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This is the group of riders - typically star sprinters or hard-working domestiques - who cannot keep up with the best climbers on the punishing climbs through the Alps or the Pyrenees. The introduction to a reprint of the four volumes of Histoire des mathematiques in gives this assessment of Montucla's contribution: Montucla has given us a double lesson in the history of mathematics. Of these lessons, the first is what he has composed for us. A Poster of Etienne Montucla. Mathematical games and recreations. Spottiswoode biography William Spottiswoode's father was Andrew Spottiswoode, a member of the printing firm of Eyre and Spottiswoode, the Queen's printers, and he was related to John Spottiswoode who was archbishop of St Andrews.

A year after William was born Andrew Spottiswoode became member of parliament for Saltash and four years later member of parliament for Colchester. William's mother, Mary Longman, was the daughter of the publisher Thomas Longman. William attended school in Laleham, then went to Eton College, one of the most prestigious schools in England situated on the Thames near London. Certainly this episode proved an advantage to Spottiswoode, who received better teaching in his favourite subject of mathematics in Harrow. Three years later he graduated with a First Class degree in mathematics. In and he was awarded mathematics scholarships at Balliol College where he became a lecturer in mathematics.

In his father had financial problems and Spottiswoode took over the firm of Eyre and Spottiswoode so becoming Queen's Printer. The firm prospered under his leadership and he created a model company with the interests of his employees at heart. His mathematical work was described as 'the incarnation of symmetry'. Besides supplying new proofs by elegant methods of known theorems, he did abundance of important original work. His series of memoirs on the contact of curves and surfaces, contributed to the 'Philosophical Transactions' of and subsequent years, mainly gave him his high rank as a mathematician.

He was also the author in of the first elementary treatise on determinants, and to his treatise much of the rapid development of that subject is attributable. The importance of his textbook Elementary Theorems Relating to Determinantsreferred to in this quote, can be seen from the fact that he was asked by Crelle's Journal to submit a paper to the journal developing his approach to determinants further; this he did in On 2 June Spottiswoode was elected a fellow of the Royal Society. He was appointed president of the mathematical section of the British Association in and was treasurer of the Association from to He also served on the council of the Royal geographical Society from to Their at-homes in Grosvenor Place, held at the height of the London season, attracted the cream of Victorian science and cabinet ministers alike.

During these events the latest news in science would invariably be demonstrated in the laboratory which occupied part of the house. He became a partner, and later a director, of his father's publishing firm of Eyre and Spottiswoode. Certainly Spottiswoode was always a keen traveller and he visited a number of countries which were certainly somewhat unusual for the period. In he visited eastern Russia and took the opportunity to use his literary skills by publishing in a fascinating account in A Tarantasse Journey through Eastern Russia in the Autumn of Inthe year of his marriage, Spottiswoode published On typical mountain ranges: Around there were major changes to the direction of Spottiswoode's research.

This was a time when he received high office in a number of societies, being president of the London Mathematical Society from to and, from tobeing treasurer of the Royal Society. He was also treasurer of the Royal Institution from to In Spottiswoode was elected president of the Royal Society and remained president until his death in Also in the year he was president of the British Association for its Dublin meeting. At the Dublin meeting he gave his presidential address on the growth of mechanised invention applied to mathematics.

We mentioned the change in direction of Spottiswoode's research which turned to physical topics. From he studied the polarisation of light and later he studied electrical discharge in rarefied gases. Spottiswoode published over papers and several books including, in addition to the one on determinants mentioned above: His interests however were not confined to mathematics and physics since he was also a leading expert on European languages and on oriental languages. He combined these different skills by undertaking research on the history of mathematics and astronomy in India. His article in Journal of the Royal Asiatic Society of Great Britain and Ireland discussed the fact that that most of the principles of the differential calculus were known in ancient Indian mathematics before the period of Bhaskara II in the 12th century.

The interesting series of communications on the contact of curves and surfaces which are contained in the Philosophical Transactions of and subsequent years would alone account for the high rank he obtained as a mathematician. The mastery which he had obtained over the mathematical symbols was so complete that he never shrank from the use of expressions, however complicated nay, the more complicated they were the more he seemed to revel in them provided they did not sin against the ruling spirit of all his work symmetry. To a mind imbued with the love of mathematical symmetry the study of determinants had naturally every attraction.

