The British Society for the History of Mathematics
Selected and annotated by June Barrow-Green (j.e.barrow-green@open.ac.uk).
The intention of this page is to give some indication of the kind of material that is available on the web, with a few examples in each case: not to list it exhaustively. Many more sites can be found through viewing the pages of Web Resources listed below.
Certain other resources are also maintained on this site: David Singmaster's Mathematical Gazetteer of the British Isles; a list of the items bequeathed by John Fauvel and held by the Open University Library on behalf of the Society (by author or by classmark); a list of books offered for sale to members from the collection of the late Neil Bibby (html or Excel spreadsheet).
Some of these sites are specifically devoted to history of mathematics while others are part of larger sites. Sites which contain, or have links which contain, images and are slow to download, or which are interactive and require a specially enabled browser, have been marked with an asterisk (*). A 'hypertext' site is one which contains pages in which there are links to other pages explicitly incorporated within the text itself. A 'hypermedia' site is one which incorporates the opportunity to access additional media, such as music or animation.
All large sites have a gateway page which gives an indication of the type of resources that are available on other pages of the site. The following are the addresses of the gateways to three of the best known of the general sites on history of mathematics. (Some of the pages on these sites are also included in other sections.)
This is the starting point to a wealth of resources provided by David Joyce of Clark University, USA. There are pages on regional mathematics, subjects, books, journals, bibliography, history of mathematics texts etc, as well as an excellent list of Web Resources clearly categorised (see below), a very extensive chronology, and timelines. A highly recommended site.
This site is part of the The Math Forum, an on-line mathematics education community centre, and provides an extensive list of annotated links to other sites. The sites are ordered alphabetically and the collection can be viewed in outline or annotated form. There is a well designed search engine which allows for a variety of searches, i.e. keywords, categories and dates.
A collection of biographies of mathematicians, and a variety of resources on the developments of various branches of mathematics. The site includes an interactive (Java) famous curves index, pages on mathematical societies, medals, and honours, and birthplace maps. An extremely rich and extensive site with some excellent pages although the quality is not always consistent. Overall, though, a good place to start.
This site, which was created and is maintained by David Wilkins, includes biographies of some seventeenth and eighteenth century mathematicians, material on Berkeley, Newton, Hamilton, Boole, Riemann and Cantor, and an extensive directory of history of mathematics websites (see below). Another good place to start.
Convergence is an online magazine on the history of mathematics and its use in teaching, published by the Mathematical Association of America. It includes articles on the history of mathematics, material on the history of mathematics that can easily be used in teaching, reviews of books, websites, and teaching materials relevant to the history of mathematics, and more.
Many sites contain pages which are devoted to links to other related sites. Providing they are kept up to date, these can be extremely useful. However, there is a tendency to provide lists of links with no annotation, which means that there is no way of telling whether a site is, for example, hypertext, interactive, image intensive, or indeed whether it has been prepared by scholars or students. You can therefore end up wasting a lot of time downloading a site which turns out not to have the information you require. So until you have visited a lot of sites and know your way around enough to recognise sites only by name, it is better to use an annotated list of resources.
A well annotated list of about twenty five sites put together by David Calvis of Baldwin-Wallace College, Ohio. Specialised sites are listed in order of earliest date covered.
An annotated but unordered list of twenty six sites, including most of the major ones but also including one or two others not found on any of the other lists. (See also Biographies).
A partially annotated list of web resources and a list of books and articles about women in mathematics. This site has a particularly well designed and informative introductory page. (See also Biographies and Student presentations).
An extremely well organised and extensive list of Web resources. The sites
are categorised but not annotated. Nevertheless, the list includes many of the
best sites currently accessible, and if you know of a good site but do not have
the address there is a reasonable chance that you will find it here.
Every academic year since 2000 BSHM and Gresham College have held a joint lecture on the history of mathematics. Most of these lectures are available in video and/or audio as part of the Gresham College Lecture Archive. This archive contains many other fascinating lectures, including others which relate to the history of mathematics.
