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  • 1. Useful Web Links on History of Mathematical Sciences† by MAN MOHAN Dept. of Mathematics & Statistics, Ramjas College, University of Delhi, Delhi 110007, India E-mail: The Internet is a wonderful place to explore the vast amount of information that it makes available around the world, but without borders and often confusing the explorer. Even well prepared surfers stumble aimlessly through cyberspace using hit-or-miss methods in search of useful information with few results, little substance and lots of frustration. The purpose of this article is to encourage and facilitate the teaching and learning of history of mathematics at all levels, using the Web. Some of the most useful resources on the history of mathematics are identified, described, and hyperlinked. The resources are divided into eleven sections. While some websites may fall in more than one section, each website appears in what seemed to be the most relevant section.INTRODUCTIONThe Internet is a wonderful place to explore the vast amount of information that it makesavailable around the world, but without borders and often confusing the explorer. Evenwell prepared surfers stumble aimlessly through cyberspace using hit-or-miss methods insearch of useful information with few results, little substance and lots of frustration. Thepurpose of this article is to encourage and facilitate the teaching and learning of history ofmathematics at all levels, using the Web. Some of the most useful resources on thehistory of mathematics are identified, described, and hyperlinked. The resources aredivided into twelve sections. While some websites may fall in more than one section, eachwebsite appears in what seemed to be the most relevant section.The section ‘Gateway Pages’ includes some of the best known general websites on historyof mathematical sciences providing historical accounts by regions of the world, timelines,a chronology, an index of files, etc. An extensive list of resources including links to stand-alone sites containing material on a single topic is provided in the section ‘Useful WebResources’. A few of the many wonderful websites that provide biographies ofmathematicians are identified and describes in the section ‘General and IndividualBiographies’. Some websites devoted to individuals like Sir Isaac Newton, Archimedes,and Paul Erdös etc. are also listed. The section ‘Regional Mathematics’ provides a short listof websites that give a variety of material on the development of mathematical sciences inspecific regions of the globe. The section ‘History of Vedic Mathematics’ describes somewebsites that offer interesting literature on the development of Vedic Mathematics, theancient system of mathematics of the Vedas.Some other sections are: ‘On-line Books and Journals’ that lists sites providing on-lineavailability of the contents of some books and journals, ‘Bibliographic Resources’ whichcontains sites giving lists of published books and/or articles relevant to history ofmathematics in an educational context, ‘Societies for Mathematics History’ which includes † Talk given at the National Seminar on History of Mathematical Sciences & Applicable Mathematics held at Gurugula Kangri Vishwavidyalaya, Hardwar on March 7-9, 2003 and at the E.M.C. Mathematics Academic Camp for Teachers held at Delhi Public School, Vasant Kunj, New Delhi on May 30, 2003. 1
  • 2. home pages of three well known societies that promote history of mathematical sciences,‘Links on History of Computing’ which lists sites related to the development of computersand computing. Using history in mathematics classes helps to increase motivation forlearning. The section ‘History in Education’ includes websites that promote the use ofhistory in mathematics classes, websites that provide examples where this concept hasbeen applied, and websites that post bibliographies and additional links that allow forextended research. Finally, the section ‘Miscellaneous Resources’ contains a few websitesthat may be helpful or interesting to visit but which do not fall naturally into any of theabove sections.GATEWAY PAGESAll general sites have a gateway page that indicates the type of resources that areavailable on other pages of the site. The gateways to some of the best-known generalsites on history of mathematical sciences are given below:David Joyce’s History of Mathematics Archivealeph0.clarku .edu/~djoyce/mathhist/mathhist.htmlMaintained at the Department of Mathematics and Computer Science of Clark University,this site features a look at the history of mathematics. Find historical accounts by regionsof the world, timelines, a chronology, an index of files, and a list of books, journals,bibliography and other resources. This is the starting point to a wealth of resourcesprovided by David Joyce of Clark University, USA. There are pages on subjects, history ofmathematics texts etc, as well as an excellent list of clearly categorized Web