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Mathematicians
MATHEMATICIANS [MATHEMATICIANS] Authors: Oliver Knill: 2000 Literature: Started from a list of names with birthdates grabbed from mactutor in 2000. Abbe [Abbe] Abbe Ernst (1840-1909) Abel [Abel] Abel Niels Henrik (1802-1829) Norwegian mathematician. Significant contributions to algebra and anal- ysis, in particular the study of groups and series. Famous for proving the insolubility of the quintic equation at the age of 19. AbrahamMax [AbrahamMax] Abraham Max (1875-1922) Ackermann [Ackermann] Ackermann Wilhelm (1896-1962) AdamsFrank [AdamsFrank] Adams J Frank (1930-1989) Adams [Adams] Adams John Couch (1819-1892) Adelard [Adelard] Adelard of Bath (1075-1160) Adler [Adler] Adler August (1863-1923) Adrain [Adrain] Adrain Robert (1775-1843) Aepinus [Aepinus] Aepinus Franz (1724-1802) Agnesi [Agnesi] Agnesi Maria (1718-1799) Ahlfors [Ahlfors] Ahlfors Lars (1907-1996) Finnish mathematician working in complex analysis, was also professor at Harvard from 1946, retiring in 1977. Ahlfors won both the Fields medal in 1936 and the Wolf prize in 1981. Ahmes [Ahmes] Ahmes (1680BC-1620BC) Aida [Aida] Aida Yasuaki (1747-1817) Aiken [Aiken] Aiken Howard (1900-1973) Airy [Airy] Airy George (1801-1892) Aitken [Aitken] Aitken Alec (1895-1967) Ajima [Ajima] Ajima Naonobu (1732-1798) Akhiezer [Akhiezer] Akhiezer Naum Ilich (1901-1980) Albanese [Albanese] Albanese Giacomo (1890-1948) Albert [Albert] Albert of Saxony (1316-1390) AlbertAbraham [AlbertAbraham] Albert A Adrian (1905-1972) Alberti [Alberti] Alberti Leone (1404-1472) Albertus [Albertus] Albertus Magnus -
Greek Mathematics Recovered in Books 6 and 7 of Clavius’ Geometria Practica
Introduction – Clavius and Geometria Practica Book 6 and Greek approaches to duplication of the cube Book 7 and squaring the circle via the quadratrix Conclusions Greek Mathematics Recovered in Books 6 and 7 of Clavius’ Geometria Practica John B. Little Department of Mathematics and CS College of the Holy Cross June 29, 2018 Greek Mathematics in Clavius Introduction – Clavius and Geometria Practica Book 6 and Greek approaches to duplication of the cube Book 7 and squaring the circle via the quadratrix Conclusions I’ve always been interested in the history of mathematics (in addition to my nominal specialty in algebraic geometry/computational methods/coding theory, etc.) Want to be able to engage with original texts on their own terms – you might recall the talks on Apollonius’s Conics I gave at the last Clavius Group meeting at Holy Cross (two years ago) So, I’ve been taking Greek and Latin language courses in HC’s Classics department The subject for today relates to a Latin-to-English translation project I have recently begun – working with the Geometria Practica of Christopher Clavius, S.J. (1538 - 1612, CE) Greek Mathematics in Clavius Introduction – Clavius and Geometria Practica Book 6 and Greek approaches to duplication of the cube Book 7 and squaring the circle via the quadratrix Conclusions Overview 1 Introduction – Clavius and Geometria Practica 2 Book 6 and Greek approaches to duplication of the cube 3 Book 7 and squaring the circle via the quadratrix 4 Conclusions Greek Mathematics in Clavius Introduction – Clavius and Geometria Practica Book 6 and Greek approaches to duplication of the cube Book 7 and squaring the circle via the quadratrix Conclusions Clavius’ Principal Mathematical Textbooks Euclidis Elementorum, Libri XV (first ed. -
A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Scholarship@Claremont Journal of Humanistic Mathematics Volume 7 | Issue 2 July 2017 A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time John B. Little College of the Holy Cross Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Ancient History, Greek and Roman through Late Antiquity Commons, and the Mathematics Commons Recommended Citation Little, J. B. "A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time," Journal of Humanistic Mathematics, Volume 7 Issue 2 (July 2017), pages 269-293. DOI: 10.5642/ jhummath.201702.13 . Available at: https://scholarship.claremont.edu/jhm/vol7/iss2/13 ©2017 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time Cover Page Footnote This essay originated as an assignment for Professor Thomas Martin's Plutarch seminar at Holy Cross in Fall 2016. -
A Short History of Greek Mathematics
