Pub Date : 2016-05-17DOI: 10.1080/17498430.2016.1162402
John . Sharp
I n his recent paper Two beginnings of geometry and folding: Hermann Wiener and Sundara Row, Michael Friedman (2016) has touched on a neglected aspect of the history of mathematics which is often referred to as recreational mathematics. There is a vast literature on the subject which has often contributed to the more formal side of mathematics and does not often feature in history textbooks although David Singmaster has published a bibliography of recreational mathematics which is extensive. Excerpts were included in BSHM newsletters. Because the history of recreational mathematics is neglected somewhat, it sometimes means that origins of some aspects of mathematics are lost. Such a case is the folding of polygons as knots particularly the pentagonal knot in Friedman’s Figure 2. He says
{"title":"Folding the regular pentagon","authors":"John . Sharp","doi":"10.1080/17498430.2016.1162402","DOIUrl":"https://doi.org/10.1080/17498430.2016.1162402","url":null,"abstract":"I n his recent paper Two beginnings of geometry and folding: Hermann Wiener and Sundara Row, Michael Friedman (2016) has touched on a neglected aspect of the history of mathematics which is often referred to as recreational mathematics. There is a vast literature on the subject which has often contributed to the more formal side of mathematics and does not often feature in history textbooks although David Singmaster has published a bibliography of recreational mathematics which is extensive. Excerpts were included in BSHM newsletters. Because the history of recreational mathematics is neglected somewhat, it sometimes means that origins of some aspects of mathematics are lost. Such a case is the folding of polygons as knots particularly the pentagonal knot in Friedman’s Figure 2. He says","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130107049","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}
Pub Date : 2016-05-03DOI: 10.1080/17498430.2016.1170358
Donald L. Opitz
discussion is offered and no strong opinions voiced, but, given the extent to which these matters have provided the material for notorious disputes, this is perhaps wise. I have a couple of minor quibbles. The lives of the scientists in the vignettes are, of course, sometimes right-censored, since they are still alive, but many are also leftcensored, as if their dates of birth were unimportant. Also the title promises us Permutation Methods but what is largely offered is Permutation Tests. This, given the nature of the field, is perhaps inevitable, but it also provides one explanation as to why not all statisticians will share the enthusiasm of the authors as regards permutation tests. They provide logical rigour within a rather limited framework. As soon as one asks for more it becomes less obvious that they are a good place to start. A major omission is that there is no reference to John Nelder’s theory of General Balance (Senn 2004) which is at the heart of the GenStat approach to analysis of variance, and which categorizes experiments in terms of block and treatment structure. This is related to deep ideas of symmetries in designed experiments and provides a natural link between analysis of variance and permutation methods. However, the ideas have made little impact in the USA and perhaps the one charge that can be laid against the authors is that their book is a little Americocentric. These are minor criticisms, however. The authors are to be congratulated on this very fine collaboration. In their acknowledgements they mention table 20 at the Rainbow Restaurant, Fort Collins, Colorado at which most of the book was written. This surely deserves a plaque. It conjures up a delightful vision of three scientists first ordering a random permutation of one starter, one main and one pudding, and then settling down to the serious business of the day. In short my recommendation to the reader is clear: buy this book! My recommendation to those invited to review using Springer’s online reviewing ‘tool’ is also clear: don’t!
{"title":"Seduced by logic: Émilie Du Châtelet, Mary Somerville and the Newtonian revolution, by Robyn Arianrhod","authors":"Donald L. Opitz","doi":"10.1080/17498430.2016.1170358","DOIUrl":"https://doi.org/10.1080/17498430.2016.1170358","url":null,"abstract":"discussion is offered and no strong opinions voiced, but, given the extent to which these matters have provided the material for notorious disputes, this is perhaps wise. I have a couple of minor quibbles. The lives of the scientists in the vignettes are, of course, sometimes right-censored, since they are still alive, but many are also leftcensored, as if their dates of birth were unimportant. Also the title promises us Permutation Methods but what is largely offered is Permutation Tests. This, given the nature of the field, is perhaps inevitable, but it also provides one explanation as to why not all statisticians will share the enthusiasm of the authors as regards permutation tests. They provide logical rigour within a rather limited framework. As soon as one asks for more it becomes less obvious that they are a good place to start. A major omission is that there is no reference to John Nelder’s theory of General Balance (Senn 2004) which is at the heart of the GenStat approach to analysis of variance, and which categorizes experiments in terms of block and treatment structure. This is related to deep ideas of symmetries in designed experiments and provides a natural link between analysis of variance and permutation methods. However, the ideas have made little impact in the USA and perhaps the one charge that can be laid against the authors is that their book is a little Americocentric. These are minor criticisms, however. The authors are to be congratulated on this very fine collaboration. In their acknowledgements they mention table 20 at the Rainbow Restaurant, Fort Collins, Colorado at which most of the book was written. This surely deserves a plaque. It conjures up a delightful vision of three scientists first ordering a random permutation of one starter, one main and one pudding, and then settling down to the serious business of the day. In short my recommendation to the reader is clear: buy this book! My recommendation to those invited to review using Springer’s online reviewing ‘tool’ is also clear: don’t!","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133621465","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}
Pub Date : 2016-05-03DOI: 10.1080/17498430.2015.1113374
D. Murphy
In the bi-centenary of the birth of George Boole, there were many celebrations of his well-known writings and achievements. This paper outlines a little known account he wrote at the request of his good friend Augustus De Morgan. It shows Boole in the unusual role of detective, seeking details on a contemporary named John Walsh. Walsh was not well known then and is completely forgotten now. The details supplied by Boole and De Morgan are now the only memories remaining of the interesting footnote in mathematical history that was John Walsh. Boole's position as professor in Queen's College, Cork, allowed him fortuitous access to the details of Walsh's biography.
