Geometry.Net - Mathematicians: Greek Mathematics

Hardy Grant - Greek Mathematics In Cultural Context
Hardy Grant greek mathematics in cultural context.
http://www.cms.math.ca/Events/winter99/abstracts/node92.html

Extractions: The often substantial prestige and influence enjoyed by mathematics through the long history of western culture can be traced to beginnings in ancient Greece. Here arose, for example, the vision of mathematical knowledge both as uniquely certainbecause attained by rigorous proof from incontestable axiomsand as potentially allowing unique insight into the cosmic order. I shall try to sketch both (i) the development, in cultural context, of the mathematical tradition that culminated in Euclid's exemplary Elements , and (ii) the concomitant influence of contemporary mathematics on such characteristically Greek achievements as Plato's theory of Forms, Aristotle's theory of scientific method, and the ``liberal arts'' tradition in education.
Myths, Lies, And Truths
The argument goes pregreek mathematics had neither a well-defined idea of proof nor Debate on the Relationship between Egyptian and greek mathematics
http://www.math.buffalo.edu/mad/myths_lies.html

Extractions: Third U.S. president Thomas Jefferson in 1792 (when he was Secretary of State): "Comparing them by their faculties of memory, reason, and imagination, it appears to me that in memory [the Negro] are equal to the whites; in reason much inferior, as I think one could scarcely be found capable of tracing and comprehending the investigations of Euclid; and that in imagination they are dull, tasteless, and anomalous." Present day AND ancient achievements contradict such statments. In response, these web page have been created to exhibit accomplishments of the peoples of Africa and the African Diaspora within the Mathematical Sciences. Mathematics Historian W. Rouse Ball : The history of mathematics cannot with certainty be traced back to any school or period before that of the ... Greeks. Mathematician Morris Kline : [The Egyptians] barely recognized mathematics as a distinct discipline ... [Mathematics] finally secured a new grip on life in the highly congenial soil of Greece and waxed strongly for a short period . . . With the decline of Greek civilization the plant remained dormant for a thousand years . . . when he plant was transported to Europe proper and once more imbedded in fertile soil. [Also see Mathematical Thought from Ancient to Modern Times
EBooks.com - The Shaping Of Deduction In Greek Mathematics EBook
This book provides a way into understanding a momentous development in human intellectual history the phenomenon of deductive argument in classical Greek
http://usa2.ebooks.com/ebooks/book_display.asp?IID=221790
BMCR-L: BMCR 2002.04.23 Serafina Cuomo, Ancient Mathematics
Sir Thomas Heath, A History of greek mathematics. Oxford Clarendon Press, 1921. See, for example, WR Knorr, The Ancient Tradition of Geometric Problems,
http://omega.cohums.ohio-state.edu/mailing_lists/BMCR-L/2002/0114.php

Extractions: Serafina Cuomo, Ancient Mathematics. London and New York: Routledge, 2001. Pp. xii + 290. ISBN 0-415-16494-X. $80.00. ISBN 0-415-16495-8. $27.95. Reviewed by Scott Carson, Ohio University (carsond@ohio.edu) Word count: 1488 words Happily Cuomo's sloppy interpretation of Aristotle does not represent a problem that is endemic to the book as a whole. By and large her illustrative "questions" chapters are both illuminating and well-argued. In addition to her excellent treatment of the text of Euclid to which I allude above, she also does a fine job explaining the various ways in which mathematics impinged on culture generally, for example, in the influence of mathematics on developments within Christianity; and she gives a fascinating account of some of the histories of mathematics preserved from antiquity. A careful teacher ought to be able to make very good use of a text such as this.
E-Ren: Student Projects
They translated many greek mathematics textbooks. Unsatisfied with existing translations of the great greek mathematics book Almagest,
http://www.idbsu.edu/courses/hy309/projects/math.html

Extractions: This lesson intends to present public school students a brief history of the progress of mathematics during the Renaissance. The lesson will combine an introduction to Renaissance mathematical developments with an explanation of its interactions with social influences of the time. Hopefully students will have a fresh understanding of the Renaissance period from this particular perspective. The development of mathematics almost stopped between the fourteenth century and the first half of the fifteenth century. Many social factors contributed to this situation. The ten years of the dreadful Black Death devastated Europe in the mid- fourteenth century. This caused nearly half of the population to die. The plague greatly distracted peoples' minds from the pursuit of knowledge. The Hundreds Years War between England and France (1337-1453) also created general instability in Europe. Partly because of these tragedies, the earlier Renaissance period suffered a general economic recession. Faced with such an unfavorable social and economic environment, the learned world could hardly devote its energy to intellectual development. The growth of mathematics was not only retarded by war, but also by the injurious influence of traditional scholastic philosophy. The scholastic scholars highly valued studies in the humanities, such as philosophy and literature. Students enthusiastically spent their energies on Aristotle's logic and philosophy. The intellectual leaders of those times also quarrelled over subtle subjects in metaphysics and theology. Useless questions, such as "How many angels can stand on the point of a needle?" was the kind of topic which attracted scholars' interests. The study of mathematics was given minimal attention. Mathematicians could hardly receive respect from scholars of other disciplines. There were few jobs in universities for mathematicians. At some universities, the curriculum requirement of mathematical learning had not changed for almost two centuries since the fourteenth.
Philosophical Origins In Mathematics
In other words, ancient greek mathematics and modern mathematics are In Szabó s views, the most striking characteristics of greek mathematics is the
http://hps.elte.hu/~kutrovatz/frankfur.htm

