In this early phase his openness, his emphasis on good communications in the process of education, and his interest in practical procedures emerge which later set the background for his successful career as a leading historian of mathematics and the founding editor of Historia Mathematica.     

Bibhutibhusan datta (1888–1958), historian of Indian mathematics

Born to a poor Bengali family, Bibhutibhusan Datta (1888–1958) was indifferent to wordly pleasures and gains. He never married. His doctoral thesis was on hydrodynamics, but he is best known for his work on the history of mathematics. He retired voluntarily from the University of Calcutta at the age of 45 and in 1938 took sany$\text{a}$sa (literally, renunciation) to become known as Swami Vidyaranya. He also wrote on Indian religion and philosophy.     

Basil Cameron Rennie

Basil Rennie was born in London on 24 December 1920. He camefrom a long line of engineers, a family tradition that surfacedin much of his later mathematical work. He attended the UniversityCollege School in London, where he obtained a Mathematical Scholarshipat Peterhouse, Cambridge. After graduating in 1941, he foundemployment first with the Rolls Royce Aero Engine division,then with Austin Motor Works. In 1943 he joined the Fleet AirArm of the Royal Navy as a radio mechanic, and he served inthe Pacific Fleet until the end of the war. This was his firstcontact with Australia, and he seems to have liked what he saw. After his service with the Navy, Rennie resumed his studiesat Peterhouse and received a PhD in 1949. Given his strong practicalbent, it is perhaps surprising that he chose lattice theoryas the subject of his thesis; apart from an article [1] in theProceedings of the London Mathematical Society (he became amember in 1947) and a small booklet [2] published at his ownexpense, he never touched lattice theory again. It was at Peterhousethat he took up rowing, an activity which became a life-longinterest. In 1950 Rennie accepted an offer of a senior lectureship atthe University of Adelaide in South Australia. This was a timeof considerable post-war expansion at the University, and itsforward-looking Vice-Chancellor A. P. Rowe recruited a numberof young and promising staff from overseas, some to leadingpositions. For instance, he established a Mathematical Physicsdepartment (unique in Australia) with the 30-year-old H. S.Green as its head, which became one of the most active researchdepartments in Australia.     

Nathan Jacobson (1910-1999)

Nathan Jacobson, who died on 5 December 1999, was an outstandingalgebraist, whose work on almost all aspects of algebra wasof fundamental importance, and whose writings will exercisea lasting influence. He had been an honorary member of the Societysince 1972. Nathan Jacobson (later known as ‘Jake’ to his friends)was born in Warsaw (in what he describes as the ‘Jewishghetto’) on 5 October 1910 (through an error some documentshave the date 8 September); he was the second son of CharlesJacobson (as he would be known later) and his wife Pauline,née Rosenberg. His family emigrated to the USA duringthe First World War, first to Nashville, Tennessee, where hisfather owned a small grocery store, but they then settled inBirmingham, Alabama, where Nathan received most of his schooling.Later the family moved to Columbus, Mississippi, but the youngNathan entered the University of Alabama in 1926 and graduatedin 1930. His initial aim was to follow an uncle and obtain adegree in law, but at the same time he took all the (not verynumerous) mathematics courses, in which he did so well thathe was offered a teaching assistantship in mathematics in hisjunior (3rd) year. This marked a turning point; he now decidedto major in mathematics and pursue this study beyond College.During his final year at Alabama he applied for admission andfinancial aid to three top graduate schools in the country:Princeton, Harvard and Chicago. He was awarded a research assistantshipat Princeton; after the first year he was appointed a part-timeinstructor for two years, and during his fourth year he wasappointed a Procter Fellow. The stipend was enough to enablehim to make a grand tour of Europe by car in 1935, in the companyof two Princeton fellow-students at the time: H. F. Bohnenblustand Robert J. Walker.     

A Hyper-Geometric Approach to the BMV-Conjecture

We prove positivity of the BMV measure in dimension d = 3 in several non-trivial cases by combinatorial methods. The second author was supported by the Wittgenstein prize program Z-36. Much of this work has been done, while he was visiting the university Paris 9. He thanks I. Ekeland and E. Jouini for their hospitality. The third author had the opportunity to spend one month at the university Paris 7 and three weeks at CREST. He thanks in particular for the kind hospitality of Laurence Carassus and Nizar Touzi. The initial motivation for our research on the problem happened during conversations with Peter Michor and Martin Feldbacher. The authors are indebted to M. Fannes and R. Werner who kindly offered us a preprint on known results concerning the BMV-conjecture. The authors also thank the anonymous referee for her/his comments.     

The life and work of André Cholesky

Cholesky’s method for solving a system of linear equations with a symmetric positive definite matrix is well known. In this paper, I will give an account of the life of Cholesky, analyze an unknown and unpublished paper of him where he explains his method, and review his other scientific works. I dedicated this work to John (Jack) Todd with esteem and respect at the occasion of his 95th anniversary.     

Toward a scientific and personal biography of Tullio Levi-Civita (1873–1941)

Tullio Levi-Civita was one of the most important Italian mathematicians of the first part of the 20th century, contributing significantly to a number of research fields in mathematics and physics. In addition, he was involved in the social and political life of his time and suffered severe political and racial persecution during the period of Fascism. He tried repeatedly and in several cases successfully to help colleagues and students who were victims of anti-Semitism in Italy and Germany. His scientific and private life is well documented in the letters and documents contained in his Archive. The authors' aim is to illustrate the events of his life by means of his large and remarkable correspondence.     

Researcher,Teacher, Education Researcher: The Evolution of a University Geoscience Instructor

This case study describes a professor's evolution from geoscience researcher to effective teacher to education researcher. The article details his initial beliefs about teaching, looks at the factors that prompted him to seek a different teaching approach, and enumerates the supports and challenges that he had on his journey. Factors essential to this evolution are early career success in discipline research, an institutional climate to reward teaching, mentoring support by colleagues, access to professional development opportunities, and involvement in action research activities. The case study is linked to education literature about teaching and education research and makes recommendations based on the findings of the study.     

Kunihiko Kodaira

Kunihiko Kodaira, who died on 26 July 1997, was the outstandingJapanese mathematician of the post-war period, his fame establishedby the award of the Fields Medal at the Amsterdam Congress in1954. He was born on 16 March 1915, the son of an agricultural scientistwho at one time was Vice Minister of Agriculture in the JapaneseGovernment and had also played an active role in agriculturaldevelopments in South America. Kodaira studied at Tokyo University,taking degrees in both mathematics and physics. From 1944 to1951 he was an associate professor of physics at the University.His PhD thesis was published in the Annals of Mathematics [18],and it immediately attracted international attention. Essentiallythis filled a significant lacuna in the basic theorem of W.V. D. Hodge on harmonic integrals. Kodaira had worked on thisfor many years but, because of the war, his research was carriedout in isolation from the international community and did notbecome known until much later. Hermann Weyl, who had been a keen supporter of Hodge's work,realised the importance of Kodaira's thesis, and arranged forhim to come to the Institute for Advanced Study in Princetonin 1949. This was the start of Kodaira's 18-year residence inthe United States, a fruitful period which saw the full blossomingof his research, much of it in collaboration with Donald Spencer.Kodaira spent many years at Princeton, divided between the Instituteand the University, but the years 1961–67 were more unsettled,seeing him successively at Harvard, Johns Hopkins and finallyStanford. In 1967 he returned to a professorship at the Universityof Tokyo, where he remained until the normal retiring age. From1975 to 1985 he worked at Gakushuin University, where retirementrestrictions did not apply.