Istorija matematike

Područje studija poznato kao istorija matematike prvenstveno je istraživanje porekla otkrića u matematici i, u manjoj meri, istraživanje matematičkih metoda i notacija prošlosti. Pre modernog doba i širenja znanja širom sveta, pisani primeri novih matematičkih dostignuća izašli su na videlo samo na nekoliko lokacija. Od 3000. godine p. n. e, mesopotamijske države Sumer, Akad i Asirija, praćene drevnim Egiptom i levantinskom državom Ebla, počele su da koriste aritmetiku, algebru i geometriju u svrhe oporezivanja, privrede, trgovine, kao i u pronicanju paterna u prirodi, na području astronomije i da beleže vreme i formulišu kalendare.

Dokaz iz *|Euklidovih elemenata* (oko 300. p. n. e.), koji se naširoko smatra najuticajnijim udžbenikom svih vremena.^[1]

Teško je sa sigurnošću tvrditi kada je i šta je početak matematike. Najverovatnije je da je to brojanje. Ono što sa sigurnošću možemo tvrditi, na osnovu arheoloških iskopavanja, je da u Egiptu i Mesopotamiji imamo prve pisane podatke nečega što možemo podvesti pod matematičke spise. U Egiptu (vidi staroegipatska matematika) su to listovi papirusa (Rajndov papirus) a u Mesopotamiji glinene pločice.^[2]^[3]

Egipćani i Stari Sumeri su matematiku razvijali za praktične potrebe, najviše za premeravanje zemlje posle izlivanja Nila, gradnju kanala, položaj zvezda, građevinarstvo, itd. Treba napomenuti da su Egipćani znali za Pitagorinu teoremu, ali ne u njenom obliku c² = a² + b² već kao određene jednakosti.^[4] Primera radi ako su imali pravougli trougao sa katetama 3 i 4 znali su da je hipotenuza 5, ovaj trougao se i danas naziva egipatski trougao.

Potom razvoj matematike preuzimaju Stari Grci, koji matematici daju novu dimenziju odnosno počinje razvoj apstraktne matematike, tj. matematike koja nema direktnu praktičnu primenu.^[5] Oni su prvi zasnovali aksiomatski pristup matematici. Grci se najviše bave geometrijom, ali i algebrom. Za Grke je matematika osnova svega, pa je tako na ulazu u Akademiju stajao natpis: „Neka ne ulazi onaj koji ne zna geometriju“. Euklidovi „Elementi“ je knjiga koja je predstavljala najbolji udžbenik iz oblasti geometrije sve do kraja 19. veka i Hilberta. Geometrija je posle Helenističkog perioda tavorila sve do Lobačevskog.

Isto tako postojala je matematika i u Kini^[6]^[7] i Indiji.^[8]^[9] Brojevi kojima danas pišemo su došli do Evrope iz Indije zahvaljujući Arapima.^[10] U srednjem veku dolazi do prestanka bavljenja matematikom u hrišćanskom svetu, pa tako Justinijan I zabranjuje rad Akademiji. Istovremeno dolazi do procvata arapske matematike. Početkom renesanse i matematika oživljava u Evropi.

Reference uredi

^ Boyer 1991, "Euclid of Alexandria" p. 119
^ J. Friberg, "Methods and traditions of Babylonian mathematics. Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations", Historia Mathematica, 8, 1981, pp. 277–318.
^ Neugebauer, Otto (1969) [1957]. The Exact Sciences in Antiquity. Acta Historica Scientiarum Naturalium et Medicinalium. 9 (2 izd.). Dover Publications. str. 1—191. ISBN 978-0-486-22332-2. PMID 14884919. Chap. IV "Egyptian Mathematics and Astronomy", pp. 71–96.
^ Heath (1931). „A Manual of Greek Mathematics”. Nature. 128 (3235): 5. Bibcode:1931Natur.128..739T. S2CID 3994109. doi:10.1038/128739a0.
^ Sir Thomas L. Heath, A Manual of Greek Mathematics, Dover, 1963, p. 1: "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."
^ George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics, Penguin Books, London, 1991, pp. 140–48
^ Georges Ifrah, Universalgeschichte der Zahlen, Campus, Frankfurt/New York, 1986, pp. 428–37
^ Robert Kaplan, "The Nothing That Is: A Natural History of Zero", Allen Lane/The Penguin Press, London, 1999
^ "The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius." – Pierre Simon Laplace http://www-history.mcs.st-and.ac.uk/HistTopics/Indian_numerals.html
^ A.P. Juschkewitsch, "Geschichte der Mathematik im Mittelalter", Teubner, Leipzig, 1964