It is remarkable that Spottiswoode was able to undertake the amount of work that he did, both scientific and administrative. He went to Italy on a short holiday to recuperate from overwork and the after-effects of a tricycle accident but after returning home contracted typhoid, and three weeks later died, on 27 Juneat his home, 41 Grosvenor Place. In recognition of his position as president of the Royal Society and his contribution to science he was buried on 5 July in Westminster Abbey in the presence of civic dignitaries and the whole scientific establishment. We should also mention his election to the Academy of Sciences in Paris and the award of honorary degrees by the universities of Cambridge, Dublin, Edinburgh, and Oxford.

She was the youngest of her parents' three surviving children a fourth child died in infancyhaving a sister Esther 4 years older and a brother Elmer 2 years older. Elmer may have lost out because of this determination to see the girls educated for he never attended college although he almost certainly had the ability to do so. Anna also gained from the efforts of her older sister Esther who recognised Anna's mathematical talents and encouraged her greatly. The professor of mathematics, Alexander Pell, recognised her talents and helped persuade Anna that she should follow a career in mathematics. Anna and her sister Esther were at university together and they boarded in the home of Alexander Pell and his wife Emma.

Many of these classes were also taken by her sister Esther. Already when at the University of South Dakota she had ambitions to go further in mathematics. I could easily stay in Germany to study Mathematics since I know so much German already. Certainly she concentrated on the academic side of university life and took relatively little part in other activities. One thing she did take on, however, was secretary and treasurer of the French Club. After winning a scholarship to study for her master's degree at the University of Iowa, she was awarded the degree for a thesis The extension of Galois theory to linear differential equations in During her year at Iowa, in addition to taking five mathematics courses and a philosophy course, she also taught a first year calculus course.

While there Alexander Pell, her former mathematics professor came to Gottingen so that they could marry. I consider her something like a demi-goddess now, for whatever she wants she gets and whatever she studies she make a success of. Anna and Alexander planned to marry, despite the objections of her family to the marriage since Alexander was 25 years older than Anna. There was another difficulty, namely that the Alice Freeman Palmer Fellowship required that the holder did not marry during the tenure of the fellowship. After returning to the United States in Augustwhere her husband was by now Dean of Engineering in South Dakota, she taught courses in the theory of functions and differential equations.

In Gottingen, she completed the work for her doctorate but, after a disagreement with Hilbert, she returned to Chicago in Decemberwhere her husband was now on the staff of the Armour Institute of Technology now the Illinois Institute of Technologywithout the degree being awarded. I send you a sample of Anna's dress goods - she has to appear before the examiner in a black dress. Back in Chicago, she enrolled at the University on 4 January and became a student of Eliakim Moore. She took various courses at Chicago: She also worked at the Chicago Observatory in the summer of Her life and work, Historia Mathematica 9 1 Since my thesis had been written independently of Hilbert, I had a right to use it at the University of Chicago.

Anna Pell had published two papers in the Bulletin of the American Mathematical Society innamely On an integral equation with an adjoined condition and Existence theorems for certain unsymmetric kernels. I had hoped for a position in one of the good universities like Wisconsin, Illinois, etc. It seems that professor Moore has also given up hope for he has inquired at some of the Eastern Girls' Colleges and Bryn Mawr is apparently the only one with a vacancy in mathematics. In the autumn ofAnna Pell taught a course at the University of Chicago then her husband Alexander Pell had a stroke in the spring of Unable to find a replacement, the Armour Institute of Technology asked Anna to substitute for her husband.

After a couple of weeks they told Mr Pell he need not return this semester but take a good rest. I have fifteen hours of subjects in Mathematics and have shown them that a woman is capable of doing a man's work in a technical school. The mathematics men at the University of Chicago were very much pleased that at last a woman had the chance to show her ability in such a place as the Armour Institute. But I know it will take a great number of years, to break down the prejudice. While at this College she published Non-homogeneous linear equations in infinitely many unknowns and with Ruth L Gordon The modified remainders obtained in finding the highest common factor of two polynomials Certainly one of the reasons for taking up this appointment was the fact that Bryn Mawr had a Ph.

