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Articles 1 - 30 of 60
Full-Text Articles in Mathematics
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler
Journal of Humanistic Mathematics
Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the …
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Journal of Humanistic Mathematics
Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.
Connecting Ancient Philosophers’ Math Theory To Modern Fractal Mathematics, Colin Mccormack
Connecting Ancient Philosophers’ Math Theory To Modern Fractal Mathematics, Colin Mccormack
Parnassus: Classical Journal
No abstract provided.
Engaging The Paradoxical: Zeno's Paradoxes In Three Works Of Interactive Fiction, Michael Z. Spivey
Engaging The Paradoxical: Zeno's Paradoxes In Three Works Of Interactive Fiction, Michael Z. Spivey
Journal of Humanistic Mathematics
For over two millennia thinkers have wrestled with Zeno's paradoxes on space, time, motion, and the nature of infinity. In this article we compare and contrast representations of Zeno's paradoxes in three works of interactive fiction, Beyond Zork, The Chinese Room, and A Beauty Cold and Austere. Each of these works incorporates one of Zeno's paradoxes as part of a puzzle that the player must solve in order to advance and ultimately complete the story. As such, the reader must engage more deeply with the paradoxes than he or she would in a static work of fiction. …
Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois
Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois
Journal of Humanistic Mathematics
Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry …
From Solvability To Formal Decidability: Revisiting Hilbert’S “Non-Ignorabimus”, Andrea Reichenberger
From Solvability To Formal Decidability: Revisiting Hilbert’S “Non-Ignorabimus”, Andrea Reichenberger
Journal of Humanistic Mathematics
The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question of solvability is commonly identified with the decision problem. Given this identification, there is not the slightest doubt that Hilbert’s conviction was falsified by Gödel’s proof and by the negative results for the decision problem. On the other hand, Gödel’s theorems do offer a solution, albeit a negative one, in the form of an impossibility proof. In this sense, Hilbert’s optimism may still be justified. Here I argue that …
Revolution In Ideology: Crafting A Holistic Scientific Dialectic, Nathan Neill
Revolution In Ideology: Crafting A Holistic Scientific Dialectic, Nathan Neill
Dialogue & Nexus
Ideology drives scientific research far more than is acknowledged. Since science itself is conducted by individuals, each scientist has a biased conception of themselves and their surroundings relative to the rest of the universe, even if it is never explicated. This sense of relation to the greater universe is what defines the ideology of the individual. It is this sense of relation and self that creates the individual, who goes on to investigate the natural world by the scientific method. In this paper I will examine extant scientific ideology, particularly in Western science, and propose changes that could be helpful.
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 …
Prove It!, Kenny W. Moran
Prove It!, Kenny W. Moran
Journal of Humanistic Mathematics
A dialogue between a mathematics professor, Frank, and his daughter, Sarah, a mathematical savant with a powerful mathematical intuition. Sarah's intuition allows her to stumble into some famous theorems from number theory, but her lack of academic mathematical background makes it difficult for her to understand Frank's insistence on the value of proof and formality.
A Philosophical Examination Of Proofs In Mathematics, Eric Almeida
A Philosophical Examination Of Proofs In Mathematics, Eric Almeida
Undergraduate Review
No abstract provided.
Tesselland: A Mathematical Oddment, Martin Glover
Tesselland: A Mathematical Oddment, Martin Glover
Humanistic Mathematics Network Journal
No abstract provided.
Bridging To Infinity, Mike Pinter
Bridging To Infinity, Mike Pinter
Humanistic Mathematics Network Journal
The author's own experiences as a mathematics student and teacher have influenced how he thinks about the infinite. Author Madeleine L'Engle has also shaped his thinking with her writing. The author offers some thoughts that connect some of L'Engle's writing with his experience.
Man's Cards And God's Dice: A Conceptual Analysis Of Probability For The Advanced Student, Elie Feder
Man's Cards And God's Dice: A Conceptual Analysis Of Probability For The Advanced Student, Elie Feder
Humanistic Mathematics Network Journal
No abstract provided.
Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips
Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips
Humanistic Mathematics Network Journal
No abstract provided.