Extractions: I. The Internalist Historiographic Tradition Since the turn of the 19 th and 20 th centuries when systematic research on antique Greek mathematics began, the general tone of historiographical work in the field has been dominated by the so-called internalist attitude. H.G. Zeuthen, P. Tannery and others initiated a research tradition whose goal is to reconstruct the mathematical development of the minus 5 th and 4 th century Greece by providing a technical and conceptual analysis of the available source texts, notably of Euclid's Elements . Such a reconstruction relies on today's conception of mathematical knowledge, inasmuch as it proceeds by decontextualising antique texts and separating their âmathematical content' from the 'form of expression', the latter regarded as incidental and irrelevant. According to this view, the history of mathematics appears as a development of interrelated mathematical concepts and propositions, and the growth of mathematical knowledge lies in our increasing understanding of the network of these conceptual relations. Thus our better understanding of mathematics can, and should, shed light on the actual content of ancient mathematical texts by disregarding the 'clumsy' and 'cumbersome' language of expression and reformulating the original problems in the more suitable mathematical language of our modern age.
¥j§ÆÃ¾¼Æ¾Ç¡]ancient Greek Mathematics¡^
The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set.
http://www.edp.ust.hk/math/history/2/2_4.htm
Greek For Euclid: Contents
They do not represent the limits of greek mathematics, only its basis. greek mathematics was further developed by Archimedes, who discussed spirals,
http://www.du.edu/~etuttle/classics/nugreek/contents.htm

Extractions: Sir Winston Churchill Go immediately to Contents Eu)klei/dou Stoixei~a , Euclid's Elements, the classical textbook in geometry, is easy to read in the original ancient Greek, but its grammar and vocabulary are not those familiar from the usual course in elementary Greek, with peculiarities that make it difficult for the beginner. The text of the Elements that we have is written in the literary koinh/ typical of the 1st century AD. This course concentrates on exactly what is necessary to read Euclid, both in vocabulary and grammar. Its sole aim is to teach how to read this work, and similar texts in Greek mathematics, and not to compose Greek sentences, nor to read the Iliad or Plato. All necessary information is included in the course. A great amount of scholarship has been devoted to Euclid, mainly in Latin or German, and this course may expose some of it to a larger audience, to whom it has been largely inaccessible. For authoritative details, reference must be made to these sources, since the present one claims no expertise. There are many websites with information on Euclid and geometry. For example, look at the link to Euclid in the Seven Wonders website that is referenced in the Classics Index page, under the heading Pharos of Alexandria. As is typical of education on the Internet, many sites are poor, repetitive or childish, however.
HEATH, Thomas., A History Of Greek Mathematics.
Illus. 446 pp.; 586 pp. Two vols. 8vo, wrappers. New York Dover, nd The classic text on the Greek legacy of mathematics.
http://www.polybiblio.com/jahill/HillBibl-Selections461.0.html

Extractions: Jonathan A. Hill, Bookseller Inc. HEATH, Thomas. A History of Greek Mathematics. New York: Dover, n.d. Illus. 446 pp.; 586 pp. Two vols. 8vo, wrappers. New York: Dover, n.d. The classic text on the Greek legacy of mathematics. This item is listed on Bibliopoly by Jonathan A. Hill, Bookseller Inc. ; click here for further details.
Greek Mathematics On Papyrus
Greek Geometry on Papyrus. Little attention is paid by many scholars of classical and hellenistic Greek culture, language and literature to the technical
http://users.ox.ac.uk/~newc0543/Work/Papyrus.htm

