The Experts below are selected from a list of 5112 Experts worldwide ranked by ideXlab platform
Joseph W Dauben - One of the best experts on this subject based on the ideXlab platform.
-
ancient chinese Mathematics the jiu zhang suan shu vs euclid s elements aspects of proof and the linguistic limits of knowledge
International Journal of Engineering Science, 1998Co-Authors: Joseph W DaubenAbstract:Abstract The following is a preliminary and relatively brief, exploratory discussion of the nature of early Chinese Mathematics, particularly geometry, considered largely in terms of one specific example: the Download : Download full-size image (Gou-Gu) Theorem. In addition to drawing some fundamental comparisons with Western traditions, particularly with Greek Mathematics, some general observations are also made concerning the character and development of early Chinese mathematical thought. Above all, why did Chinese Mathematics develop as it did, as far as it did, but never in the abstract, axiomatic way that it did in Greece? Many scholars have suggested that answers to these kinds of questions are to be found in social and cultural factors in China. Some favor the sociological approach, emphasizing for example that Chinese mathematicians were by nature primarily concerned with practical problems and their solutions, and, therefore, had no interest in developing a highly theoretical Mathematics. Others have stressed philosophical factors, taking another widely-held view that Confucianism placed no value on theoretical knowledge, which, in turn, worked against the development of abstract Mathematics of the Greek sort. While both of these views contain elements of truth, and certainly play a role in understanding why the Chinese did not develop a more abstract, deductive sort of Mathematics along Greek lines, a different approach is offered here. To the extent that knowledge is transmitted and recorded in language, oral and written, logical and linguistic factors cannot help but have played a part in accounting for how the Chinese were able to conceptualize—and think about—Mathematics.
David H Fowler - One of the best experts on this subject based on the ideXlab platform.
-
logistic and fractions in early Greek Mathematics a new interpretation
Boston studies in the philosophy of science, 2004Co-Authors: David H FowlerAbstract:Since the popularisation of techniques of decimal fractions at the end of the sixteenth century, western Mathematics has drawn inspiration from the fluent manipulations of more and more general, more and more abstract, kinds of numbers.1 I shall refer to Mathematics that uses, like this, some system of numbers sufficiently general to include fractional quantities and their arithmetic as ‘arithmetised Mathematics’. For example, Mesopotamian Mathematics and astronomy is arithmetised; but we have no unambiguous evidence of the influence of this Mesopotamian Mathematics on Greek Mathematics before the second century BC; and thereafter, in Greek texts, Mesopotamian sexagesimal numbers are found only in astronomical contexts. I am exploring a novel interpretation of early Greek Mathematics in which Mesopotamian influence on Greek Mathematics is minimal, even non-existent, and will not consider this sexagesimal evidence further here.
Reviel Netz - One of the best experts on this subject based on the ideXlab platform.
-
ludic proof Greek Mathematics and the alexandrian aesthetic
2009Co-Authors: Reviel NetzAbstract:This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor Netz argues that Hellenistic mathematical writings adopt a narrative strategy based on surprise, a compositional form based on a mosaic of apparently unrelated elements, and a carnivalesque profusion of detail. He further investigates how such stylistic preferences derive from, and throw light on, the style of Hellenistic poetry. This important book will be welcomed by all scholars of Hellenistic civilization as well as historians of ancient science and Western Mathematics.
-
imagination and layered ontology in Greek Mathematics
Configurations, 2009Co-Authors: Reviel NetzAbstract:This essay is a study in the routine use of imagination in Greek mathematical writings. By "routine" is meant both that this use is indeed very common, and that it is ultimately mundane. No flights of fancy, no poetical-like imaginative licenses are at stake. The issue rather is the systematic use made of the ability to imagine a virtual presence, and to refer to this virtual presence as if it were on equal footing with the real. This process is not merely routine in Greek Mathematics: it may well be considered one of its chief characteristics. In this essay, I describe some features of this practice in detail, and then briefly offer some interpretative comments on the history and philosophy of this practice. The emphasis, however, is on the description, and I concentrate mainly on one key element—the use of the Greek verb noein . Thus the structure of the essay is as follows: part 1 is an analysis of noein in Greek mathematical writings; part 2 is a less-detailed description of other practices of Greek Mathematics that involve "imagination" or, in general, a "layered" reality; and part 3 is a tentative interpretation.