A Brief Look At Mathematics And Theology, Philip J. Davis
A Brief Look At Mathematics And Theology, Philip J. Davis
Humanistic Mathematics Network Journal
No abstract provided.
Book Review: Fermat's Enigma By Simon Singh, Matthew Becker
Book Review: Fermat's Enigma By Simon Singh, Matthew Becker
Humanistic Mathematics Network Journal
No abstract provided.
Base And Subbase In A Number System, Walter S. Sizer
Base And Subbase In A Number System, Walter S. Sizer
Humanistic Mathematics Network Journal
No abstract provided.
History Of Mathematics, An Intuitive Approach, Alejandro R. Garciadiego
History Of Mathematics, An Intuitive Approach, Alejandro R. Garciadiego
Humanistic Mathematics Network Journal
The main goal of this essay is to discuss, informally, an intuitive approach to the history of mathematics as an academic discipline. The initial point of departure includes the analysis of some traditional definitions of the concept of 'history' taken from standard dictionaries. This concise dissection attempts to suggest the complexity of the discipline.
A Brief Look At Mathematics And Theology, Philip J. Davis
A Brief Look At Mathematics And Theology, Philip J. Davis
Humanistic Mathematics Network Journal
No abstract provided.
Notes On Formal Constructivism, D. Joyner, P. Lejarraga
Notes On Formal Constructivism, D. Joyner, P. Lejarraga
Humanistic Mathematics Network Journal
Our aim is to sketch some ideas related to how we (as in, we two) think we (as in, we humans) think. "That theory is useless. It isn't even wrong." - Wolfgang Pauli. Our hope in this paper is to provide a theory, admittedly somewhat vague, of how we think about mathematics. We also hope our ideas do not cause the reader to be reminded of Pauli's quote above. These notes were motivated by the interesting book by Changeaux and Connes.
Aphorisms, Lee Goldstein
Fivefolded Asymmetrical Hand: A Poetic Essay, S. Robert Wilson
Fivefolded Asymmetrical Hand: A Poetic Essay, S. Robert Wilson
Humanistic Mathematics Network Journal
No abstract provided.
What "Is" Mathematics?: In Memoriam Of Gian-Carlo Rota, Gian-Carlo Rota
What "Is" Mathematics?: In Memoriam Of Gian-Carlo Rota, Gian-Carlo Rota
Humanistic Mathematics Network Journal
No abstract provided.
Naïve Thoughts On The Paradox Of Gödel, Philip J. Davis
Naïve Thoughts On The Paradox Of Gödel, Philip J. Davis
Humanistic Mathematics Network Journal
No abstract provided.
Hamilton's Icosian Calculus And His Icosian Game, Katye O. Sowell
Hamilton's Icosian Calculus And His Icosian Game, Katye O. Sowell
Humanistic Mathematics Network Journal
No abstract provided.
A Note On The Decimal Numeral System, Shaharir Bin Mohamad Zain
A Note On The Decimal Numeral System, Shaharir Bin Mohamad Zain
Humanistic Mathematics Network Journal
No abstract provided.
What Is The Thing Called “Humanistic Mathematics?”, Tamar Apel
What Is The Thing Called “Humanistic Mathematics?”, Tamar Apel
Humanistic Mathematics Network Journal
No abstract provided.
A Reflection On The Word: Remembering The Word “Word” Is Reflexive, Paul Fjelstad, Ivan Ginchev
A Reflection On The Word: Remembering The Word “Word” Is Reflexive, Paul Fjelstad, Ivan Ginchev
Humanistic Mathematics Network Journal
No abstract provided.
A Collection Of Ideas On Systems And Their Extensions, Paul Fjelstad
A Collection Of Ideas On Systems And Their Extensions, Paul Fjelstad
Humanistic Mathematics Network Journal
No abstract provided.
An Informal History Of Classical Rhetoric For Mathematicians (Plato And Aristotle), Phillip Keith, Sandra Z. Keith
An Informal History Of Classical Rhetoric For Mathematicians (Plato And Aristotle), Phillip Keith, Sandra Z. Keith
Humanistic Mathematics Network Journal
No abstract provided.