Cambridge Library Co ll e C t i o n Books of enduring scholarly value Classics From the Renaissance to the nineteenth century, Latin and Greek were compulsory subjects in almost all European universities, and most early modern scholars published their research and conducted international correspondence in Latin. Latin had continued in use in Western Europe long after the fall of the Roman empire as the lingua franca of the educated classes and of law, diplomacy, religion and university teaching. The flight of Greek scholars to the West after the fall of Constantinople in 1453 gave impetus to the study of ancient Greek literature and the Greek New Testament. Eventually, just as nineteenth-century reforms of university curricula were beginning to erode this ascendancy, developments in textual criticism and linguistic analysis, and new ways of studying ancient societies, especially archaeology, led to renewed enthusiasm for the Classics. This collection offers works of criticism, interpretation and synthesis by the outstanding scholars of the nineteenth century. A Short History of Greek Mathematics James Gow’s Short History of Greek Mathematics (1884) provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II concern Greek arithmetic, including the origin of alphabetic numerals and the nomenclature for operations; Part III constitutes a complete history of Greek geometry, from its earliest precursors in Egypt and Babylon through to the innovations of the Ionic, Sophistic, and Academic schools and their followers. -
The Project Gutenberg Ebook #31061: a History of Mathematics
The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A History of Mathematics Author: Florian Cajori Release Date: January 24, 2010 [EBook #31061] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS *** Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins and the Online Distributed Proofreading Team at http://www.pgdp.net transcriber's note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for screen viewing, but may be easily formatted for printing. Please consult the preamble of the LATEX source file for instructions. A HISTORY OF MATHEMATICS A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."|J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.|Berwick & Smith. -
An Archimedean Proposition Presented by the Brothers Banū Mūsā and Recovered in the Kitāb Al-Istikmāl (Eleventh Century)
An Archimedean Proposition Presented by the Brothers Banū Mūsā and Recovered in the Kitāb al-Istikmāl (eleventh century) Lluís Pascual Abstract: Archimedes developed a geometrical method to obtain an approximation to the value of π , that appears in the encyclopaedic work of the prince al-Mu’taman ibn Hūd in the eleventh century. This article gives the edition, translation and transcription of this Archimedean proposition in his work, together with some comments about how other medieval authors dealt with the same proposition. Keywords: al-Mu’taman, Archimedes, al-Istikmāl , Banū Mūsā, Gerard of Cremona, al-Ṭūsī, the value of π, geometrical. Appearance of the proposition in Saragossa during the eleventh century There was a great burst of scientific activity in Saragossa during the eleventh century, especially in the fields of mathematics and philosophy. In mathematics, the most notable work produced in eleventh-century Saragossa was the « Kitāb al-Istikmāl », or « The book of perfection ». This encyclopaedic work was written by the prince al-Mu’taman ibn Hūd, who reigned from 1081 until the date of his death in 1085. His reign was very short, but during the very long reign of his father (al-Muqtadir ibn Hūd, king from 1046 to 1081) crown prince al-Mu’taman devoted himself to the study of mathematics, on subjects originated by Euclid and by others, and started the composition of the « Kitāb al-Istikmāl ». As Hogendijk has noted (Hogendijk, 1991) and (Hogendijk, 1995), al- Mu’taman sometimes transcribes the propositions as if he had copied them from Suhayl 14 (2015), pp. 115-143 116 Lluis Pascual their Euclidian origin, but more often he takes the initiative himself: he simplifies demonstrations, he merges symmetrical propositions into a single one, and he often changes the flow of the demonstration. -
A Concise History of the Philosophy of Mathematics
A Thumbnail History of the Philosophy of Mathematics "It is beyond a doubt that all our knowledge begins with experience." - Imannuel Kant ( 1724 – 1804 ) ( However naïve realism is no substitute for truth [1] ) [1] " ... concepts have reference to sensible experience, but they are never, in a logical sense, deducible from them. For this reason I have never been able to comprehend the problem of the á priori as posed by Kant", from "The Problem of Space, Ether, and the Field in Physics" ( "Das Raum-, Äether- und Feld-Problem der Physik." ), by Albert Einstein, 1934 - source: "Beyond Geometry: Classic Papers from Riemann to Einstein", Dover Publications, by Peter Pesic, St. John's College, Sante Fe, New Mexico Mathematics does not have a universally accepted definition during any period of its development throughout the history of human thought. However for the last 2,500 years, beginning first with the pre - Hellenic Egyptians and Babylonians, mathematics encompasses possible deductive relationships concerned solely with logical truths derived by accepted