Related papers: Tolstoy's Mathematics in "War and Peace"
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
In a previous article we gave the general foundations of the theory of movement considered from a philosophical and mathematical point of view. Philosophical it meant to understand the opposition of the one and the multiple, mathematically…
This article focuses on evolvement of the history of mathematics as a science and development of its methodology from the 4th century B.C. to the age of Enlightenment.
I try to clarify several confusions in the popular literature concerning chaos, determinism, the arrow of time, entropy and the role of probability in physics. Classical ideas going back to Laplace and Boltzmann are explained and defended…
Generalizations of the Monty Hall problem are studied according to George Boole's (1853) "An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities"
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…
Twenty years ago Breiman (2001) called to our attention a significant cultural division in modeling and data analysis between the stochastic data models and the algorithmic models. Out of his deep concern that the statistical community was…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…
I want to write about what I know and remember about the activities of Leonid Vital'evich Kantorovich, an outstanding scientist of the 20th century; about his dramatic struggle for recognition of his mathematical economic theories; about…
Analysis of wars and conflicts between regions has been an important topic of interest throughout the history of humankind. In the latter part of the 20th century, in the aftermath of two World Wars and the shadow of nuclear, biological,…
The history of the very first mathematical contests for high school students is discussed. The main body of the article is dedicated to the mathematical and scientific contests held in imperial Russia in the XIX century. More specifically,…
This chapter takes a historical view of the development of mathematics education, from its initial status as a business mostly managed by mathematicians to the birth of mathematics education as a scientific field of research. Starting from…
Aristotle is generally accepted as the father of logic. The ideas that he raised in his study of logical reasoning carried the development of science over the centuries. Today, in the era of AI, this title of the fatherhood of logic has a…
We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as `bridges' for…
Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…
Tense logic was introduced by Arthur Prior in the late 1950s as a result of his interest in the relationship between tense and modality. Prior's idea was to add four primitive modal-like unary connectives to the base language today widely…
Many economic theories have been introduced over the course of history to articulate our understanding of the economy. Classical theories by Adam Smith and David Ricardo's Comparative Advantage have been foundational for the last century's…
This paper analyzes the ergodic hypothesis in the context of Boltzmann's late work in statistical mechanics, where Boltzmann lays the foundations for what is today known as the typicality account. I argue that, based on the concepts of…