19th Century Mathematical Physics, by Professor Raymond Flood and Drs Julia Collins and Mark McCartney (31 October 2012
The Memoirs of Évariste Galois, by Dr Peter Neumann (3 November 2011)
Triangular Relationships, by Dr Patricia Fara (4 November 2010)
Mathematics, Motion and Truth, by Professor Jeremy Gray (2 November 2009)
Mathematics and the Medici, by Jim Bennett (27 November 2008)
Planes and pacifism: Activities and attitudes of British mathematicians during WWI by June Barrow-Green (15 November 2007)
From World Brain to the World Wide Web, by Professor Martin Campbell-Kelly (9 November 2006)
History from Below, by Dr Stephen Johnston (3 November 2005)
The Celestial Geometry of John Flamsteed, by Dr Allan Chapman (10 February 2005)
Mathematics in the Metropolis, by Adrian Rice (19 January 2004)
There is plenty of material on the Web concerned with lives of mathematicians. It comes in a wide variety of guises, much of it excellent, and, on the whole, the Web is a very good place to start looking for biographical material. There are sites devoted to individuals, some of which, eg The Sir Isaac Newton Home Page and The Alan Turing Home Page, even give the appearance that the person themself has created the site! These 'personal' sites generally contain a broad spectrum of material about the individual and have good links to other relevant sites. There are also sites devoted to certain groups, eg mathematicians of a particular period and/or place, and sites which are extensive compendiums of biography. Many of the sites are well illustrated, although some of the early 'portraits' should be treated with circumspection! The list below is separated into general and individual biography.
This is a collection of more than 1,000 biographies, illustrated, referenced, and indexed both alphabetically and chronologically. There are also birthplace maps, as well as a separate index of female mathematicians. Although the entries are of variable quality, it is the best place to start for basic biographical information. (See also Web resources).
This site, which was created by the late Richard Westfall, distinguished author of Never at Rest. A Biography of Isaac Newton, contains concise biographical details of about 630 members of the scientific community in the 16th and 17th centuries, of which about 170 are mathematicians. The individuals are systematically described by ten categories (which are fully explained) using twenty searchable fields. The data, which is presented formally, is well organised and includes details of the sources consulted. This is a very scholarly and reliable site. (A list of the mathematicians contained in the archive can be found through a link on the St Andrews site.)
Biographical essays or comments on many women mathematicians and some photographs. The material is indexed both alphabetically and chronologically. The site is part of an ongoing project by students at Agnes Scott College, USA. (See also Web resources and Student presentations).
A collection of biographies of 17th and 18th century mathematicians adapted from A Short Account of the History of Mathematicsby W.W. Rouse Ball. (See also Web resources and Books on-line).
An extremely rich collection of Archimedean miscellanea produced by Chris Rorres of Drexel University, Philadelphia, including a pages on different aspects of Archimedes' mathematics, books on Archimedes, information on Syracuse, and links to other related sites, eg a bibliography of Archimedean literature.
The site, which is the work of Ron Knott of the University of Surrey, contains a biographical sketch of Fibonacci, his life, times and mathematical achievements. There are also pages on the golden ratio and methods for computing pi using the Fibonacci numbers.
An extensive and partially annotated list of web resources connected with Hypatia. The internal links include a long list of published books and articles which contain information on Hypatia, as well as transcriptions from 18th and 20th century texts.
A large and well structured site on Turing's life and work maintained by Andrew Hodges, the author of Alan Turing: The Enigma. It includes material on the history of the computer as well as links to other related sites.
There are many sites on regional, particularly ancient, mathematics. Many of the general sites, notably David Joyce's site and the St Andrews site listed in Section 1, include good regional pages. The following is a short list of some smaller (in terms of their history of mathematics content) sites which illustrate a variety of presentations.
