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.     

N.G. de Bruijn’s contribution to the formalization of mathematics

N.G. (Dick) de Bruijn was the first to develop a formal language suitable for the complete expression of a mathematical subject matter. His formalization does not only regard the usual mathematical expressions, but also all sorts of meta-notions such as definitions, substitutions, theorems and even complete proofs. He envisaged (and demonstrated) that a full formalization enables one to check proofs automatically by means of a computer program. He started developing his ideas about a suitable formal language for mathematics in the end of the 1960s, when computers were still in their infancy. De Bruijn was ahead of his time and much of his work only became known to a wider audience much later. In the present paper we highlight de Bruijn’s contributions to the formalization of mathematics, directed towards verification by a computer, by placing these in their time and by relating them to parallel and later developments. We aim to explain some of the more technical aspects of de Bruijn’s work to a wider audience of interested mathematicians and computer scientists.     

John Reynolds of the Mint: A mathematician in the service of king and commonwealth

In his youth, John Reynolds showed a talent for arithmetic and was destined for a career as a mathematician at the Tower Mint in London. He became skilled in the algorithms needed to determine the correct relationship between the weight and purity of coins and their values. This was a matter of national importance, and his work came to the attention of King James I, who reigned from 1603 to 1625, and his chief ministers, including Robert Cecil and Francis Bacon. It seemed that John might attain high office himself, but the murky administration of the early Stuart period cast its shadow over his career. Nevertheless, for the next forty years he continued to play a major part in the nation's affairs. He produced books of tables for the valuation of coins in the commercial world, and for the highly technical work of the assayers. Also, he was actively involved in the production of standard measures and instruments used by the excise officers. His life and works illustrate how mathematical ideas were employed by the English government in the period of the early Stuart kings and the Commonwealth.     

Contributions of Lo Yang to Value Distribution Theory

Professor Lo Yang is a world famous mathematician of our country. He made a lot of outstanding achievements in the value distribution theory of function theory, which are highly rated and widely quoted by domestic and foreign scholars. He also did a lot of work to develop Chinese mathematics. It can be said that Professor Yang is one of the mathematicians who made main influences on the mathematical development in modern China. This paper briefly introduces Professor Yang’s life, mainly discusses his academic achievement and influence, and briefly describes his contributions to the Chinese mathematics community.     

“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.     

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.     

Ky Fan (1914�C2010), he spent every waking moment thinking about mathematics

This survey article on Dr. Ky Fan summarizes his versatile achievements and fundamental contributions in the fields of topological groups, nonlinear and convex analysis, operator theory, linear algebra and matrix theory, mathematical programming, and approximation theory, etc., and as well reveals Fan’s exemplary mathematical formation opening up the beauty of pure mathematics, with natural conditions, concise statements and elegant proofs. This article contains a brief biography of Dr. Fan and epitomizes his life. He was not only a great mathematician, but also a very serious teacher known to be extremely strict to his students. He loved his motherland and made generous donations for promoting mathematical development in China. He devoted his life to mathematics, continued his research and published papers till 85 years old.     

q-Rook Monoid Algebras, Hecke Algebras, and Schur–Weyl Duality

When we were at the beginnings of our careers, Sergei's support helped us to believe in our work. He generously encouraged us to publish our results on Brauer and Birman–Murakami–Wenzl algebras, results which had in part, or possibly in total, been obtained earlier by Sergei himself. He remains a great inspiration for us, both mathematically and in our memory of his kindness, modesty, generosity, and encouragement to the younger generation. Bibliography: 19 titles.     

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.     

Life and work of George Salmon (1819--1904)

George Salmon achieved prominence both as a mathematician and theologian during the nineteenth century. He was one of the originators, with Cayley and Sylvester, of invariant theory in the 1850s, and published a series of four textbooks on geometric topics which incorporate many of his discoveries. These works in their several editions were pre-eminent in the mathematical literature for fifty years and more, and were translated into most major European languages. I present here a brief survey of Salmon's life and work, drawing on some less familiar sources and revealing aspects of his work and character that are not mentioned in the standard biographical sources. The essay is an extended version of a lecture given by the author at Trinity College Dublin on 6 April 2005.     

The contributions of W.A. harris Jr. to difference equations

William Ashton Harris Jr. was born December 18, 1930 in New Orleans, Louisiana, USA. He studied mathematics with minors in physics and appl ied mechanics (elasticity) at the University of Minnesota receiving his Ph.D. in mathematics in 1955 with the thesis "A boundary value problem for a system of ordinary linear differential equations involving powers of a parameter". His thesis advisor was Professor H.L. Turrittin.He remained at the University of Minnesota and became professor in 1968. In 1970 he moved to the University of Southern California where he stayed until his untimely death on January 8, 1998. He has held visiting appointments at several other universities.     

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.     