{"title":"George Boole and Walsh's delusions","authors":"D. Murphy","doi":"10.1080/17498430.2015.1113374","DOIUrl":"https://doi.org/10.1080/17498430.2015.1113374","url":null,"abstract":"In the bi-centenary of the birth of George Boole, there were many celebrations of his well-known writings and achievements. This paper outlines a little known account he wrote at the request of his good friend Augustus De Morgan. It shows Boole in the unusual role of detective, seeking details on a contemporary named John Walsh. Walsh was not well known then and is completely forgotten now. The details supplied by Boole and De Morgan are now the only memories remaining of the interesting footnote in mathematical history that was John Walsh. Boole's position as professor in Queen's College, Cork, allowed him fortuitous access to the details of Walsh's biography.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129535985","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}
Pub Date : 2016-05-03DOI: 10.1080/17498430.2015.1129087
S. Senn
The extraordinary and astonishing idea of making a statistical inference by shuffling treatment labels, whilst conditioning on the actual values observed, is associated in particular with R A Fishe...
通过变换处理标签来进行统计推断的非凡和惊人的想法，同时根据观察到的实际值进行调节，特别是与R a fish…
{"title":"A Chronicle of Permutation Statistical Methods: 1920–2000, and Beyond, by K J Berry, J E Johnston, and P J W Mielke","authors":"S. Senn","doi":"10.1080/17498430.2015.1129087","DOIUrl":"https://doi.org/10.1080/17498430.2015.1129087","url":null,"abstract":"The extraordinary and astonishing idea of making a statistical inference by shuffling treatment labels, whilst conditioning on the actual values observed, is associated in particular with R A Fishe...","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121878702","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}
Pub Date : 2016-05-03DOI: 10.1080/17498430.2016.1162406
P. M. Lee
On Sunday, an interesting Russian pair came to see us,—M. and MMe. Kovalevsky [sic]: she, a pretty creature, with charming modest voice and speech, who is studying mathematics (by allowance through the aid of Kirchoff) at Heidelberg; he, amiable and intelligent, studying the concrete sciences apparently,—especially geology; and about to go to Vienna for six months, leaving his wife at Heidelberg!
{"title":"George Eliot and mathematics","authors":"P. M. Lee","doi":"10.1080/17498430.2016.1162406","DOIUrl":"https://doi.org/10.1080/17498430.2016.1162406","url":null,"abstract":"On Sunday, an interesting Russian pair came to see us,—M. and MMe. Kovalevsky [sic]: she, a pretty creature, with charming modest voice and speech, who is studying mathematics (by allowance through the aid of Kirchoff) at Heidelberg; he, amiable and intelligent, studying the concrete sciences apparently,—especially geology; and about to go to Vienna for six months, leaving his wife at Heidelberg!","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126725697","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}
Pub Date : 2016-05-03DOI: 10.1080/17498430.2015.1046038
A. Rice, Ezra Brown
This paper investigates the discovery of an intriguing and fundamental connection between the famous but apparently unrelated mathematical work of two late third-century mathematicians. This link went unnoticed for well over 1500 years until the publication of two groundbreaking but again ostensibly unrelated works by two German mathematicians at the close of the nineteenth century. In this, the second and final part of the paper, we continue our examination of the chain of mathematical events and the related development of mathematical disciplines, without which the connection might never have been noticed in the first place.
{"title":"Commutativity and collinearity: a historical case study of the interconnection of mathematical ideas. Part II","authors":"A. Rice, Ezra Brown","doi":"10.1080/17498430.2015.1046038","DOIUrl":"https://doi.org/10.1080/17498430.2015.1046038","url":null,"abstract":"This paper investigates the discovery of an intriguing and fundamental connection between the famous but apparently unrelated mathematical work of two late third-century mathematicians. This link went unnoticed for well over 1500 years until the publication of two groundbreaking but again ostensibly unrelated works by two German mathematicians at the close of the nineteenth century. In this, the second and final part of the paper, we continue our examination of the chain of mathematical events and the related development of mathematical disciplines, without which the connection might never have been noticed in the first place.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129328292","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}
Pub Date : 2016-04-14DOI: 10.1080/17498430.2015.1116052
B. Burn
That natural logarithms may be constructed from Napier's logarithms is no surprise to a modern mathematician, but the thought that this might have been done within ten years of Napier's original publication seems a historical impossibility, since by that time, most of the modern constituents of the notion had not been conceived. Nonetheless the practical use of Napier's tables required interpolation, and the systematization of that interpolation generated a new table with a remarkable similarity to natural logarithms. This interpolation table was later extended by Speidell to stand alongside his ‘New Logarithms’, as an alternative form.