Literatura uredi

Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B. (2004), Pi: A Source Book, New York: Springer, ISBN 978-0-387-20571-7
Boyer, C.B. (1991) [1989], A History of Mathematics (2nd izd.), New York: Wiley, ISBN 978-0-471-54397-8
Cuomo, Serafina (2001), Ancient Mathematics, London: Routledge, ISBN 978-0-415-16495-5
Goodman, Michael, K.J. (2016), An introduction of the Early Development of Mathematics, Hoboken: Wiley, ISBN 978-1-119-10497-1
Gullberg, Jan (1997), Mathematics: From the Birth of Numbers , New York: W.W. Norton and Company, ISBN 978-0-393-04002-9
Joyce, Hetty (jul 1979), „Form, Function and Technique in the Pavements of Delos and Pompeii”, American Journal of Archaeology, 83 (3): 253—63, JSTOR 505056, doi:10.2307/505056. CS1 održavanje: Format datuma (veza)
Katz, Victor J. (1998), A History of Mathematics: An Introduction (2nd izd.), Addison-Wesley, ISBN 978-0-321-01618-8
Katz, Victor J. (2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, NJ: Princeton University Press, ISBN 978-0-691-11485-9
Needham, Joseph; Wang, Ling (1995) [1959], Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth, 3, Cambridge: Cambridge University Press, ISBN 978-0-521-05801-8
Needham, Joseph; Wang, Ling (2000) [1965], Science and Civilization in China: Physics and Physical Technology: Mechanical Engineering, 4 (reprint izd.), Cambridge: Cambridge University Press, ISBN 978-0-521-05803-2
Sleeswyk, Andre (oktobar 1981), „Vitruvius' odometer”, Scientific American, 252 (4): 188—200, Bibcode:1981SciAm.245d.188S, doi:10.1038/scientificamerican1081-188. CS1 održavanje: Format datuma (veza)
Straffin, Philip D. (1998), „Liu Hui and the First Golden Age of Chinese Mathematics”, Mathematics Magazine, 71 (3): 163—81, doi:10.1080/0025570X.1998.11996627
Tang, Birgit (2005), Delos, Carthage, Ampurias: the Housing of Three Mediterranean Trading Centres, Rome: L'Erma di Bretschneider (Accademia di Danimarca), ISBN 978-88-8265-305-7.
Volkov, Alexei (2009), „Mathematics and Mathematics Education in Traditional Vietnam”, Ur.: Robson, Eleanor; Stedall, Jacqueline, The Oxford Handbook of the History of Mathematics, Oxford: Oxford University Press, str. 153—76, ISBN 978-0-19-921312-2
Aaboe, Asger (1964). Episodes from the Early History of Mathematics. New York: Random House.
Bell, E.T. (1937). Men of Mathematics . Simon and Schuster.
Burton, David M. The History of Mathematics: An Introduction. McGraw Hill: 1997.
Grattan-Guinness, Ivor (2003). Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. The Johns Hopkins University Press. ISBN 978-0-8018-7397-3.
Kline, Morris. Mathematical Thought from Ancient to Modern Times.
Struik, D.J. (1987). A Concise History of Mathematics, fourth revised edition. Dover Publications, New York.
Gillings, Richard J. (1972). Mathematics in the Time of the Pharaohs. Cambridge, MA: MIT Press.
Heath, Sir Thomas (1981). A History of Greek Mathematics . Dover. ISBN 978-0-486-24073-2.
van der Waerden, B.L., Geometry and Algebra in Ancient Civilizations, Springer, (1983) ISBN 0-387-12159-5.
Corry, Leo (2015), A Brief History of Numbers, Oxford University Press, ISBN 978-0198702597
Hoffman, Paul (1998). The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. Hyperion. ISBN 0-7868-6362-5.
Menninger, Karl W. (1969). Number Words and Number Symbols: A Cultural History of Numbers. MIT Press. ISBN 978-0-262-13040-0.
Stigler, Stephen M. (1990). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press. ISBN 978-0-674-40341-3.
Berriman, A. E. (1956). The Babylonian quadratic equation.
Høyrup, Jens. „Pythagorean ‘Rule’ and ‘Theorem’ – Mirror of the Relation Between Babylonian and Greek Mathematics”. Ur.: Renger, Johannes. Babylon: Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne. 2. Internationales Colloquium der Deutschen Orient-Gesellschaft 24.–26. März 1998 in Berlin (PDF). Berlin: Deutsche Orient-Gesellschaft / Saarbrücken: SDV Saarbrücker Druckerei und Verlag. str. 393—407.
Joseph, G. G. (2000). The Crest of the Peacock. Princeton University Press. ISBN 0-691-00659-8.
Joyce, David E. (1995). „Plimpton 322”.
O'Connor, J. J.; Robertson, E. F. (decembar 2000). „An overview of Babylonian mathematics”. MacTutor History of Mathematics. CS1 održavanje: Format datuma (veza)
Robson, Eleanor (2001). „Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322”. Historia Math. 28 (3): 167—206. MR 1849797. doi:10.1006/hmat.2001.2317.
Robson, E. (2002). „Words and pictures: New light on Plimpton 322”. American Mathematical Monthly. Washington. 109 (2): 105—120. JSTOR 2695324. S2CID 33907668. doi:10.1080/00029890.2002.11919845.
Robson, E. (2008). Mathematics in Ancient Iraq: A Social History. Princeton University Press.
Toomer, G. J. (1981). Hipparchus and Babylonian Astronomy.