philosophic methods of logic which the classical Greek thinkers of antiquity pioneered. Although it is normally associated with formulaic algorithms ( i.e., mechanical methods ), mathematics somehow arises in the human mind by the correspondence of observation and inductive experiential thinking together with its practical predictive powers in interpreting future as well as "seemingly" ephemeral phenomena. Why all of this is true in human progress, no one can answer faithfully. In other words, human experiences and intuitive thinking first suggest to the human mind the abstract symbols for which the economy of human thinking mathematics is well known; but it is those parts of mathematics most disconnected from observation and experience and therefore relying almost wholly upon its internal, self - consistent, deductive logics giving mathematics an independent reified, almost ontological, reality, that mathematics most powerfully interprets the ultimate hidden mysteries of nature. -
Netz R. the Transformation of Mathematics in the Early
The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations The transformation of mathematics from ancient Greece to the medieval Arab- speaking world is here approached by focusing on a single problem proposed by Archimedes and the many solutions offered. In this trajectory Reviel Netz follows the change in the task from solving a geometrical problem to its expression as an equation, still formulated geometrically, and then on to an algebraic problem, now handled by procedures that are more like rules of manipulation. From a practice of mathematics based on the localized solution (and grounded in the polemical practices of early Greek science) we see a transition to a practice of mathematics based on the systematic approach (and grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). With three chapters ranging chronologically from Hellenistic mathematics, through Late Antiquity, to the medieval world, Reviel Netz offers a radically new interpretation of the historical journey of pre-modern mathematics. reviel netz is Associate Professor in the Department of Classics at Stanford University. He has published widely in the field of Greek mathematics: The Shap- ing of Deduction in Greek Mathematics: A Study in Cognitive History (1999)won the Runciman Prize for 2000, and he is currently working on a complete English translation of and commentary on the works of Archimedes, the first volume of which was published in 2004. He has also written a volume of Hebrew poetry and a historical study of barbed wire. cambridge classical studies General editors r. l. hunter, r. g. osborne, m. -
The Modular Design of Early Byzantine Cisterns and Reservoirs
1 The Modular Design of Early Byzantine Cisterns and Reservoirs Charles Anthony Stewart In the city of Constantia (ancient Salamis), Cyprus, stands a grand Byzantine reservoir known as the Loutron (fig. 1). Its final renovation in the early seventh century resulted in a massive rectangular structure supported by 36 piers which formed 52 bays— in terms of volume, it would be the largest vaulted structure ever constructed on the island. It was clearly intended to be a showpiece; built conspicuously above ground to serve as a pendant, facing across the forum towards the famous Temple of Zeus (which had been converted to a church) (fig. 2). As such, the Loutron would have resembled the well-known nymphaea of Anatolia. In investigating the structure, wider questions have arisen regarding the development of Byzantine cisterns and reservoirs in comparison to earlier Roman designs. In Italy and North Africa, the Romans achieved a high level of sophistication in their monumental waterworks. The majority of Roman cisterns were covered with vast continuous barrel-vaults, such as the Piscina Mirabilis (Bacoli) and Malaga (Carthage).1 By contrast, beginning in the fifth century, the eastern Roman provinces broke from this tradition by incorporating domical or groin-vaults in their cisterns. I suggest in this chapter that these vaulted bays were modular units that facilitated volume calculation during the design process. Recent surveys of Byzantine and Umayyad cisterns and reservoirs in the eastern Mediterranean (Egypt, Turkey, and Palestine), indicate that the driving motivation for this redesign was a need for greater stability—most likely because of seismic activity. -
GREEK MATHEMATICS Nathan Sidoli