The couple built a summer home in the Adirondack mountains, in north-eastern New York State, which they named 'Q. As an administrator, Pell Wheeler worked to enhance the national reputation of the Bryn Mawr mathematics department. Despite the financial effects of the Depression on the college, she tried to create an atmosphere for students and faculty in which there was ample opportunity for professional growth and development, as well as for free interchange of ideas. The direction of Anna Wheeler's research was much influenced by David Hilbert. This work was done in the days when functional analysis was in its infancy and much of her work has lessened in importance as it became part of the more general theory.

In Lichtenstein made connection, without the intermediary of the theory of integral equations, between the theory of linear differential systems of the second order and the theory of linear equations in infinitely many unknowns. Although there are many points of contact between the method used by Lichtenstein and the one used in this paper, the methods are not identical. The method can be extended to yield more general results both for the orthogonal and polar cases of ordinary differential systems. She was appointed as a Trustee of the Society in and served on the Council during She served as an editor of the Annals of Mathematics from to I don't know how she did it, but before you knew it you had told her all sorts of things which you had never intended to tell her.

It was only years later that I truly appreciated the many hours of her precious time she generously gave us. A description of Mrs Wheeler as a teacher would be incomplete without mentioning her appreciation of nature and how she shared it with us. Her love of nature opened new doors. She took us on walks in the woods and taught us to listen for the titmouse and to look for the speckled leaf of the dog-toothed violet. Naimark biography Mark Aronovich was brought up by his Jewish parents Aron Iakovlevich and Zefir Moiseevna in Odessa where he showed an outstanding talent for mathematics while at school.

Inat the age of fifteen, he entered a technical college but also worked in a foundry to earn his living. In addition to these two occupations, which he undertook for four years, he also studied university level mathematics on his own completing a university course on analysis by Then, inafter graduating from the Physico-Chemico-Mathematical Institute he went to Odessa State University to undertake graduate studies in the Department of the Theory of Functions. With Krein, Naimark worked on applying Bezout's determinant to the problem of separating the roots of an algebraic equation. The two collaborated in writing three papers on this topic: It was at this time that his main scientific interests, which relate to the spectral theory of operators in Hilbert space and the representation theory of locally compact groups, were finally formed.

The theory that he developed concerning self-adjoint extensions of symmetric operators with extension of the original Hilbert space was complementary to that developed by von Neumann. They showed that these rings could always be represented as a ring of linear operators on a Hilbert space in On the imbedding of normed rings into a ring of operators in Hilbert space At the start of the war he undertook military work in a number of different places, moving to Tashkent at the end of since the Seismological Institute had been evacuated there from Moscow. He continued to publish joint papers with Gelfand, in particular in they published seven papers: On unitary representations of a complex unimodular group; Unitary representations of the Lorentz group; Unitary representations of the group of complex matrices of the second order the Lorentz group ; Unitary representations of the Lorentz group; Unitary representations of the group of linear transformations of a line; The fundamental series of the irreducible representations of a complex unimodular group; and Auxiliary and degenerate series of the representations of a unimodular group.

They published four joint papers on similar topics inand further papers in each of the years from to Here he regularly gave courses in mathematical analysis, partial differential equations and functional analysis, he also supervised a group of post-graduate students and organized research seminars.

Then inafter years of struggling against discrimination, he became professor in the Department of the Theory of Functions and Functional Analysis at the Steklov Mathematical Institute, a post he continued to hold until his death. During these years he was the only Jewish mathematician employed at the Institute out of a staff of around After his appointment to the Steklov Mathematical Institute he travelled widely and we should make special mention of his lecture tour of Canada in which did much to improve relations between Soviet and Western scientists.

He had a heavy teaching load in the early part of his career but as he became more senior he only taught graduate students and supervised research students. We have already noted that Naimark's first work was on the separation of roots of algebraic equations but, once he had established himself in Moscow, he worked on functional analysis and group representations. In he proved the Gelfand-Naimark theorem on self-adjoint algebras of operators in Hilbert space. He made a detailed analysis of the infinite-dimensional representations of the semisimple Lie groups. His important treatise Unitary representations of the classical groups with Gelfand on irreducible representations of the classical matrix groups was Coventry married women looking in qazvin in This work formed the basis for later contributions by Harish-Chandra on representations of semisimple Lie groups.