Resources.The Math Forum Resource Collection of the The Math Forum, an on-line mathematics education community centre, this siteprovides an extensive list of annotated links to other sites. These sites are arrangedalphabetically and the collection can be viewed in outline or annotated form. There is awell-designed search engine that allows for a variety of searches, like keywords,categories and dates.MacTutor History of Mathematics MacTutor History of Mathematics archive is the prominent site on the WWW forinformation on the history of mathematics. It probably contains as much information as allthe rest combined. It has 1300 biographies, 60 famous curves, 30 history topics,chronologies, birthplace maps, and posters. Maintained by John O Conner at the Universityof St. Andrews in Scotland the offers search forms, suggestions, and historical andbiographical information. It provides a variety of resources on the developments of variousbranches of mathematics and includes an interactive famous curves index, pages onmathematical societies etc.Trinity College Mathematics History Archive and maintained by David Wilkins of Trinity College, Dublin, this site includesbiographies of some seventeenth and eighteenth century mathematicians, sufficientmaterial on Berkeley, Newton, Hamilton, Boole, Riemann and Cantor, and an extensivedirectory of history of mathematics websites.USEFUL WEB RESOURCESBSHM Resources 2
  • 3. is a well-organized collection of links to Web Sites on the History of Mathematics.The resources include David Calviss History of Mathematics Web Sites.Joyces History of Mathematics Web Resources is a well categorized and annotated list of resources. Hypermedia exhibits are listedseparately and there are also links to history of science pages. The emphasis is moretowards larger sites containing sequences of internal links rather than stand-alone sitescontaining material on a single topic or person.Mathematical Quotations /mquot.htmlFrom South Carolinas Furman University, this site offers visitors quotations about math.Features include a keyword search engine and links to the sponsoring university.Calviss History of Mathematics Web Sites 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.MacTutor History of Mathematics: Links to external pages site contains an annotated but unordered list of twenty-six sites related to history ofmathematical sciences, including most of the major ones.The Mathematical Museum - History Wing History wing of The Mathematical Museum is part of the Math-Net Links to theMathematical World. It contains links to exhibitions, on-line books, information systems,museums and pages of interest for the history of mathematics, history of computing andcommunication and associated fields along with related history. It also includes somesample illustrations.Trinity College Mathematics History archive site contains an extremely well organized and extensive list of Web resources. Thesites are categorized and include many of the best sites currently accessible. If you knowof a good site but do not have the address there is a reasonable chance that you will findit here.MathWeb site provides Links to CSHPM Services; Links to Sites Related to the History andPhilosophy of Mathematics and a page of links to other related sites.History of Mathematics by the Dept. of mathematics at University of Haifa, Israel, the site provideslinks to 39 resources. The list includes AMS history of mathematics sites, Arabicmathematics, Biographies of women mathematicians, A brief history of algebra andcomputing, BSHM list of web sites on the history of mathematics, Calculating machines,Egyptian mathematics, Greek mathematics and its heirs, History and pedagogy ofmathematics, etc.History of Mathematics Sites: Math I 3
  • 4. sites have math history links, but this seems to be the grand daddy of them all. Anytopic or person of any time or region can be searched here. It contains a section onwomen mathematicians also, as well as links to other math history sites. It is worthwhileto visit for anything concerning history of mathematical sciences.Encyclopædiaædia Britannica is the Nets finest encyclopedia. Britannicas editors havedeveloped a user-friendly citation style for citing electronic publications, e.g.