An excellent site created and maintained by Scott Williams of the State University of New York at Buffalo to exhibit the accomplishments of the people of Africa and Africa Diaspora within the mathematical sciences. The history pages include the mathematics of Ancient Egypt, Pre-Colonial Nigeria, and Swaziland (the Lemombo Bone). There are good links to other related sites.
Some basic mathematical problems for high school pupils produced by artist Mark Millimore as part of his extensively illustrated Ancient Egypt site.
An investigation into Egyptian fractions using Mathematica. Several annotated links to other sites of interest on Egyptian mathematics.
The site contains a list of articles on the history of Japanese mathematics written in a European language. It is the work of Ogawa Tsukane.
A 'draft' of an informative paper by Ingrida Henina and Daina Taimina on the history of mathematics in Latvia.
Lots of interesting and historically accurate matierial, collected and written by Duncan Melville for his undergraduate history course, and an extensive annotated bibliography by Eleanor Robson.
This account, by John Fauvel, of the mathematical interests of an American President and university founder is included in this section to indicate that 'regional' or 'local' mathematics can refer to more modern times too. Jefferson, a child of the Enlightenment, used and admired mathematics throughout his life, in the context of the local needs of his beloved state and university of Virginia.
Code
of the Quipu: Databooks
http://instruct1.cit.cornell.edu/research/quipu-ascher/
The Databooks are the work of Marcia Ascher and Robert Ascher and until now were only available on microfiche. They contain detailed descriptions of 206 quipus (Inca knotted cord arrays) studied first-hand in museums and private collections spread over three continents. The Databooks also contain references to other published quipu descriptions and the locations of extant quipu specimens. There is a list of references to the Aschers more general writings about quipus.
More and more museums are now using the Web to advertise their wares, both in terms of permanent collections and special exhibitions, and history of science museums are no exception. One particular development which is to be warmly applauded is the practice of putting exhibition catalogues up on the Web. Especially as the quality of many of these on-line catalogues is extraordinarily good. The availability of these catalogues has the benefit of broadening access to students for whom an actual visit would be impossible, as well as enabling those students who are able to make a visit prepare for it. Added to which, they extend the life of the exhibition long after it has been dismantled, and also make extremely useful resources for project work. Furthermore, Web sites provide museums with the opportunity to put their exhibits into a much wider context than would otherwise be possible.
Of particular interest for the history of mathematics are two of the on-line exhibitions: The Measurers: A Flemish Image of Mathematics in the Sixteenth Century and The Geometry of War 1500-1750. These exhibition catalogues are beautifully illustrated and very well designed.
A hypertext site containing annotated Greek and Latin manuscripts of mathematics and astronomy, with very high quality images including a 9th century version of Euclid's Elements showing the Pythagorean Theorem and a 13th and 15th century versions of Archimedes' Works.
A dynamic catalogue of the models of mathematical machines stored in the Museum's Laboratory of Mathematics. Each model (of which there are 155) is introduced with a photograph, a computer animation (produced using Cabri II), a description, a proof of its properties, and a bibliography. Some interactive Java simulations are also included. The site is in Italian but there is an excellent general introduction in English. An extremely informative, beautifully illustrated and well designed site.
These are sites which make use of a variety of devices available to those with sufficiently enhanced browsers, and also tend to be very image intensive. However, it is not always necessary to enable all the tools in order to get a good sense of the potential of the sites and they are well worth visiting, if only to get an idea of what sort of things are possible.
An excellent site created by the Walters Art Gallery, Baltimore to complement their exhibition of The Archimedes Palimpsest (20 June-5 September 1999). It contains richly illustrated pages on the life of Archimedes, the history (past, present and future) of the Palimpsest and a commentary by Reviel Netz.
A superb hypertext source of information on the life and work of Galileo and the science of his time. This is an extremely rich and well designed site with very high quality images, eg the Instrument Closet, which contains text and images about the instruments used by Galileo to perform his experiments. (See also Student presentations.)
Texts on-line come in two forms: straightforward copies of original texts--particularly useful if the text in question is otherwise difficult to obtain--or copies which have been annotated or translated in order to increase accessiblility.