I E Segal begins a review of the monograph as follows: This is a fairly comprehensive account of the irreducible continuous unitary representations of the classical simple complex Lie groups, and of related aspects of harmonic analysis on such groups. It supersedes the material published in a long series of earlier notes. This treatise is not merely a technical report on Banach algebras "normed rings" in Soviet parlancebut is actually a compendium of functional analysis, containing a full treatment of those parts of the subject that are relevant to the theory of normed algebras.

The scope of the book is enormous: This work is an important contribution to the literature on the spectral theory of ordinary linear differential operators. The title is somewhat misleading in that partial differential operators are not analysed. Starting from simple facts about boundary-value problems, the author develops the theory of expansion by eigenfunctions, and the spectra of ordinary differential operators, including many of the results obtained recently by Russian mathematicians. In Naimark published Linear representations of the Lorentz group. This book is the first monograph on the representations of the Lorentz group.

It is written principally for theoretical physicists, but the principal results and methods belonging to the author must also be interesting to specialists in mathematics. The exposition begins with elementary concepts of the theory of groups and the theory of group representations; facts about the Coventry married women looking in qazvin group and the rotation group in three-dimensional Euclidean space are given in detail, so that the book can serve as a means for studying the general theory of representations. Wilhelm Magnus reviews the text in [',' W Magnus, Review: At the same time, many generalisations of the results proved are mentioned, and appropriate references are given.

This is an interesting book from several points of view. For the pure mathematician it is a systematic treatment of the Lorentz groups in the classical tradition; for the theoretical physicist the long final chapter on invariant equations is of deep interest; for the social historian this Russian account of the theory of the Lorentz groups reveals the isolation of Russian mathematicians from the work of their Western colleagues, the same isolation manifest in Russian music and literature. In all Naimark wrote papers and 5 books but he also put considerable effort into the translations and further editions of the books. For example, he worked hard to produce a second edition of Normed rings and this appeared in These improvements were incorporated into the second Russian edition of His last book was Theory of group representations published in By the time this book was written Naimark was suffering from heart disease, a problem which afflicted him during the last ten years of his life.

Too ill to sit up yet determined to continue writing the Theory of group representations, he dictated the text to his wife. Naimark's scientific activity was inseparably linked with his pedagogical work and his work on the education of young people. This feature was evident both in his lectures to students and in his scientific talks, articles, and monographs. Those who were lucky enough to be closely associated with Naimark know and remember him as a man of spiritual qualities, unusual honesty, sympathy, high morals, and kindness. Being always a man of principles and conscientiousness in science and in his everyday life, for many he was a model person and scientist.

His world-wide reputation as a leading scholar was evident but he received less recognition by the authorities in his own country than one might have expected [',' V Bilovitsky, Naimark, Mark Aronovich, The YIVO Encyclopedia of Jews in Eastern Europe. Naimark's outstanding contribution to science and his international reputation did not, however, promote him to the official Soviet "table of ranks. Russell Scott biography Died: When John was three years old, his father became minister of Colinsburgh Relief Church, near Kirkcaldy, a congregation which had seceded from the Church of Scotland; but he soon moved on to a larger congregation in Hawick, and married Anne Titterton on 28 April in Kilconquhar, Fife Coventry married women looking in qazvin had more children.

John Scott Russell was primarily an engineer and naval architect, rather than a mathematician; but his name is well-known to applied mathematicians today through his experimental discovery of the 'solitary wave'. This is now recognised as a fundamental ingredient in the theory of 'solitons', applicable to a wide class of nonlinear partial differential equations. Inhe moved to Edinburgh, where he taught mathematics at a 'South Academy', perhaps founded by himself and a friend. Later, he also taught at the Leith Mechanics Institute, and gave courses on mathematics and natural philosophy to medical students, under the auspices of the Royal College of Surgeons.

Duringfollowing the death of John Leslie, he substituted for the professor of natural philosophy at Edinburgh University; but he did not apply for the vacant post, which he was sure would go to David Brewster. InRussell was an unsuccessful applicant for the chair of Mathematics, which Philip Kelland secured. He had more success with the Union Canal Company, investigating the feasability of steam-powered canal transport and studying the connection between resistance to motion and wave-generation. He spoke of his work at early meetings of the British Association for the Advancement of Science, founded in ; and the Association appointed him and Sir John Robison of Edinburgh to a 'Committee on Waves' to conduct observations and experiments.