-
the limits of text in Greek Mathematics
Boston studies in the philosophy of science, 2004Co-Authors: Reviel NetzAbstract:This article argues for a limited role of the text in Greek Mathematics, in two senses of “text”: the verbal as opposed to the visual; and the literate as opposed to the “oral” (understood in a wide sense). The Greek mathematical argument proceeds not within the confines of the verbal alone, but essentially relies upon diagrams. On the other hand, it does not use other specific techniques, such as those of the modern cross-reference, relying instead upon verbal echoes. The two, taken together, suggest a model of scientific writing radically different from what we associate with our own Mathematics. In methodological terms, the article surveys its evidence in detail, and makes comments concerning the methodology of studying ancient texts through the evidence of those texts alone.
-
the shaping of deduction in Greek Mathematics a study in cognitive history
1999Co-Authors: Reviel NetzAbstract:Introduction: a specimen of Greek Mathematics 1. The lettered diagram 2. The pragmatics of letters 3. The mathematical lexicon 4. Formulae 5. The shaping of necessity 6. The shaping of generality 7. The historical setting Appendix: the main Greek mathematicians cited in the book.
Neuwirth Stefan - One of the best experts on this subject based on the ideXlab platform.
-
Enqu\^ete sur les modes d'existence des \^etres math\'ematiques (version augment\'ee) [An inquiry into the modes of existence of mathematical beings (expanded version)]
2020Co-Authors: Wallet Guy, Neuwirth StefanAbstract:This essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world. After a description of the problem, the work of Reviel Netz on the emergence of Greek Mathematics, and of Charles Sanders Peirce on the diagrammatic dimension of mathematical practice are presented, as well as their impact on our essay. Its central part is the development of an empirical conception of Mathematics that plays a central r\^ole in the sequel. Our analysis is based on the notion of experience according to William James; it is also inspired by certain aspects of Per Martin-L\"of's philosophy. It provides a way of thinking the firm certainty with which proofs endow theorems, while invalidating the interpretation of this certainty as the mark of a direct access to an absolute and transcendental truth. The sequel of our essay builds on this analysis for defining a sort of quasi-mode of existence appropriate for mathematical beings that respects the principal features of modes of existence according to the latourian ontology. In the conclusion, the way this quasi-mode might be integrated into this ontology is discussed, in particular with respect to the mode of reference that prevails in many other sciences.Comment: in French; the plain version has been published in Philosophia Scienti{\ae}, see http://hal.archives-ouvertes.fr/hal-0194307
-
Enquête sur les modes d'existence des êtres mathématiques
'OpenEdition', 2019Co-Authors: Wallet Guy, Neuwirth StefanAbstract:International audienceThis essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world. An answer to this question is put forward with the aid of the work of Reviel Netz on the emergence of Greek Mathematics, and of Charles Sanders Peirce on the diagrammatic dimension of mathematical practice, in the framework of an empiric conception of Mathematics based on the notion of experience according to William James, and inspired by certain aspects of Per Martin-Löf's philosophy. It provides a way of describing the firm certainty with which proofs endow theorems, while invalidating the interpretation of this certainty as the mark of a direct access to an absolute and transcendental truth.L'objet de cet essai est l'accueil des entités mathématiques dans l'architecture des modes d'existence proposée par Bruno Latour dans le cadre de son ontologie pluraliste du monde moderne. Les travaux de Reviel Netz sur l'émergence des mathématiques grecques et de Charles Sanders Peirce sur la dimension diagrammatique de l'activité mathématique sont employés pour proposer une réponse dans le cadre d'une conception empirique des mathématiques basée sur la notion d'expérience chère à William James et inspirée par certains aspects de la philosophie de Per Martin-Löf. Cette approche permet de penser la solide certitude dont la démonstration dote les résultats mathématiques tout en invalidant son interprétation comme la marque d'un accès direct à une vérité absolue et transcendante
Michael N Fried - One of the best experts on this subject based on the ideXlab platform.
-
similarity and equality in Greek Mathematics semiotics history of Mathematics and Mathematics education
for the learning of mathematics, 2009Co-Authors: Michael N FriedAbstract:In this article I want to say a few words about equality andsimilarity in Greek Mathematics. I wish to highlight, amongother things, how the formula “equal and similar” reflectsthe distinct character of “equal” and “similar” as signs inGreek mathematical discourse. Beyond this, however – and,perhaps, chiefly – I want to claim that a discussion of thistype is relevant not only to history of Mathematics but toMathematics education as well. But why should its relevance be questioned in the firstplace? Obviously, the notions of similarity and equality, orrather congruence, remain central in every geometry cur-riculum. History, it would seem, should only heighten whatit is already being covered in the classroom. The questionarises because of
