Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Einstein (2)
- American Mathematical Society (1)
- Arithmetica (1)
- Arrupe (1)
- Atomism (1)
-
- Axioms (1)
- Badiou (1)
- Benjamin Banneker (1)
- Cicada (1)
- Communism (1)
- Diophantine equations (1)
- Diophantus (1)
- Discrimination (1)
- Emigration (1)
- Epicurus (1)
- Euclid (1)
- Euclidean Geometry (1)
- Event (1)
- Fano (1)
- Germany (1)
- Hilbert's tenth problem (1)
- Historiography of mathematics (1)
- History of mathematics (1)
- Infinite divisibility (1)
- Infinitesimal; Felix Klein; Abraham Fraenkel; hyperreal; mean value theorem (1)
- Internationalism (1)
- Lobachevsky (1)
- Loyalty oaths (1)
- Mateo ricci (1)
- Mathematical notation (1)
Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Mathematicians Going East, Pasha Zusmanovich
Mathematicians Going East, Pasha Zusmanovich
Journal of Humanistic Mathematics
I survey emigration of mathematicians from Europe, before and during WWII, to Russia. The emigration started at the end of 1920s, the time of “Great Break”, and accelerated in 1930s, after the introduction in Germany of the “non-Aryan laws”. Not everyone who wanted to emigrate managed to do so, and most of those who did spent a relatively short time in Russia, being murdered or deported, or fleeing the Russian regime. After 1937, the year of “Great Purge”, only a handful of emigrant mathematicians remained, and even fewer managed to leave a trace in the scientific milieu of their new …
Irruption Of The New: Truth, Events, History, Parallels, Fidelity, David L. Neel
Irruption Of The New: Truth, Events, History, Parallels, Fidelity, David L. Neel
Journal of Humanistic Mathematics
A historical meditation on non-Euclidean geometry, three Jesuits, a radical egalitarian mathematical philosopher, and the atom bomb, structured by word-count with attention to divisors of 441 and the Fano plane.
“All Of These Political Questions”: Anticommunism, Racism, And The Origin Of The Notices Of The American Mathematical Society, Michael J. Barany
“All Of These Political Questions”: Anticommunism, Racism, And The Origin Of The Notices Of The American Mathematical Society, Michael J. Barany
Journal of Humanistic Mathematics
A recent controversy involving the Notices of the American Mathematical Society and questions of politics, racism, and the appropriate role of a professional mathematical organization began with a comparison to events the American Mathematical Society confronted in 1950. A close look at the AMS’s own archives for that period shows that the controversies that vexed the society around 1950 do indeed resonate strongly with those of today, but not in the ways recently suggested. Then, as now, the AMS confronted allegations of political and viewpoint discrimination in universities, the challenges of structural racism in American education and society, and the …
What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann
What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann
Journal of Humanistic Mathematics
Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.
Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou
Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou
Journal of Humanistic Mathematics
In this paper, we give a comprehensive summary of the discussion on the Epicurean critique of mathematics and in particular of Euclid's geometry. We examine the methodological critique of the Epicureans on mathematics and we assess whether a 'mathematical atomism' was proposed, and its implications. Finally, we examine the Epicurean philosophical stance on mathematics and evaluate whether it was on target or not.
Some Comments On Multiple Discovery In Mathematics, Robin W. Whitty
Some Comments On Multiple Discovery In Mathematics, Robin W. Whitty
Journal of Humanistic Mathematics
Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics. We are interested to know whether this phenomenon, and its close cousin repeated discovery, give rise to meaningful questions regarding causes, trends, categories, etc. With this in view we unearth many more examples, find some tenuous connections and draw some tentative conclusions.
Pythagoras Plays His Lyre, Sarah Glaz
Pythagoras Plays His Lyre, Sarah Glaz
Journal of Humanistic Mathematics
A poem about the Pythagoreans' beliefs and way of life.
The Symbolic And Mathematical Influence Of Diophantus's Arithmetica, Cyrus Hettle
The Symbolic And Mathematical Influence Of Diophantus's Arithmetica, Cyrus Hettle
Journal of Humanistic Mathematics
Though it was written in Greek in a center of ancient Greek learning, Diophantus's Arithmetica is a curious synthesis of Greek, Egyptian, and Mesopotamian mathematics. It was not only one of the first purely number-theoretic and algebraic texts, but the first to use the blend of rhetorical and symbolic exposition known as syncopated mathematics. The text was influential in the development of Arabic algebra and European number theory and notation, and its development of the theory of indeterminate, or Diophantine, equations inspired modern work in both abstract algebra and computer science. We present, in this article, a selection of problems …
The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried
The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried
Journal of Humanistic Mathematics
Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of …
A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö
A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö
Journal of Humanistic Mathematics
The history of mathematics is nowadays practiced primarily by professional historians rather than mathematicians, as was the norm a few decades ago. There is a strong consensus among these historians that the old-fashioned style of history is “obsolete,” and that “the gains in historical understanding are incomparably greater” in the more “historically sensitive” works of today. I maintain that this self-congratulatory attitude is ill-founded, and that the alleged superiority of modern historiographical standards ultimately rests on a dubious redefinition of the purpose of history rather than intrinsic merit.
Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta
Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta
Journal of Humanistic Mathematics
Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker’s naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers.
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Journal of Humanistic Mathematics
The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …
A Definition Of Mathematical Beauty And Its History, Viktor Blåsjö
A Definition Of Mathematical Beauty And Its History, Viktor Blåsjö
Journal of Humanistic Mathematics
I define mathematical beauty as cognisability and trace the import of this notion through several episodes from the history of mathematics.