Introduction: The History of Modern Mathematics – Writing and Rewriting

2004 ◽  
Vol 17 (1-2) ◽  
pp. 1-21 ◽  
Author(s):  
Leo Corry
Keyword(s):  
Nineteenth Century ◽  
History Of Mathematics ◽  
Present Issue ◽  
Tel Aviv ◽  
History Of ◽  
New Ideas ◽  
Ancient Mathematics ◽  
Modern Mathematics ◽  
September Issue

The present issue of Science in Context comprises a collection of articles dealing with various, specific aspects of the history of mathematics during the last third of the nineteenth century and the first half of the twentieth. Like the September issue of 2003 of this journal (Vol. 16, no. 3), which was devoted to the history of ancient mathematics, this collection originated in the aftermath of a meeting held in Tel-Aviv and Jerusalem in May 2001, under the title: “History of Mathematics in the Last 25 Years: New Departures, New Questions, New Ideas.” Taken together, these two topical issues are meant as a token of appreciation for the work of Sabetai Unguru and his achievements in the history of mathematics.

Reviews and Evaluations

1968 ◽  
Vol 61 (2) ◽  
pp. 190-194
Author(s):  
Harold Tinnappel
Keyword(s):  
History Of Mathematics ◽  
Limited Success ◽  
Mathematical Thought ◽  
History Of ◽  
New Ideas ◽  
Working Out ◽  
Modern Mathematics

A translation of the first venture into the history of mathematics by a professor of Greek at Lausanne University, this book seeks with only very limited success “to explain the birth of modern mathematics by describing the progress of mathematical thought at the time of Plato” and to convince the reader that “twenty-five years of thought and discussion in Plato's Academy sufficed to delimit the field of mathematics in all its breadth [and] saw the working-out of new ideas on which the whole edifice of modern mathematics rests.”

scholarly journals A short remark on Gödel incompleteness theorem and its self-referential paradox from Neutrosophic Logic perspective

2019 ◽  
pp. 21-26
Author(s):  
V. Christianto ◽  
◽  
◽  
F. Smarandache
Keyword(s):  
20Th Century ◽  
History Of Mathematics ◽  
The Self ◽  
Incompleteness Theorem ◽  
Aristotelian Logic ◽  
Binary Logic ◽  
Neutrosophic Logic ◽  
History Of ◽  
Incompleteness Theorems ◽  
Modern Mathematics

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective. Motivation of this paper: These authors are motivated to re-describe the self-referential paradox inherent in Godel incompleteness theorem. Contribution: This paper will show how Neutrosophic Logic offers a unique perspective and solution to Godel incompleteness theorem.

PER UN ARCHIVIO DELLA CORRISPONDENZA DEGLI SCIENZIATI ITALIANI

Nuncius ◽  
2000 ◽  
Vol 15 (2) ◽  
pp. 681-719
Author(s):  
LUCIANO CARBONE ◽  
FRANCO PALLADINO ◽  
ROMANO GATTO
Keyword(s):  
Nineteenth Century ◽  
Twentieth Century ◽  
Historical Development ◽  
History Of Mathematics ◽  
Mathematical Research ◽  
Conic Sections ◽  
Kingdom Of Naples ◽  
History Of ◽  
Mathematical Sciences ◽  
The University

Abstracttitle SUMMARY /title Federico Amodeo (1859-1946) was a mathematician and a historian of the mathematical sciences. As a mathematician he was "libero docente" at the University of Naples. His interests extended from projective to algebric geometry and his mathematical research was carried out for the most part from the mid-1880s until the end of the nineteenth century. As a historian he was active from the first years of the twentieth century until his death. In this capacity he was interested in mathematics, mathematicians and institutions in the Kingdom of Naples (later the Kingdom of the Two Sicilies, from 1815), and also in the historical development of analytical and projective geometry and the history of conic sections. He held the chair in History of Mathematics in the University of Naples from 1905 until 1910, the year in which the chair was suppressed. Nonetheless he continued to teach this subject as a "libero docente" until 1923. Here we present the list of more than 1.300 writings, constituting his Correspondence, amongst which the letters of Castelnuovo, Pascal, Peano, Segre and Achille Sannia are of particular significance. We also present the complete list of his publications, reconstructed thanks to the consultation of incomplete printed bibliographies and a manuscript list.