These reports, in fact all Russell's own work, contain a remarkable series of observations, at sea, in rivers and canals, and in Russell's own wave tank constructed for the purpose. There, Russell's "Great Wave of Translation" is described in detail. George Green, George Airy, Philip Kelland and Samuel Earnshaw all attempted theoretical descriptions of the solitary wave, but these were not successful. Airy objected to the emphasis placed by Russell on his "Great Primary Wave", wrongly arguing that it was neither great nor primary, but just one consequence of the linear shallow water theory which he Airy had given.

A correct approximate theory was at last given by Boussinesq and Rayleigh ; but the issue was not really settled until the appearance of the important paper by Korteweg and de Vries The full significance of the solitary wave and its generalisation was finally uncovered in He first worked on a railway magazine, and he became secretary of the Society of Arts, a post which led to major involvement in planning the Great Exhibition of Thereafter, he became increasingly involved in the design of yachts, boats, barges and ships, and he became a director of a ship-building company. He collaborated with Isambard Kingdom Brunel on the construction of the pioneering iron vessels Great Britain and Great Eastern; and was alone responsible for the successful iron warship Warrior.

In the s, Russell's reputation suffered a number of setbacks from which it never recovered. He became embroiled in a lengthy financial dispute about an armaments contract; the Great Eastern suffered a serious breakdown; and he was controversially expelled from the Institute of Civil Engineers. Much later, he revisited his work on solitary waves, published posthumously as The Wave of Translation in the Oceans of Water, Air and Ether Russell's great love was applied science, and it was perverse fate which channelled him into complicating it with the economic cares of a large and uncertain business. A Poster of John Scott Russell.

Kintala biography Chandra was born in Berhampur which is a town in the south east of the state of Orissa in eastern India. He lost his father in his early teens, which made him face the reality of life quite early and which had a formative influence on him, both as a person and as a scientist. As a scientist in the sense that, although he loved theoretical work, he never lost sight for the so-called more practical aspects and problems of computer science. The College was quite a new one at the time, having been set up in when Jawaharlal Nehru, the Prime Minister of India, laid the foundation stone. The first such courses were established in the Electrical Engineering department in and, init began teaching a programme of Computer Science and Engineering leading to a Master's degree, the M.

However, in Fischer moved to Pennsylvania State University in the United States to take up the position of Head of Department, and Kintala decided to move with his thesis advisor and enrolled in the Ph. He was awarded his doctorate in for his thesis Computations with a restricted number of nondeterministic steps. Following the award of his doctorate, Kintala was appointed as an Assistant Professor at the University of Southern California in The author establishes four infinite hierarchies of families of context-free languages based on i finite unions, ii number of nondeterministic moves of nondeterministic pushdown automata, iii finite intersections, and iv finite concatenations, respectively.

All these hierarchies lie between the families of deterministic and unambiguous context-free languages. The authors investigate the nature of nondeterminism by restricting the number of nondeterministic moves in accepting computations of a multitape Turing machine. Despite one erroneous "theorem", the paper presents some interesting facts which add to our understanding of automata-based complexity theory. As well as being years in which he undertook deep research into the theory of computation, particularly working with his colleague Seymour Ginsburg and with Ronald Book who was working at the University of California at Santa Barbara, he also married and settled into a family life [',' M Kappes, A Malcher and D Wotschke, Remembering Chandra Kintala, in I McQuillan and G Pighizzini eds.

As much as Chandra enjoyed life there, professionally and privately, he missed a close interaction with the more practical side of computer science. Those years were, in his own words, among the happiest years of his life, as the research culture at Bell Labs provided exactly the close and stimulating interaction between theory and applications that he had always been looking for. And since he always liked teaching, he also taught courses at Steven's Institute of Technology in New Jersey, first as an Adjunct Professor and later as a Distinguished Industry Professor. Some of the noteworthy accomplishments in Bell Labs are: Together with David Belanger, Kintala was awarded a patent for "A generator of program generators" in Our innovative code generation technique interprets a program abstraction, derived after studying a class of programs, against an attributed tree, representing a specification of problem instance, to generate a target program for solving the problem from the specification.