An extremely useful and labour-saving resource which provides direct links to nearly 2,000 digitised books and over 120 digitised journals. There is also a link to an article in the Notices of the AMS which describes the inception and ongoing work of the DML.
"Early Modern Thought Online" (EMTO) is a database offering access to about 2000 digitized source texts from early modern philosophy and related disciplines like history of science and theology provided by libraries in Europe and overseas. In the present stage of its development, EMTO merely presents links to external resources. EMTO has been developed at the Lehrgebiet I of the Institut für Philosophie at the FernUniversität in Hagen, Germany. It uses litw3 for database management, and has been funded by the Gerda-Henkel-Stiftung.
A partial transcription of a very rare 18th century text, the full title of which is The History Of Hypatia, A most Impudent School-Mistress of Alexandria: Murder'd and torn to Pieces by the Populace, In Defence of Saint Cyril and the Alexandrian Clergy. From the Aspersions of Mr. Toland.
Excerpts from Rouse Ball's A Short Account of the History of Mathematics (4th edition, 1908). (See also Web resources and Biographies.)
A full text interactive version of Euclid's Elements with historical and mathematical comments produced by David Joyce. With a Java enabled browser (Netscape or Internet Explorer Version 3 or higher) it is possible to dynamically change the diagrams. A remarkable site which makes the Elements accessible in a completely new way. Highly recommended.
Student projects are now well established across the curriculum, and the Web can be an extremely useful resource in this context. It can be used not only as a means of supplying information for the project, but also as the medium by which the students present their work. In the latter case students not only have the chance to share the fruits of their labours with others, but also have the opportunity to receive feedback too. The following sites are examples of student projects, some collective and some individual, which have used the Web as the medium of presentation.
An ongoing project by students in mathematics classes at Agnes Scott College, Atlanta, Georgia, to illustrate the achievements of women in the field of mathematics. The site includes biographies, a page on prizes and honours for women mathematicians, and a list of other resources. (See also Web resources and Biographies.)
An excellent collection of student projects which derived from a course on Galileo in Context. (See also Special exhibits).
These sites contain lists of published books and/or articles which are relevant to using history of mathematics in an educational context.
An annotated list of published papers which discuss the teaching of history of mathematics courses.
A list of possible textbooks for a history of mathematics course. These are books mostly suitable for teaching an undergraduate course but they also provide good background reading for anyone with a general interest in the history of mathematics.
Brief abstracts, sorted alphabetically by author, of papers published in journals and books. There is a separate education section covering abstracts of papers on the uses of history of mathematics in education, history of mathematics courses, and the history of mathematics education.
A list of texts including textbooks and similar general references. There is no annotation so only useful if you know the name of a source and need further details.
The British
Society for the History of Science List of Theses (NEW!)
http://www.bshs.org.uk/theses/
The List gives details of theses and dissertations currently in progress, or
recently completed, in the history, philosophy and social studies of science,
technology, medicine, mathematics, engineering and studies of mind, at academic
institutions in the UK and Republic of Ireland.
Most academic disciplines have societies which exist to help the promotion of their subject at a variety of levels. The Web now provides a very convenient way to find out what such Societies offer their membership, how much it costs to join, as well as supplying a means of obtaining an application form.
The site includes membership details, BSHM abstracts (see Bibliography), an archive containing a list of talks given to the Society, and a page of links to other sites.
An extensive site containing information about all the RS's activities, publications, library etc.
The site includes membership details, free access to the History and Pedagogy of Mathematics Newsletter, and a page of links to other sites.
Increasingly journals are being made available on the Web. Sometimes this is on open access, sometimes you need to make arrangements to pay, but there are generally indexes and quite full information about the journal. This is a good source for very recent information in a scholarly field, although in its nature the articles tend to be on the specialised side for much general classroom use.
Contains information about the journal and links to journals of related interest.
Contains information about the journal and tables of contents from 1995.