“mathematics, history of". For each topic it has an exhaustive table of contents, completeindex entries, and citation information to simplify your research. Britannica cant be beatfor researching famous (and not-so-famous) people, places, and things, althoughcomplete articles are not available for free.GENERAL AND INDIVIDUAL BIOGRAPHIESA wide variety of material is available on the Web concerned with lives of mathematicians.There are sites devoted to certain groups, e.g. mathematicians of a particular periodand/or place, and sites that are extensive compendiums of biography. There are also sitesdevoted to ‘individuals’, like The Sir Isaac Newton Home Page and The Alan Turing HomePage, which generally contain material about the individual and have good links to otherrelevant sitesSt Andrews Archive is a collection of more than 1,000 biographies, of mathematicians  illustrated,referenced, and indexed both alphabetically and chronologically. There are also birthplacemaps, as well as a separate index of female mathematicians. It is the best place to startfor basic biographical information.Alphabetical Index of site provides an alphabetical index of mathematicians with links to their detailedbiographies. A chronological index, a short biographies index and a history topics indexare also available.Hall of Great Mathematicians page is maintained by David Collins, Jr. at Southern Illinois University. Here one findsan alphabetical list of mathematicians with short biographies.Women dle/women/women.htmThe Agnes Scott College Mathematics Department hosts this collection of biographies ofwomen mathematicians. Browse the biographies by alphabetical or chronological order,read the photo credits or link to related resources on the Web.Mathematicians of the 17th and 18th Centuries is a collection of biographies of the 17th and 18th century mathematicians adaptedfrom W.W. Rouse Ball’s A Short Account of the History of MathematicsSome Famous Mathematicians 4
  • 5. by Alexander Velasquez at the Central University of Venezuela, the page providesinformation on about 20 famous mathematicians.Portraits of Statisticians site gives a nice collection of portraits of approximately two hundred statisticians,including several mathematicians who dabbled in statistical work, ranging from the 15thcentury to the present day, compiled by Peter Lee of York University. However the sitedoes not include any text but the sources, together with some biographical references, areincluded.Archimedes site has a rich collection of Archimedean miscellanea produced by Chris Rorres ofDrexel University, Philadelphia, including a pages on different aspects of Archimedesmathematics, books on Archimedes, information on Syracuse, and links to other relatedsites, e.g. a bibliography of Archimedean literature.History of Mathematics: Mathematicians has a limited number of pages on mathematicians from Europe, China, India, andEgypt. It also includes a section on special topics. Len Berggren at Simon Fraser Universityin Burnaby, Canada hosts it.Paul Erdös site is created and maintained by Paul Hoffman, the author of the book The Man WhoLoved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth. Thebook is a work of oral history based on the recollections of Erdös, his numerouscollaborators, and their spouses.Fibonacci (Leonardo of Pisa) work of Ron Knott of the University of Surrey, this site contains a biographical sketchof Fibonacci, his life, times and mathematical achievements. There are also pages on thegolden ratio and methods for computing pi using the Fibonacci by Andrew McNab of Manchester University this site provides a wide-rangingcollection of material about Newton, as well as information about places and peoplesignificant to him. It includes a nice detailed explanation, About Newtonia, of the genesisof the site. There are good links to other Newton resources.Isaac Newton Institute for Mathematical national institute located at Great Britains Cambridge University, the Isaac NewtonInstitute for Mathematical Sciences offers this overview of its history, ongoing scientificwork and services.REGIONAL MATHEMATICS 5
  • 6. Many of the gateway pages, notably David Joyces site and the Mac Tutor site listed inSection 1, include good regional pages. The following is a short list of some smaller sitesthat give a variety of material on specific regions.Mathematicians of the African Diaspora and maintained by Scott Williams of the State University of New York at Buffalo,this site exhibits the accomplishments of the people of Africa and Africa Diaspora withinthe mathematical sciences. The history pages include the mathematics of Ancient Egypt,Pre-Colonial Nigeria, and Swaziland (the Lemombo Bone). There are good links to otherrelated sites.Egyptian Mathematics Problems and /maths2.htm and /maths3.htmHere one finds some basic mathematical problems for high school pupils, produced byartist Mark Millimore as part of his extensively illustrated Ancient Egypt site.Egyptian Fractions is an investigation into Egyptian fractions using Mathematica. Several annotated linksto other sites of interest on Egyptian mathematics.Ancient Indias Contribution to Mathematics site provides a broad outline of the achievements of Indian mathematicians between1000BC and 1000AD, extracted from Birodkar Sudheers book Indias Contribution toWorld Culture.Japanese Mathematics site contains a list of articles on the history of Japanese mathematics written in aEuropean language. It is the work of Ogawa Tsukane.History of Mathematics: Chinaaleph0.clarku.ed u/~djoyce/mathhist/china.htmlThe Department of Mathematics and Computer Science at Clark University in Worcester,Mass., maintains this site to outline the history of mathematics in China. Visit here to viewa chronology of Chinese math studies, read profiles of noted mathematicians, and link toother Chinese historic and cultural resources.History of Mathematics Home Page by David Joyce at Clark University provides valuable information onmathematicians arranged chronologically and by the following regions: Europe, Greece,Japan, China, Arab Sphere, India, Egypt, and Babylonia. It also contains data by subjectsand timelines.Mathematics in Latvia site gives a draft of an informative paper by Ingrida Henina and Daina Taimina onthe history of mathematics in Latvia.HISTORY OF VEDIC MATHEMATICS 6
