COMPRAR UNA MACHIMBRADORA: El objetivo de esta propuesta es diversificar los productos que se fabrican, en el muestreo y en la hoja de hallazgos no se ve directamente este factor, pero

The World Wide Web contains a vast and diverse array of material on various aspects of history of mathematics, and is potentially one of the most powerful resources in the subject commonly available. Sites cover from a broad spectrum from interactive texts and museum catalogues, through to high school student projects and a wide of reference sources.

However, since anyone, anywhere, can place material on the Web, and since the contents of a site can change at any time without notice, it is essential to maintain a critical awareness when viewing sites. In particular, the location of a site is no guarantee of reliability. It is therefore important to develop a strategy for judging the quality of the information found. Such a strategy should include assessing the authority of the author of the site as well as the accuracy and currency of the information. Many contain links to other sites, for which they bear no responsibility, and thus whose quality needs to be assessed independently.

The following is a categorization of Web sites relating to the history of mathematics. The categorization, which is by subject matter, has been chosen in order to give a sense of the type of areas the Web now covers rather than to fit in with a rigid predetermined scheme. Each category contains a number of sites which have been selected because, at the time of writing, they represent good examples of their type. The list of sites is obviously not intended to be exhaustive (nor indeed is the

characterization) but rather its aim is to provide an indication of the type of material currently available. Since the Web is a dynamic object and the lifetime of a site unpredictable, especially in the case of a site created and maintained by an individual, there is no absolute guarantee that the standard of any particular site will remain high or up to date or that it will remain accessible indefinitely.

Some of the special features noted in the annotations, such as

high-quality images and large texts can be slow to download; some sites are interactive and require a specially enabled browser.

General

These are large sites that have several pages ranging across a variety of topics.

43. The MacTutor History of Mathematics Archive (http://www-history .mcs.st-and.ac.uk/history/) was created and is maintained by John O’Connor and Edmund Robertson of St Andrews University, and contains the most comprehensive collection of biographies of mathematicians currently available. The collection of more than 1,000 biographies is illustrated, referenced, and indexed both alphabetically and

chronologically. There are birthplace maps, as well as a separate index of female mathematicians. It also contains a variety of resources on the developments of various branches of mathematics, including an interactive

(Java) famous curves index, and pages on mathematical societies, medals, and honors. It is an extremely rich and extensive site with some excellent pages although the quality is not always consistent. In particular, some of the biographies should be viewed with care.

44. David Joyce’s History of Mathematics Home Page (http://aleph0 .clarku.edu/~djoyce/mathhist/mathhist.html) is the starting point to a wealth of resources provided by David Joyce of Clark University.

There are pages on regional mathematics, mathematical topics, books, journals, bibliography, history of mathematics texts etc, as well as an excellent list of clearly categorized Web resources, a detailed chronology, and timelines.

45. The Mathematical Museum - History Wing (http://www.math-net.de/

links/show?collection=math.museum) is part of the Math-Net Links to the Mathematical World which has been developed by the

Konrad-Zuse-Zentrum fur Informationstechnik, Berlin (ZIB). It contains links to exhibitions, hyperbooks, information systems, museums and pages of interest for the history of mathematics and associated fields.

There are sections on history of mathematics, history of computing and communication, and related history information. It is well annotated and includes some sample illustrations.

46. The Math Forum Internet Resource Collection (http://forum

.swarthmore.edu/) is part of the Math Forum, an on-line mathematics education community centre, hosted by Swarthmore College, 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.

47. Trinity College, Dublin, History of Mathematics archive (http://www .maths.tcd.ie/pub/HistMath/HistMath.html) is the work of David Wilkins, contains mathematical papers and other material relating to Hamilton, Riemann, Berkeley, Boole, Cantor and Newton. It also includes biographies of some seventeenth and eighteenth century mathematicians taken from A Short Account of the History of Mathematics (4th edition, 1908) by Ball, W. W. Rouse, and a directory of Web sites.

48. WWW Virtual Library. History of Science, Technology and Medicine (http://www.asap.unimelb.edu.au/hstm/) is part of the WWW Virtual Library Project. It was developed and is maintained by Tim Sherratt, formerly of the Australian Archives Project. It is the gateway into a wide range of resources covering the history of many scientific fields including mathematics. A particular feature of the site is its rating system that, with given criteria, evaluates the depth, content and design of each site listed.

Biography

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. General sites include compendiums of biography as well as sites devoted to particular groups, e.g. mathematicians of a particular period and/or place. There are also many sites devoted to individuals. The latter generally contain a broad spectrum of material about the individual with links to other relevant sites. Many of the sites are well illustrated, although some of the early ’portraits’ should be treated with circumspection.

General Biography

49. A Bibliography of Collected Works of Mathematicians (http://www.math .cornell.edu/~library/collectedwks.html) is an extensive

bibliography compiled and maintained by Steven Rockey, the

mathematical librarian at Cornell University. Though this bibliography is also the basis for the Collected Works section of the present Selective Bibliography, the World Wide Web version is continually augmented.