scholarly journals The Early History of Glacial Theory in British Geology

1970 ◽  
Vol 9 (55) ◽  
pp. 135-141 ◽  
Author(s):  
Bert Hansen
Keyword(s):  
Nineteenth Century ◽  
Early History ◽  
Ice Age ◽  
Modern Theory ◽  
Charles Lyell ◽  
Glacial Epoch ◽  
Drift Theory ◽  
History Of ◽  
New Ideas

AbstractMuch of the history of British geological thought in the second quarter of the nineteenth century centered on problems which are now explained by reference to the events of the Ice Age. This paper reviews the data and theories then current among British geologists as the background of the British response to Louis Agassiz’s “modern” theory of a glacial epoch. Today, as we read Agassiz’s amazing speculation, our own sympathy for the striking accuracy of his ideas masks from us the difficulty they faced in gaining acceptance. By first examining the context into which the glacial theory was introduced, we can then appreciate the novelty of Agassiz's efforts and understand the long delay in their achieving prominence. The present examination suggests that this delay was due to the unfortunate merger of Agassiz’s new ideas with the older drift theory of Charles Lyell.

Mathematics, Epistemology, Ethics: Robert Musil, the Man Without Qualities

2018 ◽  
pp. 93-125
Author(s):  
Nina Engelhardt
Keyword(s):  
History Of Mathematics ◽  
Analytic Philosophy ◽  
Profound Change ◽  
Robert Musil ◽  
Double Function ◽  
History Of ◽  
Critical Questioning ◽  
Modern Mathematics ◽  
Literary Aesthetic

Chapter 3 argues that mathematics in Musil’s The Man without Qualities not only exemplifies the side of rationality but also encompasses mystical elements and transitional states between these opposites, tracing the identification of a non-rational element in mathematics to the debate between the logicist/formalist and the intuitionist schools. The chapter thus re-examines notions of the rational and non-rational and attempts at their synthesis from the perspective of the history of mathematics. It also demonstrates that, for Musil, mathematics answers to two major instances of modern crisis: the failing of reason and the loss of trust. Paradoxically combining critical questioning of its foundations and confidence in its usefulness, modern mathematics connects the approaches of analytic philosophy and outcome-focused pragmatism. The chapter thus argues that mathematics becomes a model not only of exactitude but also of vagueness and that in this paradoxical double-function it serves to inspire the critical trust needed to adjust epistemology, ethics and aesthetics in a time of profound change. Not least, in its own form The Man without Qualities translates the model of mathematics into literary aesthetic by reflecting simultaneous examination of its conditions and trust in the credit of fiction.

Transcultural Networks and Connectivities: The Circulation of Mathematical Ideas between India and England in the Nineteenth Century

2021 ◽  
pp. 097318492110645
Author(s):  
Dhruv Raina
Keyword(s):  
Nineteenth Century ◽  
Mathematics Teaching ◽  
First Generation ◽  
History Of Mathematics ◽  
East India Company ◽  
Institutional Autonomy ◽  
Mathematical Research ◽  
Mathematical Ideas ◽  
History Of ◽  
And Mathematics

The nineteenth century has been characterised as a period in which mathematics proper acquired a disciplinary and institutional autonomy. This article explores the intertwining of three intersecting worlds of the history of mathematics inasmuch as it engages with historicising the pursuit of novel mathematics, the history of disciplines and, more specifically, that of the British Indological writings on Indian mathematics, and finally, the history of mathematics education in nineteenth century India. But, more importantly, the article is concerned with a class of science and mathematics teaching problems that are taken up by researchers—in other words, science and mathematics teaching problems that lead to scientific and mathematical research. The article argues that over a period of 50 years, a network of scholars crystallised around a discussion on mathematics proper, the history of mathematics and education. This discussion spanned not just nineteenth-century England but India as well, involving scholars from both worlds. This network included Scottish mathematicians, East India Company officials and administrators who went on to constitute the first generation of British Indologists, a group of mathematicians in England referred to as the Analytics, and traditional Indian scholars and mathematics teachers. The focus will be on the concerns and genealogies of investigation that forged this network and sustained it for over half a century.