  • 7. Rediscovered between 1911 and 1918 by Sri Bharati Krsna Tirthaji, this is the ancientsystem of mathematics of the Vedas. According to him all of mathematics is based onsixteen Sutras, or word-formulae. The following sites offer interesting literature on thesubject.What is Vedic Mathematics? History of Vedic Mathematics Maths Tutorials Magic of Vedic Maths - Whats This? is an all-in-one site to know about Vedic Mathematics and Bharati Krishna Tirthaji,who delved into the ancient Vedic texts and established the techniques of this system inhis pioneering work — Vedic Mathematics (1965), which is considered the starting pointfor all work on Vedic math.Math can be 2001/09/19/stories/0219b15b.htmVisit this site to learn how to use Vedic Mathematics. The concept of Vedic mathematics isexplained more than makes up. There are separate drop-down links to what the subject isall about, its history and tutorial…..ON-LINE BOOKS AND JOURNALSCornell University Library Math Book Collection collection consists of 571 books that have been scanned from originals held by CornellUniversity Library. It is indexed by author and by title, although without the date of theedition. Since all books were dismounted and all pages scanned (even the blank ones!)the reproduction quality is extremely good.Rouse Balls History of Mathematics from Rouse Balls well know book A Short Account of the History of Mathematics(4th edition, 1908).Euclids Elements site gives an interactive version of Euclids Elements with historical and mathematicalcomments produced by David Joyce. With a Java enabled browser it is possible todynamically change the diagrams. The site makes the Elements accessible in a completelynew way.Historia Mathematica in 1974, Historia Mathematica is the official journal of the InternationalCommission on the History of Mathematics. It publishes research articles in all areas of 7
  • 8. history of mathematics, book reviews, abstracts of recently published books and articles,and miscellaneous items of interest to historians of mathematics. The site containsinformation about the Journal, a table of contents of all volumes, a list of journals inrelated fields, and links to other sites.BIBLIOGRAPHIC RESOURCESThe following sites contain lists of published books and/or articles which are relevant tousing history of mathematics in an educational context.Teaching History of Mathematics contains a list of published papers which discuss the teaching of history of mathematicscourses.Textbooks for a History of Mathematics Course will here a list of possible textbooks for a history of mathematics course. These arebooks mostly suitable for teaching an undergraduate course but they also provide goodbackground reading for anyone with a general interest in the history of mathematics.BSHM Abstracts site contains brief abstracts, sorted alphabetically by author, of papers published injournals and books. A separate section covers abstracts of papers on the uses of history ofmathematics in education, history of mathematics courses, and the history ofmathematics education.Texts on the History of Mathematics one finds a list of texts including textbooks and similar general references. There isno annotation, so only useful if you know the name of a source and need further details.Non-Euclidean of non-Euclidean geometries had a profound impact on the development ofmathematics in the 19th and 20th centuries. The site provides links to the references thatgive a good account of development that took place before and after the discovery. Itincludes links on the Fifth Postulate, Drama of the Discovery. Some of the listed resourcesare T. Heath: Euclids Elements, D. Hilbert: Foundations of Geometry, J.Fauvel and J.Gray,ed:The History of Mathematics, M.Kac and S.Ulam: Mathematics and Logic, etc.SOCIETIES FOR MATHEMATICS HISTORYThe Indian Society for History of Mathematics http://www.indianshm.comThe site was launched in 2003. It includes latest news concerning history of mathematicalsciences, information on forthcoming conferences, reports of recently held ISHMconferences, membership details, contents pages of all volumes of Ganita Bharati andsome selected articles in the field. The site provides a platform to exchange views onanything concerning mathematics history. It also provides links to other important sites inthe area. 8