Extractions: Little attention is paid by many scholars of classical and hellenistic Greek culture, language and literature to the technical and scientific genres, beyond perhaps the obvious authors like Euclid. The fascination of the amateur in antiquity with what now seems to be very elementary material is often overlooked, despite the fact that much of this kind of work was at the cutting edge in the period. Most important in our understanding of this is the selection of surviving non-literary written evidence including everyday calculations, school texts and the like. These have received far less consideration than they deserve and while I make no claim to be exhaustive, the study presented is one which attempts to address some of the key aspects of one part of the evidence, namely mathematical and specifically geometric texts surviving on papyrus. Written as an undergraduate thesis, the aim is to provide a survey of the relevant evidence together with a catalogue of that evidence. A portion of the thesis relating to an as yet unpublished text cannot yet be made available online, but scholars interested in the area are invited to contact the author who may be able to supply a copy of the newly edited texts. They will, however, appear in a subsequent volume of the
PS One Human Remark. Your Statement About The Ancient Greek
Basically, judging Ancient greek mathematics from Euclid is like judging 20th century math from Bourbaki, or from a college Calculus and Analytic Geometry
http://www.math.rutgers.edu/~zeilberg/fb43

Extractions: P.S. One "human" remark. Your statement about the ancient Greek straightjacket does not apply to ancient Greeks. As Archimedes' papers show, he used heuristic methods and algorithms to discover his results and only then did he prove them formally. This was also probably true of all the other great ancient mathematicians. In fact, Euclid probably did not discover what he wrote in his Elements, so is not a good example. Basically, judging Ancient Greek mathematics from Euclid is like judging 20th century math from Bourbaki, or from a college Calculus and Analytic Geometry textbook.
Erratum In The Review Of Shaping Of Deduction In Greek Mathematics
Erratum and addendum for my review of R. Netz The Shaping of Deduction in greek mathematics, in Endeavour 242(2000), pp. 8586.
http://wwwhs.cias.osakafu-u.ac.jp/~ksaito/shaping_erratum.html

Extractions: BACK Erratum and addendum for my review of R. Netz' The Shaping of Deduction in Greek Mathematics , in Endeavour 242(2000), pp. 85-86. Page 85, Column 2, line 13: Diagrams, however, do themselves consititute demonstrations. READ: Diagrams, however, do not themselves consititute demonstrations. Adendum: another review of the same book by Ch. Marinus Taisbak is available on the web.
Ken SAITO's Home Page
Translate this page Bibliography of greek mathematics I have revised the greek mathematics section (by Len Berggren) of the so-called Dauben Bibliography, in its revised
http://wwwhs.cias.osakafu-u.ac.jp/~ksaito/

Extractions: Last update 21/Feb/2004 Bibliography of Greek mathematics: I have revised the Greek mathematics section (by Len Berggren) of the so-called Dauben Bibliography, in its revised Edition on CD-ROM appeared in 2000 (ed. Albert C. Lewis). The official name of this bibliography is: The History of Mathematics from Antiquity to the Present: A Selective Annotated Bibliography. You can find and order this CD-ROM from American Mathematical Society. Index of Propositions used in the Conics Index of the Propositions Used in Book 7 of Pappus' Collection List of publication ... Japanese page here
Arabic Mathematics
Explains contributions of Arabian mathematicians by translating early greek texts, developing early algebraic ideas, number theory and astronomical calculations. Includes information about key people during this time period.
http://www-history.mcs.st-and.ac.uk/history/HistTopics/Arabic_mathematics.html

Extractions: Version for printing Recent research paints a new picture of the debt that we owe to Arabic/Islamic mathematics. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks. There is a widely held view that, after a brilliant period for mathematics when the Greeks laid the foundations for modern mathematics, there was a period of stagnation before the Europeans took over where the Greeks left off at the beginning of the sixteenth century. The common perception of the period of 1000 years or so between the ancient Greeks and the European Renaissance is that little happened in the world of mathematics except that some Arabic translations of Greek texts were made which preserved the Greek learning so that it was available to the Europeans at the beginning of the sixteenth century. That such views should be generally held is of no surprise. Many leading historians of mathematics have contributed to the perception by either omitting any mention of Arabic/Islamic mathematics in the historical development of the subject or with statements such as that made by Duhem in [3]:-
3.1415926535 - History And Philosophy Of Pi
Probably no symbol of infinity in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number and greek letter of Pi. Interesting facts and trivia about Pi.
http://briantaylor.com/Pi.htm

Extractions: romanticism, misconception and human interest as the number Pi ( Socrates Plato Aristotle Pi 3.14 ... Problems Pi (noun) ... plural = pis. Mathematics. A transcendental number, approximately 3.14159, represented by the symbol , that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions. The 16th letter of the Greek alphabet. : BEYOND INFINITY Deep in the nature of man is the will to go further than any human has ever been before. This quest is symbolized by the Greek letter , which evokes infinity. Humans are still in pursuit of the end of its innumerable string of decimals... No number (3.14...) has captured the attention and imagination of number fanatics and nerds throughout the ages as much as the ratio of a circle's circumference to its diameter - a.k.a. Pi. With incisive historical insight and a refreshing sense of humor, this page brings us the story of Pi and humankind's fascination with it, from Archimedes to da Vinci to the modern day Chudnovsky brothers, who holed up in their Manhattan apartment with a homemade supercomputer churning out digits of pi into the billions.
Bible Numerics
A Study in Biblical mathematics. Numerical analysis of the Hebrew and greek Text.
http://biblemaths.com