Useful Objects

2021 ◽  
Author(s):  
Reed Gochberg
Keyword(s):  
Nineteenth Century ◽  
Literary Criticism ◽  
American Culture ◽  
Science And Literature ◽  
Useful Knowledge ◽  
Nineteenth Century America ◽  
Alternative Systems ◽  
Wide Range ◽  
History Of ◽  
New Ideas

Useful Objects: Museums, Science, and Literature in Nineteenth-Century America explores the debates that surrounded the development of American museums during the nineteenth century. Throughout this period, museums included a wide range of objects, from botanical and zoological specimens to antiquarian artifacts and technological models. Intended to promote “useful knowledge,” these collections generated broader discussions about how objects were selected, preserved, and classified. In guidebooks and periodicals, visitors described their experiences within museum galleries and marveled at the objects they encountered. And in fiction, essays, and poems, writers embraced the imaginative possibilities represented by collections and proposed alternative systems of arrangement. These conversations spanned spheres of American culture, raising deeper questions about how objects are valued—and who gets to decide. Combining literary criticism, the history of science, and museum studies, Useful Objects examines the dynamic and often fraught debates that emerged during a crucial period in the history of museums. As museums gradually transformed from encyclopedic cabinets to more specialized public institutions, many writers questioned who would have access to collections and the authority to interpret them. Throughout this period, they reflected on loss and preservation, raised concerns about the place of new ideas, and resisted increasingly fixed categories. These conversations extended beyond individual institutions, shaping broader debates about the scope and purpose of museums in American culture that continue to resonate today.

scholarly journals The Early History of Glacial Theory in British Geology

1970 ◽  
Vol 9 (55) ◽  
pp. 135-141
Author(s):  
Bert Hansen
Keyword(s):  
Nineteenth Century ◽  
Early History ◽  
Ice Age ◽  
Modern Theory ◽  
Charles Lyell ◽  
Glacial Epoch ◽  
Drift Theory ◽  
History Of ◽  
New Ideas

AbstractMuch of the history of British geological thought in the second quarter of the nineteenth century centered on problems which are now explained by reference to the events of the Ice Age. This paper reviews the data and theories then current among British geologists as the background of the British response to Louis Agassiz’s “modern” theory of a glacial epoch. Today, as we read Agassiz’s amazing speculation, our own sympathy for the striking accuracy of his ideas masks from us the difficulty they faced in gaining acceptance. By first examining the context into which the glacial theory was introduced, we can then appreciate the novelty of Agassiz's efforts and understand the long delay in their achieving prominence. The present examination suggests that this delay was due to the unfortunate merger of Agassiz’s new ideas with the older drift theory of Charles Lyell.

scholarly journals Research on HPM Teaching Supported by Hawgent Dynamic Mathematics Software: Take “The Recognition of Circle” as an Example

2021 ◽  
Vol 5 (8) ◽  
pp. 148-154
Author(s):  
Linfeng Han ◽  
Qian Tao
Keyword(s):  
Mathematics Education ◽  
Mathematical Knowledge ◽  
History Of Mathematics ◽  
Educational Value ◽  
Research Fields ◽  
Education Community ◽  
History Of ◽  
Dynamic Mathematics ◽  
Modern Mathematics ◽  
Mathematics Software

History and Pedagogy of Mathematics (HPM) is one of the important research fields in mathematics education, which has received widespread attention from the mathematics education community because of its educational value. Modern mathematics education technology plays an important auxiliary role in mathematics teaching. Hawgent is a dynamic mathematics software that can present abstract mathematical knowledge visually and static mathematical knowledge dynamically. In view of this, this research takes “the recognition of circle” as an example to conduct a research on HPM teaching supported by Hawgent Dynamic Mathematics Software in three aspects: analyze the contents and uncover the history of mathematics, make the products and show the history of mathematics, design the teaching and integrate the history of Mathematics.

Sign in / Sign up

Export Citation Format

Share Document