{"title":"Early tables resembling those of natural logarithms","authors":"B. Burn","doi":"10.1080/17498430.2015.1116052","DOIUrl":"https://doi.org/10.1080/17498430.2015.1116052","url":null,"abstract":"That natural logarithms may be constructed from Napier's logarithms is no surprise to a modern mathematician, but the thought that this might have been done within ten years of Napier's original publication seems a historical impossibility, since by that time, most of the modern constituents of the notion had not been conceived. Nonetheless the practical use of Napier's tables required interpolation, and the systematization of that interpolation generated a new table with a remarkable similarity to natural logarithms. This interpolation table was later extended by Speidell to stand alongside his ‘New Logarithms’, as an alternative form.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121515791","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}
Pub Date : 2016-04-11DOI: 10.1080/17498430.2015.1090096
Elizabeth F. Lewis
This paper explains how the discovery of a pocket notebook brings to light P G Tait's surprising involvement in statistics. Tait (1831–1901) was Professor of Mathematics at the Queen's College, Belfast and later of Natural Philosophy at the University of Edinburgh. He was a Fellow of the Royal Society of Edinburgh and a former Fellow of Peterhouse, Cambridge (senior wrangler and first Smith's prizeman in 1852).
{"title":"P G Tait's statistical models","authors":"Elizabeth F. Lewis","doi":"10.1080/17498430.2015.1090096","DOIUrl":"https://doi.org/10.1080/17498430.2015.1090096","url":null,"abstract":"This paper explains how the discovery of a pocket notebook brings to light P G Tait's surprising involvement in statistics. Tait (1831–1901) was Professor of Mathematics at the Queen's College, Belfast and later of Natural Philosophy at the University of Edinburgh. He was a Fellow of the Royal Society of Edinburgh and a former Fellow of Peterhouse, Cambridge (senior wrangler and first Smith's prizeman in 1852).","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132898407","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}
Pub Date : 2016-04-11DOI: 10.1080/17498430.2015.1091969
R. Pisano
Leonardo da Vinci (1452–1519) maintained a strong relationship with mathematics, but the benefits of this connection unfortunately had little impact in his time. His meeting with Luca Pacioli (1445–1517) in Milan in 1496 was crucial: the two men would become friends and a deep mutual respect would preside over Leonardo da Vinci's improving his mathematical knowledge while contributing to the drawings of Pacioli's De divina proportione (Milano, 1496–98) (Pacioli 1509a). Based on my recent works on the relationship between mathematics and physics during the Renaissance, here I resume some results on the conceptual mathematical frameworks between two Italian scholars.
{"title":"Details on the mathematical interplay between Leonardo da Vinci and Luca Pacioli","authors":"R. Pisano","doi":"10.1080/17498430.2015.1091969","DOIUrl":"https://doi.org/10.1080/17498430.2015.1091969","url":null,"abstract":"Leonardo da Vinci (1452–1519) maintained a strong relationship with mathematics, but the benefits of this connection unfortunately had little impact in his time. His meeting with Luca Pacioli (1445–1517) in Milan in 1496 was crucial: the two men would become friends and a deep mutual respect would preside over Leonardo da Vinci's improving his mathematical knowledge while contributing to the drawings of Pacioli's De divina proportione (Milano, 1496–98) (Pacioli 1509a). Based on my recent works on the relationship between mathematics and physics during the Renaissance, here I resume some results on the conceptual mathematical frameworks between two Italian scholars.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132091114","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}
Pub Date : 2016-04-11DOI: 10.1080/17498430.2015.1116053
J F Harper
Continuity of a real function of a real variable has been defined in various ways over almost 200 years. Contrary to popular belief, the definitions are not all equivalent, because their consequences for four somewhat pathological functions reveal five essentially different cases. The four defensible ones imply just two cases for continuity on an interval if that is defined by using pointwise continuity at each point. Some authors had trouble: two different textbooks each gave two arguably inconsistent definitions, three more changed their definitions in their second editions, two more claimed continuity at a point for functions not defined there, and one gave a definition implying it for a function with no limit there.
{"title":"Defining continuity of real functions of real variables","authors":"J F Harper","doi":"10.1080/17498430.2015.1116053","DOIUrl":"https://doi.org/10.1080/17498430.2015.1116053","url":null,"abstract":"Continuity of a real function of a real variable has been defined in various ways over almost 200 years. Contrary to popular belief, the definitions are not all equivalent, because their consequences for four somewhat pathological functions reveal five essentially different cases. The four defensible ones imply just two cases for continuity on an interval if that is defined by using pointwise continuity at each point. Some authors had trouble: two different textbooks each gave two arguably inconsistent definitions, three more changed their definitions in their second editions, two more claimed continuity at a point for functions not defined there, and one gave a definition implying it for a function with no limit there.","PeriodicalId":211442,"journal":{"name":"BSHM Bulletin: Journal of the British Society for the History of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126865104","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}
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