Spoljašnje veze uredi

Rana matematika (RTS, 16. april 2016)
BBC (2008). The Story of Maths.
Renaissance Mathematics, BBC Radio 4 discussion with Robert Kaplan, Jim Bennett & Jackie Stedall (In Our Time, Jun 2, 2005)

Obrazovni materijal uredi

MacTutor History of Mathematics archive (John J. O'Connor and Edmund F. Robertson; University of St Andrews, Scotland). An award-winning website containing detailed biographies on many historical and contemporary mathematicians, as well as information on notable curves and various topics in the history of mathematics.
History of Mathematics Home Page (David E. Joyce; Clark University). Articles on various topics in the history of mathematics with an extensive bibliography.
The History of Mathematics (David R. Wilkins; Trinity College, Dublin). Collections of material on the mathematics between the 17th and 19th century.
Earliest Known Uses of Some of the Words of Mathematics (Jeff Miller). Contains information on the earliest known uses of terms used in mathematics.
Earliest Uses of Various Mathematical Symbols (Jeff Miller). Contains information on the history of mathematical notations.
Mathematical Words: Origins and Sources (John Aldrich, University of Southampton) Discusses the origins of the modern mathematical word stock.
Biographies of Women Mathematicians (Larry Riddle; Agnes Scott College).
Mathematicians of the African Diaspora (Scott W. Williams; University at Buffalo).
Notes for MAA minicourse: teaching a course in the history of mathematics. (2009) (V. Frederick Rickey & Victor J. Katz).

Istorija matematike

Reference uredi

Literatura uredi

Spoljašnje veze uredi

Obrazovni materijal uredi

Bibliografije uredi

Organizacije uredi

Časopisi uredi