scholarly journals The myth of the three crises in foundations of mathematics Part 1

2021 ◽  
Vol 26 (2) ◽  
pp. 64-77
Author(s):  
V.A. Shaposhnikov ◽  
Keyword(s):  
18Th Century ◽  
Philosophy Of Mathematics ◽  
History Of Mathematics ◽  
General Question ◽  
Foundations Of Mathematics ◽  
Historical Evidence ◽  
Zeno's Paradoxes ◽  
History Of ◽  
Greek Mathematics ◽  
Modern Myth

The story of “the three crises in foundations of mathematics” is widely popular in Russian publications on the philosophy of mathematics. This paper aims at evaluating this story against the background of the contemporary scholarship in the history of mathematics. The conclusion is that it should be considered as a specimen of modern myth-making activity brought to the fore by an unconscious tendency to model the whole history of mathematics on the pattern of the foundational crisis of the first decades of the 20th century. What is more, the consideration of the specific role and character of the foundations in both early Greek mathematics and 18th-century mathematics gives an occasion to raise a more general question regarding the true meaning of the historicity of mathematics. The first part of this paper deals with the point whether there was a foundational crisis in pre-Euclidean Greek mathematics caused by the discovery of incommensurable magnitudes and Zeno’s paradoxes. The result is negative: we have no direct historical evidence of such a crisis; as for secondary considerations, they also mainly count against it. The idea of the first crisis in foundations of mathematics has emerged as a result of the unjustified transference of the modern grasp of foundational issues and the modern “mentalité de crise” to the ancient past.

Scientific novelties implemented into teaching mathematics in secondary schools on the Polish territories in the 19th century. The case of descriptive geometry

2020 ◽  
pp. 205-218
Author(s):  
Karolina Karpińska
Keyword(s):  
Mathematics Education ◽  
19Th Century ◽  
18Th Century ◽  
History Of Mathematics ◽  
Descriptive Geometry ◽  
Teaching Mathematics ◽  
Education History ◽  
Secondary School Education ◽  
History Of ◽  
The 19Th Century

This article is dedicated to discussing the implementation of the descriptive geometry, i.e. the scientific novelty from the end of the 18th century, in secondary school education on the Polish territories in the 19th century. At that time, Polish lands were under the occupation of three empires: Prussia, Austria, and Russia. Over the time, the policy of the partition empires toward the Poles was changing in intensity. As a consequence, in the 19th century, there were schools on the Polish territories with Polish, Prussian, Austrian and Russian curricula and relevant lecture languages. The article analyses the implementation of descriptive geometry into teaching mathematics in schools located in all three partitions. Keywords: descriptive geometry, history of mathematics education, history of mathematics

On the ‘List of Thalassocracies’ in Eusebius

1907 ◽  
Vol 27 ◽  
pp. 75-89 ◽  
Author(s):  
J. K. Fotheringham
Keyword(s):  
Textual Criticism ◽  
General Question ◽  
Original Text ◽  
Historical Evidence ◽  
Greek History ◽  
History Of ◽  
The Subject

All students of Eusebius will feel grateful to Mr. J. L. Myres for his attempt in the last volume of this Journal to discover the original text underlying the list of thalassocracies, preserved in the Chronica of Eusebius, and to reassert its value as historical evidence. The problem that Mr. Myres has set himself is rendered difficult not only by the general obscurity in which the sources of early Greek history are shrouded and by our almost total ignorance of the history of many of the thalassocrats during the period assigned to them in the list, but by the complicated questions of textual criticism which surround the Chronica, and which this problem raises in a particularly aggravated form. While not venturing to follow Mr. Myres through the wealth of historical learning, which he has brought to bear upon the subject, I have thought that I might be able to contribute something by bringing my own studies in the Chronica into relation to the general question.

scholarly journals Um Mapeamento de Estudos Históricos da Matemática nos Periódicos Nacionais de Qualis A1, A2 e B1 em Ensino no Período de 2013 a 2018

2021 ◽  
Vol 14 (1) ◽  
pp. 110-118
Author(s):  
Eliane Siviero da Silva Dalbon ◽  
Dulcyene Maria Ribeiro
Keyword(s):  
Mathematics Education ◽  
Philosophy Of Mathematics ◽  
History Of Mathematics ◽  
Mathematical Education ◽  
Education History ◽  
History Of Mathematics Education ◽  
Mathematics History ◽  
History Of ◽  
Em 12 ◽  
Education Field