50. Biographies of Women Mathematicians (http://www.agnesscott.edu/

lriddle/women/women.htm) is part of an ongoing project by students in mathematics classes at Agnes Scott College, Atlanta, to illustrate the achievements of women in mathematics. It includes biographical essays or comments on many women mathematicians and some photographs. The material is indexed both alphabetically and chronologically. The site also includes a page on prizes and honors for women mathematicians, and a list of other resources. It is maintained by Larry Riddle.

51. Portraits of Statisticians (http://www.york.ac.uk/depts/maths/

histstat/people/) is a collection of portraits of approximately two hundred statisticians, including several mathematicians who dabbled in statistical work, ranging from the 15th century to the present day, compiled by Peter Lee of York University. There is no text but the sources, together with some biographical references, are included.

52. Richard Westfall’s Archive of the Scientific Community in the 16th and 17th Centuries (http://es.rice.edu/ES/humsoc/Galileo/Catalog/

catalog.html) 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 organized and includes details of the sources consulted. (It is not obvious on this site which biographies are of most interest to historians of mathematics: a list of the mathematicians can be found through a link on the St

Andrew’s site.)

53. St Andrews Archive (http://www-history.mcs.st-and.ac.uk/

history/BiogIndex.html) See the entry under ’The MacTutor History of Mathematics Archive’ in the General section above.

Individual Biography

54. Archimedes (http://www.mcs.drexel.edu/~crorres/Archimedes/

contents.html) is 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, e.g. a bibliography of Archimedean literature.

55. George Green (http://www.nottingham.ac.uk/~ppzwww/green/) is an attractively illustrated introduction to George Green’s life and work produced by the Physics Department at Nottingham University. The site includes a short biography, a list of Green’s publications, a list of further references, as well as sources of archival material. There is also a link to Green’s Mill and Science Centre.

56. Hypatia of Alexandria (http://poly.polyamory.org/~howard/

Hypatia/) is an extensive and partially annotated list of Web resources connected with Hypatia collected by Howard Landman. 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.

58. Newtonia (http://www.newton.org.uk) contains a wide-ranging collection of material about Isaac Newton, as well as information about places and people significant to him. It was created by of Andrew McNab of Manchester University and there are good links to other Newton resources.

59. Henri Poincar´e (http://uhp.u-nancy.fr/~riess/poincare/index .html) is an extensive site devoted to Poincar´e maintained by the University of Nancy. It includes a short biography, a chronology, photographs, links to the Poincar´e archives and to other related sites.

60. The Alan Turing Home Page (http://www.turing.org.uk/turing/) is a large and well-structured site on Turing’s life and work maintained by Andrew Hodges. It includes material on the history of the computer as well as links to other related sites.

Regional

Although there are several sites on regional and ancient mathematics, many of them are the work of students and relatively few are the result of scholarship, although some of the general sites, notably David Joyce’s site and the St Andrews’ site, listed in the General section above, do include good regional pages.

61. Mesopotamian Mathematics (http://it.stlawu.edu/~dmelvill/

mesomath/index.html) contains a considerable amount of interesting and historically accurate material, collected and written by Duncan Melville of St Lawrence University for his undergraduate history course, with an extensive annotated bibliography by Eleanor Robson of the Oriental Institute, Oxford.

62. Mathematicians of the African Diaspora (http://www.math.buffalo .edu/mad/mad0.html) was created and is maintained by Scott Williams of the State University of New York at Buffalo, to exhibit the

accomplishments of the people of Africa and the African Diaspora within the mathematical sciences. Among the history pages are pages on the mathematics of Ancient Egypt, Pre-Colonial Nigeria, and Swaziland (the Lemombo Bone). There are good links to other related sites.

Museums

It is now fairly standard practice for museums to use the Web to promote their current exhibitions as well as their permanent collections, and overall the quality of museum sites is extremely high. Some museums put their exhibition catalogues on-line, and these provide a very useful resource.

63. IMSS - The Institute and Museum of the History of Science, Florence:

Galileo Room (http://galileo.imss.firenze.it/museo/b/egalilg .html) is a hypermedia catalogue of the Museum’s Galileo room. It contains a biography of Galileo as well as exhibits devoted to his

contributions to mechanics, astronomy, the microscope, thermometry and magnetism. There are also short biographies of other individuals

connected to Galileo. This is an extremely well illustrated site.

64. Library of Congress Vatican Exhibit Mathematics Room (http://lcweb .loc.gov/exhibits/vatican/math.html) is 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.

65. The Museum of the History of Science, Oxford (http://www.mhs.ox.ac .uk/) contains three on-line exhibitions which are of particular interest for the history of mathematics: The Measurers: A Flemish Image of Mathematics in the Sixteenth Century ; The Geometry of War 1500-1750 and The Noble Dane: Images of Tycho Brahe.

Virtual Exhibitions

These are sites which have been specially developed for the Web from a variety of sources. They make use of a variety of devices, some of which are only available to those with sufficiently enhanced browsers, and tend to be very image intensive. It is not always necessary to enable all the tools in order to get a good sense of the potential of the sites.