  • 9. The British Society for the History of Mathematics site includes membership details, BSHM abstracts, an archive containing a list of talksgiven to the Society, and a page of links to other sites. The site contains some 50 pagescompiled by prominent British academics at the Open University, U.K. working in thehistory of mathematics.The Canadian Society for the History and Philosophy of Mathematics is the Home Page of The Canadian Society for the History and Philosophy ofMathematics which manages Links to CSHPM Services; Links to Sites Related to theHistory and Philosophy of Mathematics. This site includes membership details, free accessto the History and Pedagogy of Mathematics Newsletter, two official journals, HistoriaMathematica and Philosophia Mathematica and a page of links to other sites.The Kurt Gödel Society in 1987, the Kurt Gödel Society is an international organization for the promotionof research in the areas of Logic, Philosophy, History of Mathematics, the biography ofKurt Gödel, and in other areas to which Gödel made contributions, especiallymathematics, physics, theology, philosophy etc. A. Setzer of Uppsala university hasprovided a list of research groups for mathematical logic, philosophical logic andtheoretical computer science on the WWW, which contains links to related topics as well.LINKS ON HISTORY OF COMPUTINGCharles Babbages Analytical Engine site exhibits texts of historical documents, including Menebreas description of theEngine translated by Ada Lovelace, and a detailed description of an Analytical Engineemulator.History of Computing Informationhttp:// by Mike Muuss, this site gives information about the history of computing, witha focusing on the Electronic Numerical Integrator and Computer (ENIAC), the worlds firstelectronic digital computer. The purpose of this Archive is to help the public rememberthat it was the U. S. Army which initiated the computer revolution by building ENIACduring World War II, giving birth to a technology which would change the world. There are14 links giving information, stories and photographs of the early days of the machine. Thesite also provides links to 37 other web sites related to the history of computers andcomputing including the origins and development of the Internet.The Virtual Museum of computing and maintained by J. Bowen of South Bank University, this site is an extensivecollection of links to sites connected with the history of computing and computer-basedexhibits. It is divided into galleries covering a variety of topics. 9
  • 10. HISTORY IN EDUCATIONUsing History in Math Class purpose of this site is to encourage and facilitate the use of the history ofmathematics in the teaching and learning of mathematics at all levels. Gerald L. Marshallcreated it as a Ph.D. project. Here some of the most useful resources on the history ofmathematics that provide assistance for the inclusion of history in the mathematicsclassroom are identified, described, and hyperlinked. The resources are divided into fivebroad categories. The category ‘Instructional’ includes sites that promote the use ofhistory in mathematics classes, those providing examples where the concept has beenapplied, and those which post bibliographies. A teacher can find samples of classroomproved projects here. The category ‘Topical’ includes sites that develop mathematicalsubjects, historical topics, and famous curves. An instructor can provide historicalintroductions to concepts that are new to their pupils. The category ‘Biographical’ identifiesand describes only a few of the many wonderful sites that provide biographies ofmathematicians. An instructor can quickly find anecdotes on notable mathematicians toshare. Likewise, the category ‘Informational’ contains locations with abstracts, informalnotes, and on-line discussions and courses. A teacher should encourage the creation ofposters and papers that have an historical theme.Fred Rickeys Home Page Page of Fred Rickey of Bowling Green University, USA, one of the leadingproponents of using history in mathematics education. The site contains annotated links towide variety of resources, including a description of his history of mathematics course.Syllabus: History of site gives the syllabus for a history of mathematics class and its instructional plan byInstructor Jim Carlson. The outline follows the major headings of Calingers book Classicsof Mathematics and spans a 3500 year period, from about 1750 BC to 1750 AD. The aimof the course is to gain an understanding of how mathematical ideas have developed overtime, how social, cultural, and historical factors influenced the development ofmathematics, and, conversely, how mathematics contributed to society and humanculture, leading eventually to a scientific view of nature.History of Mathematics with Original Sources site, which is the work of Gary Stoudt of Indiana University of Pennsylvania, containsa reading list, and a collection of discussion questions and homework problems, togetherwith some images of famous works. It is good collection of materials for using originalsources in a history of mathematics class.Teaching with Original Historical Sources in Mathematics by David Pengelley at New Mexico State University, this page offers experiencesand materials from using original historical sources in teaching mathematics. It containsarticles on and about history of mathematics and its role in teaching.Mathematical Connections on-line publication on the history and philosophy of mathematics, it presentsapplications of history of mathematics in the classroom. Keith Luoma at Augusta StateUniversity manages it. 10