Extractions: This book is summarised in two DVD presentations on one DVD. Each presentation is 44 slides and lasts about one hour each. The presentation has synchronized narration with each Presentation. L ecture one - Bible Numerics and Lecture two - The 70 Sevens of Daniel with some aspects of the Second Advent. The DVD can be used in Bible Studies Via the TV or Schools via a PC projector. The presentations Prove that the Bible is the true source of our existence and shows the evidence of how we Prove that Jesus Christ is the Messiah BOOK DVD Only BOOK and DVD
Mathematicians Born In Greece
Biographies of greek Mathematicians, with supplemental maps and timeline. From the MacTutor, History of mathematics.
http://www-gap.dcs.st-and.ac.uk/~history/BirthplaceMaps/Countries/Greece.html
Mathematics, Greek: New & Used Books Category Search Result For Mathematics, Gre
mathematics, greek New Used Books Category Search Result for mathematics, greek. Compare new and used books prices among 122 book stores in a click.
http://www.fetchbook.info/fwd_topics/id_1520791.html
Bryn Mawr Classical Review 2004.03.47
CJ Tuplin, TE Rihll, Science and mathematics in Ancient greek Culture. Oxford Oxford University Press, 2002. Pp. xvi + 379. ISBN 019-815248-5. $85.00.
http://ccat.sas.upenn.edu/bmcr/2004/2004-03-47.html

Extractions: The excellent collection of essays edited by Tuplin and Rihll (hereafter TR) reflects two major changes that the history of ancient science has experienced in the last thirty years. First is the great broadening of materials considered relevant to the field. Whereas in the not so distant past scholarship would concentrate on a few great works by a few great men, the modern historian of ancient science takes advantage of a much wider range of sources, including, for instance, materials documenting connections between magic and medicine or astrology and astronomy. The second major development has been an increased attention paid to the broader social context out of which scientific practices emerged. Economic and political forces have come to be recognized as important determinants of scientific activities, as have the close connections between practical achievements and theoretical innovation. Both developments are central to the aims and achievements of TR's anthology. Its sixteen papers (and a substantial introduction) arise from a 1996 conference in Liverpool that sought to bring together scholars working in diverse areas of ancient science, including mathematics, astronomy, mechanics, chemistry, medicine, and technology. The aim was not just for participating scholars to share their findings with one another but to demonstrate the relevance and value of historical studies of ancient science to what the editors term "mainstream" classicists and ancient historians. On the whole, the papers succeed in doing this by emphasizing precisely the two trends that have transformed the field. Because so many different and complex papers cannot be adequately treated in a limited review, I shall highlight what seem to me the contributions of greatest interest to the readers for whom the collection is intended.
The Research Notebook Of A Beleaguered Hack.: Struik: A Concise History Of Mathe
Eudoxus solved the crisis in greek math and determined the course of greek math mathematics is intimately tied to astronomy, which was the science first
http://arsenal.media.mit.edu/notebook/archives/000104.html

Extractions: The research notebook of a beleaguered hack. Struik: A Concise History of Mathematics: Greece As the Mediterranean basin transitioned from the Bronze Age to the Iron Age there were enormous economic and political changes. Iron's introduction changed warfare but also cheapened production, causing a surplus, and allowing more people to be involved in public life. Additionally the introduction of coined money and the alphabet stimulated trade. Culture began to flourish, no longer exclusively the domain of the elite. Sea-raiders upset cultural, scientific, and mathematical progress as they destroyed Minoan civilization, and disrupted Egyptian and Babylonian development. The rise of the Greek city-state in 7th-6th centuries BCE allowed new freedoms to citizens. More leisure (begotten from slavery and wealth) stimulated the growth of rationalism, philosophy, and science. In contrast to oriental approaches, the Greeks did not just "how?" but sought to know "why?" Thales of Milete (who had traveled to Babylon and Egypt) is considered the father of Greek math. In seeking a rational scheme to the universe his tradition added an element of rationalism to mathematics. Only small fragments remain, but through careful analysis a consistent picture of Greek math emerges. The rise of Persia led to conflict and an eventual Greek victory, which expanded the power of Athens. Democratic ideals flourished from 450-400 BCE, paving the path for the Golden Age of Greece. Sophists had greater freedom to examine ideas more abstract than useful. The only complete fragment of this period is written by Hippocrates of Chios. The work shows perfected mathematical reasoning and deals with the impractical: the

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