Related papers: Mathemagical 2014 - An Indian Perspective
"I am an industrial mathematician." When asked to identify my profession or academic field of study, this is the most concise answer I can provide. However, this seemingly straightforward statement is commonly greeted by a blank stare or an…
The question of the origins of logic as a formal discipline is of special interest to the historian of physics since it represents a turning inward to examine the very nature of reasoning and the relationship between thought and reality. In…
In the words of the twentieth-century British mathematician G. H. Hardy, "the human function is to 'discover or observe' mathematics" (1). For centuries, starting from the ancient Greeks, mankind has hunted for beauty and order in arts and…
Physics is formulated in terms of timeless classical mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality.
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
The nature of the scientific method is controversial with claims that a single scientific method does not even exist. However the scientific method does exist. It is the building of logical and self consistent models to describe nature. The…
The Fields Medal, often referred as the Nobel Prize of mathematics, is awarded to no more than four mathematician under the age of 40, every four years. In recent years, its conferral has come under scrutiny of math historians, for…
In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…
The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even to the way we interpret mathematical…
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…
Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays,…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some…
Our understanding of ordinary matter is remarkably accurate and complete, but it is based on principles that are very strange and unfamiliar. As I'll explain, we've come to understand matter to be a Music of the Void, in a remarkably…
The view of nature we adopt in the natural attitude is determined by common sense, without which we could not survive. Classical physics is modelled on this common-sense view of nature, and uses mathematics to formalise our natural…
In this book the authors probe into Vedic Mathematics (a concept that gained renown in the period of the religious fanatic and revivalist Hindutva rule in India): and explore whether it is really 'Vedic' in origin or 'Mathematics' in…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
This work explores a possible course of evolution of mathematics in ancient times in India when there was no script, no place-value system, and no zero. Reviewing examples of time-reckoning, large numbers, sacrificial altar-making, and…
The purpose of this paper is to explain at the simplest possible level why finite mathematics based on a finite ring of characteristic $p$ is more general (fundamental) than standard mathematics. The belief of most mathematicians and…