ResumoO trabalho tem por objetivo apresentar um mapeamento dos artigos envolvendo estudos históricos da Matemática publicados nos periódicos nacionais de qualis A1, A2 e B1 em ensino, no período de 2013 a 2018. Os dados foram coletados a partir da leitura dos títulos, resumos e palavras-chave dos artigos, que foram classificados entre os campos temáticos: História da Matemática, História da Educação Matemática e História na Educação Matemática. De um total de 13 revistas com 212 edições e 2516 publicações, foram categorizados 255 artigos, sendo 91 no campo História da Matemática, 123 no campo História da Educação Matemática e 41 no campo História na Educação Matemática. Dentre os periódicos analisados, a Revista Brasileira de História da Matemática (RBHM), que tem como foco a publicação de trabalhos acadêmicos originais sobre História da Matemática em geral e sobre suas relações com outros campos, como a Educação Matemática e a Filosofia da Matemática, foi o periódico com maior número de artigos identificados na análise, 72 ao todo. Com relação a quantidade de trabalhos classificados em História da Matemática, apesar de serem computados 91 artigos, desses, 59 se encontram na Revista Brasileira de História da Matemática (RBHM), restando 32 artigos identificados em 12 periódicos. Todos os outros periódicos tiveram um volume maior de artigos classificados no campo História da Educação Matemática, 113 ao todo, incluindo duas edições temáticas em dois periódicos. O campo História na Educação Matemática, foi o que teve menos trabalhos classificados, 41 ao todo. Os dados refletem uma mudança no panorama das produções de estudos históricos da Matemática, que inicialmente eram voltados principalmente para a História da Matemática e que, no decorrer do tempo passou-se a ter o crescimento de um movimento em torno da História da Educação Matemática. Palavras-chave: Publicações em Periódicos. História da Matemática. História da Educação Matemática. História na Educação Matemática. AbstractThe work aims to present a mapping of articles involving historical studies of Mathematics published in national journals of qualis A1, A2 and B1 in teaching, from 2013 to 2018. Data were collected from the reading of titles, abstracts and words -key of the articles, which were classified among the thematic fields: History of Mathematics, History of Mathematics Education and History in Mathematics Education. From a total of 13 magazines with 212 editions and 2516 publications, 255 articles were categorized, 91 in the History of Mathematics field, 123 in the History of Mathematics Education field and 41 in the History in Mathematics Education field. Among the journals analyzed, the Revista Brasileira de História da Matemática (RBHM), which focuses on the publication of original academic works on the History of Mathematics in general and on their relations with other fields, such as Mathematics Education and the Philosophy of Mathematics, was the journal with the largest number of articles identified in the analysis, 72 in all. Regarding the number of papers classified in the History of Mathematics, although 91 articles are computed, of these, 59 are in the Revista Brasileira de História da Matemática (RBHM), leaving 32 articles identified in 12 journals. All other journals had a higher volume of articles classified in the History of Mathematical Education field, 113 in all, including two thematic editions in two journals. The History in Mathematics Education field had the least classified jobs, 41 in all. The data reflect a change in the panorama of the production of historical studies of Mathematics, which initially were mainly focused on the History of Mathematics and which, over time, began to have the growth of a movement around the History of Mathematics Education. Keywords: Publications in Journals. History of Mathematics. History of Mathematics Education. History in Mathematics Education.

Visual Thinking in Mathematics

Philosophy ◽  
2019 ◽  
Author(s):  
Jessica Carter
Keyword(s):  
20Th Century ◽  
Euclidean Geometry ◽  
18Th Century ◽  
History Of Mathematics ◽  
Mathematical Practice ◽  
Visual Representations ◽  
Visual Thinking ◽  
General Acceptance ◽  
History Of ◽  
Euclid’S Elements

In contemporary philosophy, “visual thinking in mathematics” refers to studies of the kinds and roles of visual representations in mathematics. Visual representations include both external representations (i.e., diagrams) and mental visualization. Currently, three main areas and questions are being investigated. The first concerns the roles of diagrams, or the diagram-based reasoning, found in Euclid’s Elements. Second is the epistemic role of diagrams: the question of whether reasoning based on diagrams can be rigorous. This debate includes the question of whether beliefs based on visual input can be justified, and whether visual perception may lead to mathematical knowledge. The third observes that diagrams abound in (contemporary) mathematical practice, and so tries to understand the role they play, going beyond the traditional debates on the legitimacy of using diagrams in mathematical proofs. Looking at the history of mathematics, one will find that it is only recently that diagrammatic proofs have become discredited. For about 2,000 years, Euclid’s Elements was conceived as the paradigm of (mathematical) rigorous reasoning, and so until the 18th century, Euclidean geometry served as the foundation of many areas of mathematics. One includes the early history of analysis, where the study of curves draws on results from (Euclidean) geometry. During the 18th and 19th centuries, however, diagrams gradually disappear from mathematical texts, and around 1900 one finds the famous statements of Pasch and Hilbert claiming that proofs must not rely on figures. The development of formal logic during the 20th century further contributed to a general acceptance of a view that the only value of figures, or diagrams, is heuristic, and that they have no place in mathematical rigorous proofs. A proof, according to this view, consists of a discrete sequence of sentences and is a symbolic object. In the latter half of the 20th century, philosophers, sensitive to the practice of mathematics, started to object to this view, leading to the emergence of the study of visual thinking in mathematics.

scholarly journals Facets of the cultural history of mathematics

2000 ◽  
Vol 8 (4) ◽  
pp. 487-497
Author(s):  
Hansjörg Geiges
Keyword(s):  
Cultural History ◽  
18Th Century ◽  
History Of Mathematics ◽  
Western Civilization ◽  
Greek Philosophy ◽  
Gothic Architecture ◽  
History Of ◽  
General Culture

This article highlights the position of mathematics within general culture at various stages of the development of Western civilization. Special emphasis is given to the role of mathematics in Greek philosophy, the influence of mathematics on Gothic architecture and the place of mathematics in 17th and 18th century society. Literary quotations illustrate the shifts in the view of mathematics in society.