First, a basic part allows flexibility within a domain by interpreting many abstractions of problems. Although much of Kintala's work falls outside what we would call mathematics, there is still quite a substantial number of papers which do fall within that topic and are reviewed in Mathematical reviews. Among these are the multi-authored articles Strict interpretations of deterministic pushdown acceptorsConcurrent conciseness of degree, probabilistic, nondeterministic and deterministic finite automataOn measuring nondeterminism in regular languagesand Concise representations of regular languages by degree and probabilistic finite automata As to his teaching, let us note the courses he gave at Stevens Institute of Technology, Hoboken.

Motorola Labs is at the forefront of applied research and leading the team in India will be a great opportunity as well as an honour. Sadly he only held this position for a few months before a heart attack led to his sudden death at the age of Kintala was honoured with the award of the Smithsonian medal, sponsored by Computer World, in Let us end by quoting one of the tributes from [',' Chandra M Kintala Ph. Chandra Kintala was a man of learning and insight and possessed extraordinary clarity of mind. He was very fond of geography, and considered this might be the topic for him, but he also had a great passion for butterflies - this was his schoolboy hobby.

However, there were other influences on the young boy [',' J Muukkonen, Science is universal, Academy of Finland. I also considered going into the field of law. My uncle was a professor at Helsinki University of Technology and tried to lure me into the field of technology, but I knew all along that it wasn't for me. My father had a Master's degree in mathematics. I figured that the field would offer me an enormous range of possibilities after graduation. Because World War II broke out, Lehto never took his matriculation examination and had to sit behind an artillery gun on Finland's eastern border. However, we need to look at some Finnish history in order to understand the events that took place during World War II.

Finland had taken the opportunity of declaring its independence in December when Russia was occupied with its own internal affairs of the Russian Revolution. The Soviet Union clearly did not trust their German allies, for they demanded territory from Finland to improve the security of Leningrad. The Finns put up a remarkably good defence against their massive neighbour but, after initial Finnish victories, they were forced to sign the Treaty of Moscow in March which leased large parts of south east Finland to the Soviet Union. When Germany attacked their former ally, the Soviet Union, on 22 JuneFinland moved their forces to retake the land given up to the Soviet Union in the Treaty of Moscow.

Despite not having taken the matriculation examinations, Lehto was able to enter the University of Helsinki in German defeats, however, eventually led to the Soviet Union again taking land from Finland in June and in September of that year they agreed again to the terms of the Treaty of Moscow. This "War of Lapland" dragged on until 27 April Lehto was a soldier in the Finnish army training at the Riihimaki Artillery Training Academy in Riihimaki, about 70 km north of Helsinki. As well as fighting the Soviets on Finland's eastern border, he was also involved in the "War of Lapland" in the north where he fought against the Germans [',' J Muukkonen, Review: Mathematics hit me like a tsunami when I was almost exactly 20 years old, when I was able to get over the war years during which I had suppressed my desire to learn new things.

From that time on he was an outstanding student but his chance of an international education came through a piece of good fortune. During World War II, Rolf Nevanlinna had been rector of the University of Helsinki but, after the defeat of Germany inthe authorities at Helsinki University felt that it would be inappropriate to have a rector who was known to have German sympathies so he was asked to resign from that role. This marks the beginning of a fifteen year period during which he was a guest lecturer in Zurich. Nevanlinna played an important role in Lehto's career beginning from the time that he was an examiner of Lehto's Master's thesis.

Impressed with Lehto's work, Nevanlinna arranged for him to receive a scholarship to study with him at Zurich [',' Logic and a stroke of luck, Helsinki University Bulletin 2 A review of the page thesis by Z Nehari indicates the areas that it covered: In Chapters of this thesis, the author largely restates earlier results, due mainly to Bergman and Schiffer, concerning the application of complete sets of complex orthonormal functions to the theory of conformal mapping. Despite its great intrinsic elegance and its adaptability for numerical computations, the theory of complex orthonormal functions centring about the concept of the Bergman kernel function had the drawback of being a mere representation theory; the fundamental existence theorems had to be borrowed from other fields.

In Chapter 4 the author fills this gap in one important instance by giving an existence proof for the parallel slit mappings in the case of simply-connected domains this is identical with the Riemann mapping theorem within the framework of the orthonormal function theory.

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