British Journal for the History of Mathematics最新文献

{"title":"‘What to solve?’ – on Judita Cofman’s research on mathematics and its teaching","authors":"Martina R. Schneider","doi":"10.1080/26375451.2022.2047575","DOIUrl":"https://doi.org/10.1080/26375451.2022.2047575","url":null,"abstract":"In 2021 Mainz university (founded in 1477) celebrated the seventy-fifth anniversary of its re-opening after its closure in the wake of the Napoleonic Wars. The mathematical department seized the opportunity to commemorate its first female professor of mathematics, Judita Cofman (1936–2001), by an online symposium in November 2021, which was organized by Dr Martina R Schneider. Judita Cofman was trained as a mathematics teacher and did a PhD in the field of finite geometries in Novi Sad (Yugoslavia) in 1963, after a research stay in Rome. She worked as a mathematician at the universities of Frankfurt amMain, London, Tübingen and Mainz. In 1978 she quit her job as professor at Mainz university to become a teacher of mathematics at Putney High School in London. In 1993 she was appointed professor of didactics of mathematics at the university of Erlangen-Nürnberg. After her retirement in 2001 she re-located to Debrecen (Hungary) and continued her work at the local university (Nikolić 2012, 2014). This short biography alone raises many questions. The symposium has made clear that Judita Cofman’s research and biography are not only of local historical interest. In addition to that, they touch upon several topics in the history of twentieth-century European mathematics that have been neglected or need further investigation. To mention only one: the exploration of Cofman’s biographical trajectory from Yugoslavia via Italy, the UK, and (West) Germany to Hungary promises new insights into the processes of circulation of mathematical and teaching practices and cultures between the East and the West during the Cold War and thereafter. The first section of the symposium was devoted to Cofman as a mathematician in Mainz. Andrea Blunck (Hamburg) gave a talk on women in mathematics in Germany. This made clear that Cofman’s appointment as professor in Mainz in 1973 fell in a","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"37 1","pages":"96 - 98"},"PeriodicalIF":0.4,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44071888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Women’s participation in mathematics in Scotland, 1730–1850","authors":"Amie Morrison, Isobel Falconer","doi":"10.1080/26375451.2022.2053370","DOIUrl":"https://doi.org/10.1080/26375451.2022.2053370","url":null,"abstract":"The eighteenth century saw a flourishing of scientific and philosophical thought throughout Scotland, known as the Scottish Enlightenment. The accomplishments of prominent male figures of this period have been well documented in all disciplines. However, studies of women’s experiences are relatively sparse. This paper partially corrects this oversight by drawing together evidence for women’s participation in mathematics in Scotland between 1730 and 1850. In considering women across all social classes, it argues for a broad definition of ‘mathematics’ that includes arithmetic and astronomy, and assesses women’s opportunities for engagement under three headings: education, family, and sociability. It concludes that certain elements of Scottish Enlightenment culture promoted wider participation by women in mathematical activities than has previously been recognized, but that such participation continued to be circumscribed by societal views of the role of women within family formation.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"37 1","pages":"2 - 23"},"PeriodicalIF":0.4,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48112216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BSHM Meeting News","authors":"Bshm Meeting Coordinator, Isobel Falconer, P. Neumann, Cheryl E Prager, K. Parshall, J. Gray, Niccolo Guicciardini Milan, Brigitte Stenhouse, K. Falconer, T. H. Kjeldsen","doi":"10.1080/26375451.2022.2039514","DOIUrl":"https://doi.org/10.1080/26375451.2022.2039514","url":null,"abstract":"s from past meetings History of Decision Mathematics Saturday 15 May 2021 Online from Birkbeck College, London Tinne Hoff Kjeldsen (University of Copenhagen) The emergence of nonlinear programming: Duality and WWII The significance of internal and external driving forces in the history of mathematics. In this talk we will discuss the emergence of nonlinear programming as a research field in mathematics in the 1950s. We will especially focus on various kinds of driving forces both from inside and outside of mathematics, and discuss the significance of their influence on its development. The term ‘nonlinear programming’ entered into mathematics when the two Princeton mathematicians Albert W Tucker and Harold W Kuhn at a conference in 1950 proved what became known as the Kuhn-Tucker theorem. Later it turned out that a similar result had been proved earlier, even twice: in 1939 and 1948, but nothing came of it. Kuhn and Tucker’s workon nonlinear programming grew out their work on duality in linear programming, which in itself originated from investigations of a mathematical model of a logistic problem in the US Air Force from the Second World War. This short outline prompts several questions: Why could the result of the Kuhn-Tucker theorem all of a sudden launch a new research field in mathematics in 1950? How did ideas of duality emerge in linear programming, and what role did they play for the development of nonlinear programming? How did the Air Force logistic problem cross the boundary to academic research in mathematics? What role did the military play and what influence did it have for the emergence of