Related papers: K\=aty\=ayana \'Sulvasutra : Some Observations
I shall discuss the history of Indian astronomy, Aurveda (life science), chemistry and metallurgy to illustrate how downgrading experiments from scientific learning lead to the decline of ancient Indian science and civilization. We shall…
Large language models (LLMs) have achieved strong results in mathematical reasoning, and are increasingly deployed as tutoring and learning support tools in educational settings. However, their reliability for students working in…
We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The…
In point of fact the Indian tradition in mathematics is long and glorious. It dates back to earliest times, and indeed many of the Indian discoveries from 5000 years ago correspond rather naturally to modern mathematical results.
In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop…
This article is an abridged and commented translation into Spanish of the 1815 memoir where Gauss introduced the quadrature rules now associated with his name. Gauss' work does not resemble at all the stardard text-book treatment of…
This is the text of a series of three lectures given at the CMA of the Australian National University on the recent solution of the square root problem for divergence form elliptic operators, a long-standing conjecture posed by Kato in the…
Econophysics is a new research field, which makes an attempt to bring economics in the fold of natural sciences or specifically attempts for a "physics of economics". The term Econophysics was formally born in Kolkata in 1995. The entry on…
A paper of Thomas Young (1773-1829) on the behavior of streams of air makes a good starting point for discussing the not always fair, sometimes serendipitous, association of a physical phenomenon with its discoverer. In a didactic context,…
X-ray astronomy is a mature area of observational astronomy. After the discovery of the first non-solar X-ray source in 1962, X-ray astronomy proliferated during the Apollo era's space race. Then, it matured as an established area of…
Context: In the context of exploring the art, science and engineering of programming, the question of which programming languages should be taught first has been fiercely debated since computer science teaching started in universities.…
The early Greek and Indian cosmologies are summarized in this paper. The two traditions appear to have developed independently although after the time of Alexander they were consciously aware of each other. The focus and style of the two…
Context: Several researchers have reported their experiences in applying secondary studies (Systematic Literature Reviews - SLRs and Systematic Mappings - SMs) in Software Engineering (SE). However, there is still a lack of studies…
The amoebas associated to algebraic varieties are certain concave regions in the Euclidean space whose shape reminds biological amoebas. This term was formally introduced to Mathematics in 1994 by Gelfand, Kapranov and Zelevinski. Some…
Hilary Putnam's biography and philosophical development reflect the history of Anglo-Saxon philosophy over the last 40 years. Putnam has influenced this history significantly for almost as long. In this introduction, the main aim is to…
To flourish in the new data-intensive environment of 21st century science, we need to evolve new skills. These can be expressed in terms of the systemized framework that formed the basis of mediaeval education - the trivium (logic, grammar,…
Due to the shift of civilization from the Industrial Age to the Information Age, mathematical literacy has become a necessity in the twenty-first century. However, in order to learn and contribute to the mathematical community, one has to…
We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika…
We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached;…
The present volume is the written version of the series of lectures the author delivered at the Catholic University of Leuven, Belgium during the period of June-July, 1990. The main purpose of these talks is to present some of author's work…