Related papers: K\=aty\=ayana \'Sulvasutra : Some Observations
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
This thesis is concerned with a realisation of topological theories in terms of statistical models known as Calabi-Yau crystals. The thesis starts with an introduction and review of topological field and string theories. Subsequently…
This paper presents mathematics as a general science of computation in a way different from the tradition. It is based on the radical philosophical standpoint according to which the content, meaning and justification of experience lies in…
The use of statistical software in academia and enterprises has been evolving over the last years. More often than not, students, professors, workers, and users, in general, have all had, at some point, exposure to statistical software.…
This soliloquy outlines some naive philosophical arguments underlying the thesis that mathematics ought to be viewed simply as a universal set of languages, some of precise expression, and some of effective communication.
Initially applied in astronomy and geodesy, the linear regression model aimed to find the best estimates for parameters with predefined meanings. E.g., orbital elements, geodetic constants. As its use expanded to other disciplines, often to…
Mathematical challenges punctuate the history of early modern mathematics. While cultural historians have attempted to contextualize these challenges among contemporary practices, in particular duels or advertisements in a competitive…
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible…
The aim of this paper is to describe the origin, first solutions, further progress, the state of art, and a new ansatz in the treatment of a problem dating back to the 1920's, which still has not found a satisfactory solution and deserves…
This note is a survey of the enumerative geometry of rational curves on Calabi-Yau threefolds, based on a talk given by the author at the May 1991 Workshop on Mirror Symmetry at MSRI. An earlier version appeared in "Essays on Mirror…
The aim of this work is to develop a study from the perspective of Abstract Algebraic Logic of some bilattice-based logical systems introduced in the nineties by Ofer Arieli and Arnon Avron. The motivation for such an investigation has two…
These notes were originally prepared as additional material for the lessons I have given at the summer school Gamma-ray Astrophysics and Multifrequency: Data analysis and astroparticle problems, organized by the Department of Physics of the…
This textbook is based on lectures given by the authors at MIPT (Moscow), HSE (Moscow), FEFU (Vladivostok), V.I. Vernadsky KFU (Simferopol), ASU (Republic of Adygea), and the University of Grenoble-Alpes (Grenoble, France). First of all,…
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community.…
In 1934, in Bernays preface to the 1st edn. of the 1st vol. of Hilbert-Bernays "Grundlagen der Mathematik", a nearly completed draft of the the finally two-volume monograph is mentioned, which had to be revoked because of the completely…
Cultural Astronomy is interdisciplinary connecting the arts, humanities, social & physical sciences. Data collection methods and theories are used from many disciplines and meld with methods and theories within cultural astronomy. The…
Despite explainable AI (XAI) has recently become a hot topic and several different approaches have been developed, there is still a widespread belief that it lacks a convincing unifying foundation. On the other hand, over the past…
In the last two decades, Bayesian inference has become commonplace in astronomy. At the same time, the choice of algorithms, terminology, notation, and interpretation of Bayesian inference varies from one sub-field of astronomy to the next,…
This is mainly a translation of Proc. of the 29th Symp. on History of Mathematics, Tsuda University, held Oct. 2018, of my talk. The first occasion when I studied the history of the theory of invariant integrals (or measures) was an…
The Ramayana is among the most influential literary traditions of South and Southeast Asia, transmitted across numerous linguistic and cultural contexts over two millennia. Despite extensive scholarship on regional Ramayana traditions,…