66. The Art of Renaissance Science: Galileo and Perspective (http://www .crs4.it/Ars/arshtml/arstitle.html) is a beautifully illustrated discussion by J. W. Dauben of the interconnections between art and science in the Renaissance, in particular the development of perspective, and how these connections relate to the role of Galileo in the Scientific Revolution. As well as excellent images, the pages also contain

animations, video clips and music.

67. Galileo Project at Rice University (http://es.rice.edu/ES/humsoc/

Galileo/) is 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, e.g. the “Instrument Closet,” which contains text and images about the instruments used by Galileo to perform his experiments.

Texts

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 accessibility.

68. Edwin Abbott: ‘Flatland’ (http://attila.stevens-tech.edu/

math history/authors/Abbott/flat10.txt) contains the full text of Flatland in plain text. Although there are no illustrations, the length of the text means that it takes time to download.

69. Euclid’s Elements (http://aleph0.clarku.edu/~djoyce/java/

elements/toc.html) contains the full text interactive version of Euclid’s Elements with historical and mathematical comments produced by David Joyce. With a Java enabled browser it is possible to dynamically change the diagrams. A remarkable site which makes the Elements accessible in a completely new way.

70. The History of Hypatia (http://poly.polyamory.org/~howard/

Hypatia/) is 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.

71. The Perseus Project, Tufts University. (http://www.perseus.tufts .edu/Texts/chunk TOC.html) contains translations (and originals) of many works of ancient Greek authors, including the works of Aristotle, and Euclid’s Elements with Heath’s commentary.

72. The Mathematical Papers of Bernhard Riemann (http://www.maths.tcd .ie/pub/HistMath/People/Riemann/Papers.html) contains papers by Riemann, extracts from Riemann’s correspondence and further material from Riemann’s Nachlass, collected together by David Wilkins.

Scholarly Articles

Several authors have incorporated articles into their own sites which may or may not have been published elsewhere.

73. The art of algebra from Al-Khwarizmi to Vi´ete: A study in the natural selection of ideas (http://www.lib.virginia.edu/science/parshall/

algebra.html) is an article by Karen Parshall of the University of Virginia, that first appeared in the journal History of Science.

74. A Brief History of Algebra and Computing: An Eclectic Oxonian View (http://www.museums.reading.ac.uk/vmoc/algebra/) is an article by Jonathan Bowen of Reading University, that was first published in the IMA Bulletin.

75. Greek Diagrams: their Use and their Meaning (http://www.mrc-cbu.cam .ac.uk/projects/twd/contributions/netz-paper.html) is an article by Reviel Netz of Cambridge University. It is based on talk given at the Third International Conference for the History of Greek Mathematics.

76. The Mathematics of Fermat’s Last Theorem (http://www.best.com/

%7Ecgd/home/flt/flt01.htm) is a hypertext site created by Charles Daney to provide an overview of some of the mathematics that has been developed over the years to try to solve the problem (directly or

indirectly) and some other mathematics that has been found to be relevant. The emphasis is on the overall picture rather than technical details.

Education

A variety of sites provide resources for teachers and others with interest in the use or incorporation of historical material in mathematical education.

79. BSHMEducation Abstracts (http://www.dcs.warwick.ac.uk/bshm/abs .html) See ‘BSHMAbstracts’ under Resources.

80. History of Mathematics with Original Sources (http://www.nsm.iup .edu/ma/gsstoudt/history/ma350/sources home.html) contains 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 images of famous works.

Philosophy of Mathematics

The history of the philosophy of mathematics appears on the Web in a variety of ways. For example, there are sites devoted to philosophy in general which include material on the philosophy of mathematics; there are sites devoted to individual philosophers of mathematics; and there are sites which contain the texts (in translation if appropriate) of

philosophers of mathematics.

81. The Bertrand Russell Archives at McMaster University (http://www .mcmaster.ca/russdocs/russell.htm) is an extensive site containing an enormous array of Russell resources including scanned images of Russell documents, correspondence records, a guide to Russell’s writings, and many other resources.

82. The Internet Encyclopaedia of Philosophy (http://www.utm.edu/

research/iep/) is a general site on philosophy which includes articles on the philosophy of, amongst others, Aristotle, Descartes, and Poincar´e.

Computing

History of computing is well represented on the Web, both in terms of individuals and institutions, and in terms of calculating machines/devices, and computers.

83. Alan Turing (http://www.turing.org.uk/turing/) See entry under Individual Biography’ above.

84. Bletchley Park (http://www.cranfield.ac.uk/ccc/bpark/) is a well-illustrated site giving detailed information about Bletchley Park—activities past and present—and a good collection of links to related sites.

85. Charles Babbage’s Analytical Engine (http://www.fourmilab.ch/

babbage/contents.html) contains texts of historical documents, including Menabrea’s description of the Engine translated by Ada Lovelace, and a detailed description of an Analytical Engine emulator which runs as a Java applet.

86. The Virtual Museum of Computing (http://www.museums.reading.ac .uk/vmoc/) is a site developed and maintained by Jonathan Bowen of Reading University. It consists entirely 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.

Resources

The ability of the Web to provide continually updated information, particularly textual information, is an extremely valuable feature of the

The ability of the Web to provide continually updated information, particularly textual information, is an extremely valuable feature of the