The sixth in a series of math history seminars, this seminar will continue our study of greek mathematics. Historians traditionally place the beginning of greek mathematics proper to the age of thales of miletus ca. Mathematics and its history available for download and read online in other formats. It opens the way to providing the fi rst comprehensive, textually based history of proof.
The unique feature that sets mathematics apart from other sciences, from philosophy, and indeed from all other forms of intellectual discourse, is the. This work is known as euclids elements 1, pg 19 by the 400bc the center of greek civilization and math moved from athens to alexandria and greek became the dominant culture and language 1, pg 19. He acknowledges the suggestion that the author drew many di. It is therefore designed for junior or senior mathematics majors. The history of mathematical proof in ancient traditions. The greeks view mathematics as a very important aspect of life, education and view it as a necessary tool to help assist in the forward progress of technology. Ancient greek civilization generally accepted to date from around 800 bc. The study of mathematics as a subject begins in the 6th century bc when the pythagoreans originate the word mathematics. Heath covers in sequence greek numerical notation, pythagorean arithmetic, thales and pythagorean geometry, zeno, plato, euclid, aristarchus, archimedes, apollonius, hipparchus and trigonometry, ptolemy, heron, pappus, diophantus of alexandria and. From aristarchus to diophantus sir thomas little heath full view 1921.
Little is known about the life and work of thales, so little indeed that his date of birth and death are estimated from the eclipse of 585 bc, which probably occurred while he was in his prime. But most of greek mathematics was based on geometry. Greek mathematics constitutes an important period in the history of mathematics. In ancient greek writings other word variations exist including manthanein and manthanousin, and relate either to. Euclids elements and its role in the history of mathematics 8. A history of greek mathematics by heath, thomas little, sir, 18611940. The purpose of this paper, however, is to situate this multiple view in an embodied practice of geometers as they draw diagrams and prove theorems.
Early greek mathematics introduction history and heritage, 1 mathematicians have a vested interest in telling the story of past mathematics in a particular way one that sheds direct light on their own activity. Squares, cubes, square roots, cube roots solve quadratic equations but no quadratic formula uses. Recently, william duham and john stillwell, have tried to make histories of mathematics with the books stuffed with the actual mathematics. This is the earliest known recorded attempt at proving mathematical concepts.
A history of mathematics amirkabir university of technology. You can also make use of the search facility at the top of each page to search for individual mathematicians, theorems, developments, periods in history, etc. A one or twosemester course taught at the senior level can dig deeper into the history of mathematics, incorporating many ideas from the 19 th and 20 centuries that could only be approached with difficulty by less prepared students. Thales, one of the seven sages of ancient greece, who lived on the ionian coast of asian minor in the first half of the 6th century bce, is usually considered to have been the first to lay down guidelines for the abstract development of geometry, although what we know of his work such as on similar and right.
Its students included the ancient greek philosopher aristotle, ancient greek astronomer eudoxus of cnidus, and possibly ancient greek mathematician euclid. Heath records that history with the scholarly comprehension and comprehensiveness that marks this work as obviously classic now as when it first appeared in 1921. Greek mathematics, page 2 at this time, they began to formulate proofs, and worked with basic assumptions or postulates. Geometry was one of the two fields of premodern mathematics, the other being the study of numbers classic geometry was focused in compass and straightedge constructions. The best estimate is that the greek civilization dates back to 2800 bce just about the time of the construction of the great pyramids in egypt. The greeks worked many geometrical construction problems using a straightedge and compass. The detailed study of greek mathematics reveals much about modern mathematics, if not the modern directions, then the logic and methods.
In the case of mathematics, it is the greek contribution which it is most essential to know, for it was the greeks who first made mathematics a science. As a supplement to my interest in the history of science, i figured that i ought to take a look into the history of mathematics, since the two are quite intimately related. The main story of mathematics is supplemented by a list of important mathematicians and their achievements, and by an alphabetical glossary of mathematical terms. Euclid made a number of discoveries in geometry shortly after 300 bce and was the first to suggest that there are an infinite amount of prime numbers. The greeks are to be credited with making mathematics abstract making mathematics abstract was the greatest contribution that greeks made and it was of immeasurable signi cance and value. Pdf history of greek mathematics from aristarchus to. The history and concept of mathematical proof steven g.