Charles Peirce's place in philosophy

Peirce's publications on the method of scientific investigation (as distinct from his work in formal logic and mathematics) are his most important and valuable contributions to philosophy. His views on this subject are superior in clarity and cogency to his voluminous writings on metaphysics and cosmology. He subscribed to a fallibilistic conception of knowledge that is poles apart from a wholesale skepticism; his formulations of the conditions for meaningful discourse and of the pragmatic maxim, though not free from difficulties, have been fruitful sources of much subsequent philosophical and scientific analyses; and his classification of and discussions of types of argument or reasoning employed in scientific inquiry continue to be valuable and insightful clarifications of this important subject. In contrast to his account of scientific method, Peirce's evolutionary theory of ultimate reality, though marked by originality and ingenious speculation, has little merit as a contribution to genuine knowledge.     

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.     

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.     

Affine MDS-codes on Groups

We consider the problem of determining the maximum length of affine MDS-codes on a given finite group G. We show that this problem is closely connected with problems concerning sets of automorphisms of G. For abelian groups the problem is solved. The maximum length is given in terms of invariants of the group.Dedicated to Oswald Giering on the occasion of his 60 th birthdayThis work was done while the second author was visiting Technische Universität München. He wishes to thank the Technische Universität for its hospitality and the DAAD for financial assistance.     

Minimal classes and maximal class inp-groups

The number of conjugacy classes of a given size (not 1) in ap-group is divisible byp-1. We study groups in which the number of classes of minimal size is exactlyp-1, and characterise metabelian groups and groups of maximal class with this property. Part of the work of this author was done during his visit to the University of Napoli, under a CNR grant. He is grateful to that university for its hospitality, and also to Y. Berkovich for interesting discussions on the subject matter of this note.     

论高斯

高斯(C.F.Gauss,1777—1855)生于德国Brunswick,1795—98求学于Gttinsen大学。1807—55任天文观测台台长及Gttingen大学教授。 大家都知道高斯的名言:“数学是科学的女王,算术是数学的女王”这里“算术”是在古希腊人的意义下理解的,指的初等数论,而区别于近代的解析数论。     

Privacy Preserving Link Analysis on Dynamic Weighted Graph

Link analysis algorithms have been used successfully on hyperlinked data to identify authoritative documents and retrieve other information. They also showed great potential in many new areas such as counterterrorism and surveillance. Emergence of new applications and changes in existing ones created new opportunities, as well as difficulties, for them: (1) In many situations where link analysis is applicable, there may not be an explicit hyperlinked structure. (2) The system can be highly dynamic, resulting in constant update to the graph. It is often too expensive to rerun the algorithm for each update. (3) The application often relies heavily on client-side logging and the information encoded in the graph can be very personal and sensitive. In this case privacy becomes a major concern. Existing link analysis algorithms, and their traditional implementations, are not adequate in face of these new challenges. In this paper we propose the use of a weighted graph to define and/or augment a link structure. We present a generalized HITS algorithm that is suitable for running in a dynamic environment. The algorithm uses the idea of “lazy update” to amortize cost across multiple updates while still providing accurate ranking to users in the mean time. We prove the convergence of the new algorithm and evaluate its benefit using the Enron email dataset. Finally we devise a distributed implementation of the algorithm that preserves user privacy thus making it socially acceptable in real-world applications. This material is based upon work supported by the National Science Foundation under Grant No. 0222745. Part of this work was presented at the SDM05 Workshop on Link Analysis in Newport Beach, California, April 2005. Yitao Duan is a Ph.D. candidate in Computer Science at the University of California, Berkeley. His research interests include practical privacy enhancing technologies for a variety of situations including: ubiquitous computing, collaborative work, smart spaces, and location-aware services etc. His research goal is to develop provably strong (cryptographic and information-theoretic) protocols that are practically realizable. He received his B.S. and M.S. in Mechanical Engineering from Beijing University of Aeronautics and Astronautics, China in 1994 and 1997. Jingtao Wang is a Ph.D. student in Computer Science at the University of California, Berkeley. His research interests include context-aware computing, novel end-user interaction techniques and statistical machine learning. He was a research member, later a staff research member and team lead at IBM China Research Lab from 1999 to 2002, working on online handwriting recognition technologies for Asian languages. He received his B.E. and M.E. in electrical and computer engineering from Xi'an Jiaotong University, China in 1996 and 1999. He is a member of the ACM and ACM SIGCHI since 2000. Matthew Kam is a Ph.D. student in computer science at the University of California, Berkeley working on educational technology and human-computer interaction for low-income communities in developing regions. He received a B.A. in economics and a B.S. in Electrical Engineering and Computer Sciences, also from Berkeley. He is a member of the ACM and Engineers for a Sustainable World. John Canny is the Paul and Stacy Jacobs Distinguished Professor of Engineering in Computer Science at the University of California, Berkeley. His research is in human-computer interaction, with an emphasis on modeling methods and privacy approaches using cryptography. He received his Ph.D. in 1987 at the MIT AI Lab. His dissertation on Robot Motion Planning received the ACM dissertation award. He received a Packard Foundation Faculty Fellowship and a Presidential Young Investigator Award. His peer-reviewed publications span robotics, computational geometry, physical simulation, computational algebra, theory and algorithms, information retrieval, HCI and CSCW and cryptography.     

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.