18 GREEK MATHEMATICS Nathan Sidoli This chapter discusses the tradition of theoretical mathematics that formed a part of Greek literary culture. This was not the only kind of mathematics that existed in the ancient Greek world. There were also traditions of elementary school mathematics, and the subscientific traditions of mathe- matics that were handed down by various professionals who used mathe- matics in their work, such as tradesmen, builders, accountants, and 1 astrologers. In fact, in the ancient Mediterranean, these subliterary tradi- tions almost certainly formed the vast majority of all the mathematics studied and practiced, while literary, theoretical mathematics was practiced 2 by only a privileged few. Nevertheless, the elite, literary status of the theoretical mathematicians, along with the brilliance of their work, ensured that much of their project was preserved for posterity, while the predomi- nantly oral, subscientific tradition survives only in scattered, material frag- ments and a few collections passed down through the manuscript tradition, attributed, probably erroneously, to Heron (ca. mid-first to third cen- tury ce). In the classical period, when the forms of literary mathematical texts were being established, elite, theoretical mathematicians appear to have done as much as they could to separate themselves from professionals who used mathematics, just as they strove to distinguish themselves from other elites, such as sophists and philosophers who did not engage in mathematical activity. Theoretical mathematics was originally not a professional, institu- tionalized activity. During the Hellenistic period, when this, now more 1 The term “subscientific” is due to J. Høyrup. See, for example, J. Høyrup, “Sub-scientific Mathematics: Observations on a Pre-Modern Phenomena,” History of Science 27 (1990), 63–87. -
Reflections on the Antikythera Mechanism Inscriptions
ARTICLE IN PRESS Available online at www.sciencedirect.com Advances in Space Research xxx (2009) xxx–xxx www.elsevier.com/locate/asr Reflections on the antikythera mechanism inscriptions Maria K. Papathanassiou Faculty of Mathematics, National and Kapodistrian University of Athens, Athens, Greece Received 10 January 2008; received in revised form 30 April 2008; accepted 2 May 2008 Abstract A close look at the fragmentary inscriptions of the Antikythera Mechanism published by Freeth et al. [Freeth, T., Bitsakis, Y., Moussas, X., Seiradakis, J.H., Tselikas, A., Magkou, E., Zafeiropoulou, M., Hadland, R., Bate, D., Ramsey, A., Allen, M., Crawley, A., Hockley, P., Malzbender, T., Gelb, D., Ambrisco, W., Edmunds, M.G. Decoding the Antikythera mechanism: investigation of an ancient astronomical calculator. Nature 444 (7119), 587–591, 2006] reveals some elements, which could help to decode its function and use. The Back Door Inscription seems to give a detailed description of some external parts of the instrument and the related instructions for their use. We especially refer to the term «ecliptic» as compared to that in Ars Eudoxi and other papyri and inscriptions. The Back Plate Inscription seems to give instructions for the proper orientation and use of the instrument. The Front Door Inscription refers to the sta- tionary points of planetary motion, but only two planetary names have been read, that of Venus and Mercury, as far as we know. After a study of the works of Alexandrian scholars Ptolemy, Theon, Paulus and Heliodorus regarding the -
Notes on the Second Sophistic in Palestine
^ 20 Notes on the Second Sophistic in Palestine JOSEPH GEIGER The Second Sophistic has got its fair share of attention in the last twenty- five years or so.^ The present paper aims at reporting its impact on a part of the Empire removed from the centres of the movement. Furthermore, it is hoped that incidentally this will shed some light on a question of important cultural implications not normally associated with the Second Sophistic. I The travels of the sophists are a well-known subject, effortlessly noticed even by the most inattentive reader of Philostratus. While much of this action took place in the central domains of the movement, it is only to be expected that the peripheral lands had their due share. In fact, we possess some evidence for visits of important sophists in Palestine. Most notable is the visit of Aelius Aristides to Palestine. It is cocrectly connected with his sojourn in Egypt 141-42, on his way there or back: I heard it myself at Scythopolis, the city of Palaestina-Syria, that in the place which brings forth the famous dates and the juice [i.e. of balsam], there is a lake which indicates whenever the Nile rises. That was said by my hosts, who maintained that it happened during the increase of the lake.3 Unfortunately, we do not know who Aelius Aristides' hosts were, nor do we possess any further information regarding their conversations; even less are we able to tell whether the great orator's visit passed without some display of his art. However, we get a glimpse of the sort of people Aehus Aristides' hosts may have been from an accidental detail regarding a contemporary * An earlier, and very different version of this paper was delivered at the 21st Annual Meeting of the Israel Society for Qassical Studies, Jerusalem, 29 May 1992.