In order to do this, they transform a past result, n, into their own conception. Sep 24, 20 the birth of greek mathematics owes its impetus to the influence of some of its neighbours, especially egypt. The egyptian and babylonian influence was greatest in miletus, a city of ionia in asia minor and the birthplace of greek philosophy, mathematics and science. Greek mathematics also contributed importantly to ideas on number theory, mathematical analysis, applied mathematics, and, at times, approached close to integral calculus. The story of mathematics a history of mathematical thought. I told him that i gave what i hoped was a critical account of the whole history of mathematics in a series of lectures, trying to go beyond what they would. It is primarily derived from the ancient greek word mathema meaning any study which a person may learn. As the greek empire began to spread its sphere of influence into asia minor, mesopotamia and beyond, the greeks were smart enough to adopt and adapt useful elements from the societies they conquered. Hm 11 history of greek mathematics 395 searched than that of modern mathematics, then of course they are quite true. Early preeuclidean greek mathematics euclids elements forms a natural breakpoint in greek mathematical history. Primarily centered on the aegean sea between modernday greece and turkey. Jeremy gray, professor of the history of mathematics, open university each of the papers in this volume, starting with the amazing. This was as true of their mathematics as anything else, and they adopted elements of mathematics from both.
The linkage and unity of mathematics and philosophy suggest the outline for the entire history. History of ancient greek mathematics research papers. Greek mathematicians lived in cities spread over the entire eastern mediterranean, from italy to north africa, but were united by culture and language. As such it has more to do with ethnomethodological and phenomenological studies of mathematical practice. The story of mathematics a history of mathematical. The most notable early achievements were from the school associated with pythagoras in c. Pdf mathematics and its history download full pdf book.
The word mathema is a noun from the verb manthano meaning a subj. Thales, one of the seven sages of ancient greece, who lived on the ionian coast of asian minor in the first half of the 6th century bce, is usually considered to have been the first to lay down guidelines for the abstract development of geometry, although what we know of his work such as on similar and right triangles now seems quite. The ancient greek civilization lasted until about 600 bce originally, the egyptian and babylonian influence was greatest in miletus, a city of ionia in asia minor. In actual fact, our direct knowledge of greek mathematics is less reliable than that of the older egyptian and babylonian mathematics, because none of the original manuscripts are extant. Curves in the greek geometry, apollonius the great geometer 10. Though the greeks certainly borrowed from other civilizations, they built a culture and civilization on their own which is the most impressive of all civilizations, the most influential in western culture, the most decisive in founding mathematics as we know it.
This work is known as euclids elements 1, pg 19 by the 400bc the center of greek civilization and math moved from athens to alexandria. The first proof in the history of mathematics is considered to be when thales proved that the diameter of a circle divides a circle into two equal parts. Page 3 his hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed. A concise history of mathematics, fourth revised edition. To show how the greeks view the concept of mathematics, dissect the word. It serves those who see philosophys vocation in questioning and challenging prevailing assumptions about ourselves and our place in the world, developing new ways of thinking about physical existence, life, humanity and society, so. However, far from awaiting only the fillingin of minor details, the history of greek mathematics is an area where there is still controversy over some of the. Search the history of over 431 billion web pages on the internet. Building, planning, selling, astronomy later a brief history of mathematics. The reason is no doubt that he was an astronomer, and therefore it might be supposed that his work would have no sufficient interest for the mathematician. Geometry was one of the two fields of premodern mathematics, the other being the study of numbers.
The origins of greek mathematics1 department of mathematics. View history of ancient greek mathematics research papers on academia. Or, at least, sir thomas heaths a history of greek mathematics in two volumes. The origins of greek mathematics1 though thegreekscertainlyborrowedfromother civilizations, they built a culture and civilization on their own which is the most impressive of all civilizations, the most influential in western culture, the most decisive in founding mathematics as we know it. John stillwell is professor of mathematics at the university of san francisco. Krantz1 february 5, 2007 amathematicianisamasterof criticalthinking,of analysis, andof deductive reasoning. Well explore some of these constructions, and specifically look at the. Or, at least, sir thomas heaths a history of greek mathematicsin two volumes. He is the author of several highly regarded books published by springer, including the four pillars of geometry 2005, elements of number theory 2003, mathematics and its history second edition, 2002, numbers and geometry 1998 and elements of algebra 1994. Preeuclidean mathematics is therefore largely a discussion of the origins of some of the ideas in euclid. Timeline for the history of greek mathematics each step is 25 years. Solved systems of equations with many unknowns no negative numbers.915 1497 1221 513 477 1065 895 1117 1136 1086 494 1034 562 1465 1155 241 1144 1191 1101 102 1264 945 321 1346 803 1508 504 1515 14 1178 12 1489 460 1493 1126 85 13 273 913 717 563 1013 305