mathematical programming as a research area in mathematics in academia? The talk will be governed by these questions, and the answers will show that both internal and external factors influenced the mathematicians’ work in crucial ways, illustrating the interplay between developments of mathematics and the historical conditions of its development. Norman Biggs (London School of Economics) Linear Programming from Fibonacci to Farkas Linear Programming is a 20th-century invention, but its roots can be traced back to the tenth century, when the Islamic mathematician Abu Kamil wrote about ‘The Problem of the Birds’ This was one of several problems on ‘mixtures’ that appeared in Fibonacci’s 1202 manual of commercial arithmetic, the Liber Abbaci — in a chapter on ‘The Alloying of Monies’. His work was repeated in the early printed books of arithmetic, many of which contained chapters on Alligation, as the subject became known. Around 1600 the introduction of modern notation clarified the link with the study of linear inequalities and Diophantine problems. The next step was Fourier’s work on Statics, which led him to suggest a procedure for handling linear inequalities based on a combination of logic and algebra. He also introduced the idea of describing the set of feasible solutions geometrically. In 1898, inspired by Fourier’s work, Gyula Farkas prove","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"37 1","pages":"86 - 95"},"PeriodicalIF":0.4,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48512182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symbols and things: mathematics in the age of steam","authors":"J. Wess","doi":"10.1080/26375451.2022.2036410","DOIUrl":"https://doi.org/10.1080/26375451.2022.2036410","url":null,"abstract":"simple algebra based on the laws of probability, under certain assumptions. For example, he assumes that if A and B die in the same year, the probability that A dies first is the same as the probability that B dies first. In this paper Morgan does not use anything that might be called ‘higher’ mathematics: his main concern is to extract useful information from the tables of life expectancy. He recommends the table culled from the records of the town of Northampton. Morgan wrote several more papers on actuarial matters for the Philosophical Transactions and was elected a Fellow of the Royal Society in 1790. He also wrote some highly controversial pamphlets about the government’s economic policies, and he became involved in radical activities. This led to his being summoned to appear as a witness in the trial of Horne Tooke for High Treason in 1793, although he did not, in fact, have to give evidence. His statements on the affairs of the Equitable Assurance Company were increasingly attracting adverse comments from influential and knowledgeable people. It was clear that the tables from Northampton were not a good basis for insurance valuations, particularly in the case of the people who actually had the means to invest in life policies. In 1819, the young Charles Babbage became interested in the subject and drew up a scheme of his own, which he sent to Morgan, asking for his opinion. Morgan’s reply was phrased in the elaborate language of the time, but in effect it was a curt refusal to engage in debate. The controversy came to a head in 1826, with the publication of Babbage’s Comparative View of the Various Institutions for the Assurance of Lives. In the same year, Francis Baily, who was later to become famous for his astronomical discoveries but had already published books on actuarial matters, wrote a letter critical of Morgan to the Times, to which Morgan responded in his typically assertive way. A couple of years later, an anonymous letter addressed to Morgan appeared in the Philosophical Magazine, with the opening ‘Dear Sir, Having unfortunately failed on some former occasions, of fully comprehending the meaning of your expressions... ’. The author was in fact Thomas Young, the eminent polymath, and the letter is printed in his MiscellaneousWorks, edited by Peacock. The need for improved data and amore sophisticated basis for the calculation of premiums was generally recognized. When William Morgan died in 1833, he had been overtaken in his position as the leader of the actuarial profession, but he is rightly remembered as one of the pioneers in the field.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"37 1","pages":"82 - 85"},"PeriodicalIF":0.4,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46840905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear algebra and multivariate analysis in statistics: development and interconnections in the twentieth century","authors":"N. Bingham, W. Krzanowski","doi":"10.1080/26375451.2022.2045811","DOIUrl":"https://doi.org/10.1080/26375451.2022.2045811","url":null,"abstract":"The most obvious points of contact between linear and matrix algebra and statistics are in the area of multivariate analysis. We review the way that, as both developed during the last century, the two influenced each other by examining a number of key areas. We begin with matrix and linear algebra, its emergence in the nineteenth century, and its eventual penetration into the undergraduate curriculum in the twentieth century. We continue with a similar account for multivariate analysis in statistics. We pick out the year 1936 for three key developments, and the early post-war period for three more. We then turn to some special results in linear algebra that we need. We briefly discuss four of the main contributors, and close with thirteen ‘case studies’, showing in a range of specific cases how these general algebraic methods have been put to good use and changed the face of statistics.