Related papers: Mathemagical 2014 - An Indian Perspective
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
This paper is concerned with a dialogue between Rabindranath Tagore and Albert Einstein, where Tagore argued that our knowledge is essentially human, while Einstein maintained that some kinds of knowledge are more objective. Arguments by…
Do we have two kinds of reality: physical and mathematical? What is the role of mathematics in physics? These fundamental questions have intrigued original and brilliant minds since ancient times. A recent article (Aharonov, Cohen and…
This paper is the second in series of the Indian physics of the Nyaya-Vaisheshika school. It is significant that the school defines matter not in terms of something gross that is anchored to the commonsensical notion of an object, but…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
One can notice that quite often difference between so-called "standard students" and "gifted" ones is not because that first are less smart, but they have different "orientation", they consider subject as a collections of rules which should…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
We show that many ancient Indian mythological legends are really allegorical depictions of astronomical and other physical phenomena of which the composers had a good idea. This detail enables us to also use techniques of astronomical…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
Metaphysics is traditionally conceived as aiming at the truth -- indeed, the most fundamental truths about the most general features of reality. Philosophical naturalists, urging that philosophical claims be grounded on science, have often…
Mammalian brain is one of the most complex objects in the known universe, as it governs every aspect of animal's and human behavior. It is fair to say that we have a very limited knowledge of how the brain operates and functions.…
Perhaps one of the most intriguing questions in philosophy concerns the true nature of external reality. In this paper, we discuss some of the theories that have been put forth regarding the nature of reality and of our perceived universe.…
We extend Langdon Winner's idea that artifacts have politics into the realm of mathematics. To do so, we first provide a list of examples showing the existence of mathematical artifacts that have politics. In the second step, we provide an…