A general site on philosophy which includes articles on the philosophy of, amongst others, Aristotle, Descartes, and Poincaré.
A well laid out site which includes links to portraits of statisticians, biographies of statisticians, statistical tables, and several other images of statistical interest. The site is the work of Peter Lee of York University.
A well-illustrated site giving detailed information about Bletchley Park - activities past and present - and a good collection of links to related sites.
This site, which has been created by Frode Weierud of CERN, contains numerous links to sites on the history of cryptology. There are links to the Alexander papers, Turing’s treatise on Enigma, historical papers incuding a recent English translation of Marian Rejewski’s 1980 paper on the breaking of the Enigma cipher (the first paper on the subject to be published), historical cipher machines, simulators of Enigma machines, and many more.
A site, developed and maintained by Jonathan Bowen of South Bank University, made up of an extensive collection of links to sites connected with the history of computing and computer-based exhibits. The site is divided into galleries covering a variety of topics such as general historical information, on-line exhibits etc.
An excellent site containing texts of historical documents, including Menebrea's description of the Engine translated by Ada Lovelace, and a detailed description of an Analytical Engine emulator which runs as a Java applet.
Fred Rickey of Bowling Green University, USA, is one of the leading proponents of using history in mathematics education. His Home Page contains annotated links to wide variety of resources, including a description of his own history of mathematics course.
A collection of materials for using original sources in a history of mathematics class. The site, which is the work of Gary Stoudt of Indiana University of Pennsylvania, contains a reading list, and a collection of discussion questions and homework problems, together with some images of famous works.
HPM is the International Study Group on the Relations between History and Pedagogy of Mathematics affiliated to ICMI. Researchers in mathematics education, teachers, curriculum developers, mathematicians, and historians of mathematics are members of the group. Amongst other things, HPM organises satellite meetings of the ICME conference. The site contains HPM Newsletters, notices of HPM meetings, and links to other sites of interest.
The experiences of Reinhard Laubenbacher and David Pengelley of New Mexico State University in using original historical sources in teaching mathematics. The site is well referenced and there are links to several of the articles mentioned (mostly in the form of .dvi or .ps files) as well as links to other resources. There is also a detailed synopsis of Laubenbacher and Pengelley's recently published book Mathematical Expeditions: Chronicles by the Explorers.
A few extra sites which you may find helpful or interesting to visit but which do not fall naturally into any of the categories above.
The above two sites, which are the product of multiple contributors, are very high quality and provide an excellent resource. They are maintained by Jeff Miller of Gulf High School, Florida and contributions are welcomed.
The site, which is also maintained by Jeff Miller, contains images of postage stamps featuring mathematicians and mathematics, as well as links to other sites displaying mathematical stamps.
The site of the US version of 'the' television programme. It includes a transcript of the programme, a page on Sophie Germain's contribution to the problem. It contains several links including one to the The Mathematics of Fermat's Last Theorem, a hypertext site created by Charles Daney which provides an overview of some of the mathematics that has either been developed over the years to try to solve the problem (directly or indirectly) or else which has been found to be relevant.
A series of about thirty informal notes devoted to a variety of topics in history of mathematics, ranging from the general, eg Negative Numbers, to the particular, eg Did PoincarŽ discover relativity? The articles, which are not referenced, represent a personal but informed view.
A description of the geometric theorems used in the construction of Ptolemy's table of chords with an attempt to relate them to their contemporary trigonometric counterparts.
The site for the 4th International Laboratory for the History of Science, which was held during May/June 2001, and took place over three sessions: Brunelleschi's perspectival experiments and the historical development of drafting instruments; Masaccio's Trinity: looking again and again; and The theory and practice of vision in Leonardo and his followers. The site contains abstracts of papers and lists of participants.
The British Society for the History of Mathematics is registered as a company limited by guarantee, no. 3326816, and as a charity, no. 1061229. Its registered office is c/o Andrew Thurburn & Co, 38 Tamworth Road, Croydon, Surrey CR0 1XU, UK.