ON THE FIRST ARTICLE FROM THE RUSSIAN HISTORY OF MATHEMATICS

2020 ◽  
pp. 86-106
Author(s):  
Galina I. Sinkevich ◽  
◽  
Olga V. Solov'eva ◽  
Keyword(s):  
18Th Century ◽  
History Of Mathematics ◽  
Popular Science ◽  
Russian History ◽  
Russian Culture ◽  
Old Russian ◽  
Russian State ◽  
History Of ◽  
History Of Sciences ◽  
Academy Of Sciences

The article is a publication of the first Russian printed work on the Russian history of mathematics. It is dedicated to the ancient Russian numeral systems and was published anonymously in 1787 in the “New monthly works” of St. Petersburg Academy of Sciences. The author tells about the Old Russian numeral system, Russian calendar and commercial account. In the popular science editions of the 18th century Imperial St. Petersburg Academy of Sciences there were many publications on the history of sciences, arts, crafts, the history of discoveries and inventions in other countries. At the same time, there was a clear lack of publications on the history of Russian culture. Russian scientists were dissatisfied with the interpretation of Russian history presented by the historiographer of the Russian state, an academician G. F. Müller, as well as with descriptions of Russia and its history by other foreign authors. In the Catherine’s time, many articles appeared, sometimes anonymous, defending the originality and ancientry of Russian culture. To analyze the data on the authorship of the work, the popular scientific editions of Academy in the 18th century and are described, information about their authors is presented, hypotheses are expressed, and the terminology of the article and the names mentioned in it are commented.

Black Thoughts Matter

2017 ◽  
Vol 48 (3) ◽  
pp. 256-278 ◽  
Author(s):  
C. K. Raju
Keyword(s):  
18Th Century ◽  
Philosophy Of Mathematics ◽  
Recent Attempt ◽  
Colonial Education ◽  
Faith Based ◽  
Deductive Proof ◽  
Late 18Th Century ◽  
History Of ◽  
Open Discussion ◽  
Set Up

In postapartheid South Africa, Whites dominate academics and Black students are agitating for decolonization. Decolonization requires contesting the false history of science used to set up colonial education essential to colonization—the same false history that was used to morally justify racism, by asserting the noncreativity of Blacks. The “evidence” for this false history is often faith-based, so White-controlled academics disallows any open discussion. Furthermore, this false history is sustained by another trick: a little known interplay between history and philosophy. Thus, geometry has been credited to Greeks on the ground that they had a “superior” philosophy of mathematics as deductive proof. In fact, the “Pythagorean” proposition had no valid deductive proof before the 20th century. Furthermore, this claim of philosophical “superiority” was never academically debated, and is not allowed to be. A recent attempt to explain the falsehood of this claim, along with the counterevidence against purported Greek achievements in math, was publicly censored. In fact, in Egypt, Iraq, and India, there was a different and immensely superior understanding of the “Pythagorean” proposition, which superior way was not grasped in the West, resulting in its persistent navigational problems until the late 18th century.

Land use and settlement history of the southern Inner Hebrides

1983 ◽  
Vol 83 ◽  
pp. 549-566
Author(s):  
Margaret C. Storrie
Keyword(s):  
Land Use ◽  
18Th Century ◽  
Historical Evidence ◽  
Medieval Period ◽  
Present Stage ◽  
Late Medieval Period ◽  
History Of ◽  
19Th And 20Th Century ◽  
River Valleys

SynopsisThe earliest evidence of prehistoric activity in Scotland comes from Jura. Most of Jura has been rather inimical to settlement, in comparison with other islands of the southern Inner Hebrides—Colonsay and Oronsay, Gigha and Cara, and Islay—all endowed with deposits more useful to man than Jura. Land use and settlement in these islands spread from the coasts into and up the river valleys until the first half of the19th century, after which they retreated. There have, however, been several waves of retreat and readvance.This paper assesses the present stage of research in the chronicle of these changes in the southern islands, pointing to some of the unanswered questions. The archaeological, onomastic and historical evidence is briefly examined against a slowly changing environment that has been relatively favourable, in a Hebridean context. Areal expansion, upward extension and intensified use of the land increased in momentum, with interruptions, after the late medieval period. The time of greatest change began just after the middle of the 18th century and lasted for another century.Elements of this change and its effects on settlement are discussed, using records and maps from private and official archives, topographic and other writings, and population and agrarian censuses. The important role of landlords, their agents and subsequent planners in instituting, and even containing, change is briefly assessed. In the southern Inner Hebrides an unusual, non-crofting landscape resulted: an estate, farming and sporting landscape, with, in the case of Islay, over a dozen industrial and service villages.The characteristic ‘Highland Problem’ of landscape and land use, increasingly ill-suited to the needs of later 19th and 20th century economy and society, has been less evident in these islands than in others in the Hebrides, although they now show disturbing trends. Present land use and settlement are briefly examined.

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