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"37 1","pages":"43 - 63"},"PeriodicalIF":0.4,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44238381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Why was Leonhard Euler blind?","authors":"J. Bullock, R. Warwar, H. Hawley","doi":"10.1080/26375451.2022.2052493","DOIUrl":"https://doi.org/10.1080/26375451.2022.2052493","url":null,"abstract":"Leonhard Euler was one of the most eminent mathematicians of all time. In 1735, he developed right periocular swelling, partial loss of vision, and the onset of lifelong recurrent fevers from a heretofore-unknown affliction. Three years later, he developed an infection in the right eye area resulting in right eye blindness, a drooping right upper eyelid with a smaller right pupil, and a right vertical eye muscle imbalance. In 1771, complications from a left cataract operation rendered him almost totally blind now in both eyes. On 18 September 1783, Euler lost the remaining vision in his left eye, and later that day died suddenly from a presumed brain haemorrhage. For centuries, an essential part of the Russian diet had been raw milk, the consumption of which is a significant risk factor for brucellosis (undulant fever) which was endemic in Russia in the eighteenth century (and still is today). Given the history of an acute recurrent infectious febrile illness with ophthalmic and neurological complications and having the probable terminal event being a haemorrhagic stroke, Euler’s most likely posthumous diagnoses are ocular, systemic, and neuro-brucellosis with a cerebral haemorrhage from a ruptured Brucella-infected aneurysm.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"37 1","pages":"24 - 42"},"PeriodicalIF":0.4,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47336736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A history of solving some famous problems in mathematical analysis","authors":"P. Enflo, M. Moslehian, J. Seoane-Sepúlveda","doi":"10.1080/26375451.2022.2037358","DOIUrl":"https://doi.org/10.1080/26375451.2022.2037358","url":null,"abstract":"This paper provides a historical view of what functional analysis is, a biography of Per H. Enflo and a short view of four fundamental problems in the geometry of Banach spaces. It gives the story of how Enflo, after several years of work, managed to solve three of these problems. It is a story of trying many ideas, testing them on simpler problems, trying to combine different techniques for handling different aspects of the problems, making many failed attempts and finally succeeding. In 1966 Enflo found a general strategy for solving many problems in infinite dimensions, by combining appropriate finite-dimensional techniques with induction procedures. When applied to the old, fundamental problems in functional analysis, this has led to new concepts, problems, techniques and results in analysis. These developments have been applied also in several other areas of mathematics and computer science.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"37 1","pages":"64 - 80"},"PeriodicalIF":0.4,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46736138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kepler’s derivation of the bisection of the earth’s orbit in Astronomia Nova","authors":"G. Recio","doi":"10.1080/26375451.2021.1984061","DOIUrl":"https://doi.org/10.1080/26375451.2021.1984061","url":null,"abstract":"Chapter 22 of Astronomia Nova is focused on the calculation of the Earth’s eccentricity. This is carried out by observing the effect of the Earth’s motion on the apparent position of Mars. Kepler’s method to derive the exact eccentricity, however, requires as data a set of longitudes of Mars while that planet and the Earth are in a very particular and restricted number of possible configurations. This paper explains how Kepler understood and tackled the Earth problem in theoretical terms, and also how he drew information from Tycho’s observational registers in a methodical way in order to obtain the necessary data to calculate the desired parameter, i.e. the eccentricity of the Earth’s orbit. In doing so, I will analyze not only Astronomia Nova’s relevant passages, but also Kepler’s preliminary annotations, as published in the Gesammelte Werke.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"36 1","pages":"151 - 169"},"PeriodicalIF":0.4,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46920781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Calculus Gems","authors":"Danny Otero","doi":"10.1080/26375451.2021.1997199","DOIUrl":"https://doi.org/10.1080/26375451.2021.1997199","url":null,"abstract":"","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"36 1","pages":"219 - 221"},"PeriodicalIF":0.4,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49310936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical women in the British Isles 1878–1940: using the Davis archive","authors":"J. Aldrich","doi":"10.1080/26375451.2021.2003657","DOIUrl":"https://doi.org/10.1080/26375451.2021.2003657","url":null,"abstract":"The Davis Historical Archive identifies the women who obtained an honours degree in mathematics in the British Isles between 1878 and 1940 and gives information on them. This note uses the Archive to pick out patterns in women's mathematical education in England and Wales, adding the necessary historical and institutional context. It pays special attention to the dominant institutions of the period, viz., the women's colleges in Cambridge and London. It also glances at the careers of the graduates.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"36 1","pages":"210 - 218"},"PeriodicalIF":0.4,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47366814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}