  • 11. MISCELLANEOUS RESOURCESWe list below a few sites that may be helpful or interesting to visit but which do not fallnaturally into any of the above categories:Welcome to a Mathematical Journey through Time by Frances Rosamond at the National University, this site provides aninteractive timeline from 3000 BC to the present and beyond.Earliest Uses of Various Mathematical Symbols Earliest Known Uses of Mathematics Words of multiple contributors, the above two identify the names of individuals who firstused various common mathematical symbols or words and the dates the symbols/wordswere first used. The site is maintained by Jeff Miller of Gulf High School, Florida andwelcomes any further contributions.Images of Mathematicians on Postage Stamps site maintained by Jeff Miller. It contains images of postage stamps featuringmathematicians and mathematics, as well as links to other sites concerning mathematicalstamps.Famous Problems in the History of site presents a portion of the history of mathematics by investigating some of thegreat problems that have inspired mathematicians throughout the ages. The problemsincluded are suitable for middle school and high school students, with links to solutions, aswell as links to mathematicians biographies and other math history sites.Mathematics Archives –Topics in Modern Mathematics by Earl Fife at the University of Tennessee, the site provides links to importantrecourses on History, Reports, Articles; Books, Journals, Preprints, Web Sites andDatabases etc. It covers all topics of modern mathematical sciences. Links to variousresources are organized by topics. Two additional features make this site a usefuldatabase: use of additional keywords to describe a site; and use of icons to quickly showthe level of mathematical background to read the materials on the site and the type ofmaterials available on the site.Hilberts 23 Unsolved Problems 1900, David Hilbert addressed the International Congress of Mathematicians in Paris. Inhis address, he outlined 23 major mathematical problems that would be studied in thenext century. The address was not only a collection of problems; it was also his philosophyof mathematics and problems important to that philosophy. This site gives in a tabularform, the statement, present status and the reaction/contribution of variousmathematicians who have solved or have been attempting to prove or disprove theseproblems.Fermats Last Theorem 11
  • 12. It contains several links including one to the The Mathematics of Fermats Last Theorem, ahypertext site created by Charles Daney which provides an overview of some of themathematics 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.The History of history-of-algebra.htmCreated and maintained by DiAnn Sones, this web-quest site provides important links forlearning about the origin and meaning of the word algebra and about who developedalgebraic concepts. With available links it takes you on a journey through time and thehistory of mathematics to discover the answers to these questions and allows you tocreate a time-line to show how the mathematician and the mathematical developments fitinto history.The Collected Works of Mathematicians: Index and maintained by Steven Rockey of Cornell University, the site provides anextensive bibliography of collected works and correspondence of mathematicians. Theitems are assessed by author’s name on the Index page.The Internet Encyclopaedia of Philosophy is a general site on philosophy which includes articles on the philosophy of, amongstothers, Aristotle, Descartes, and Poincaré.Math and by Jackson Creek Middle School, this site includes information about sixspecific mathematicians and also links to other sites categorized into four groups: WomenMathematicians, Mathematicians, Links and Photos and General Biographical Information.Contributions of Different Cultures to the Development pathfinders/akerman/bib.htmlMaintained by Calvis, this page gives an annotated list of nearly 50 sites pertaining tomathematics in different cultures and the history of mathematics in general.Mathematics History Internet site gives a list of Links to 12 History of Mathematics resources. It includes History ofnumerals and counting, algebra, geometry, arithmetic and number theory, mathematicalanalysis, probability and statistics. 12