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This paper is a top down historical perspective on the several phases in the development of probability from its prehistoric origins to its modern day evolution, as one of the key methodologies in artificial intelligence, data science, and…
This introductory text arises from a lecture given in G\"oteborg, Sweden, given by the first author and is intended for undergraduate students, as well as for any mathematically inclined reader wishing to explore a synthesis of ideas…
In the scientific literature the equation $Q=\{Q\}[Q]$ is frequently quoted, where $Q$ denotes a quantity, $\{Q\}$ a numerical value, and $[Q]$ a unit. During the last years some experts claimed, that this equation is due to James Clerk…
Prof. K.G Ramanathan was a legendary Indian Mathematician, working in Number Theory and a prolific Institution builder. Apart from this, he was an excellent teacher and influenced several brilliant students. In this article, we overview his…
These notes are an extension of the rough notes provided for my four lecture graduate level course on "Quadratic Forms and Automorphic Forms" at the March 2009 Arizona Winter School on Quadratic Forms. They are meant to give a survey of…
The Jacobian algebras are introduced and their various properties are studied.
In this article, I discuss the relationship of mathematics to the physical world, and to other spheres of human knowledge. In particular, I argue that Mathematics is created by human beings, and the number $\pi$ can not be said to have…
This memorial paper tells the story of the beginning of Boris (Boaz) Trakhtenbrot's long and rich life path, full of unusual and sometimes tragic events. This path led a boy from a Jewish settlement in Eastern Europe to be recognized as one…
This is a short obituary of Saunders Mac Lane (1909--2005).
This is a contribution for the discussion on "A Gibbs sampler for a class of random convex polytopes" by Pierre E. Jacob, Ruobin Gong, Paul T. Edlefsen and Arthur P. Dempster to appear in the Journal of American Statistical Association.
This article is about Artin's braid group and its role in knot theory. We set ourselves two goals: (i) to provide enough of the essential background so that our review would be accessible to graduate students, and (ii) to focus on those…
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
The aim of this paper is to honor Ivo G. Rosenberg by describing some of his most influential results and their impact in logic, discrete mathematics, algebra, and computer science.
Honorary degrees and particularly doctorates are important instruments to enhance the standing of universities and professors, in addition to receiving these as a measure of a scientist's recognition. Jacobus C. Kapteyn from the University…
We describe our adventures in creating a new first-year course in Experimental Mathematics that uses active learning. We used a state-of-the-art facility, called The Western Active Learning Space, and got the students to "drive the…
This is an introduction of the volume of the journal Commentationes Mathematicae Universitatis Caroalinae dedicated to the memory of V\v{e}ra Trnkov\'a}.
Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and…
The article shows the pioneering role of the British scientist, Professor G.W.Scott Blair, in the creation of the application of fractional modelling in rheology. Discussion of his results is presented. His approach is highly recognized by…
We discuss two realizations of the colored Jones polynomials of a knot, one from an unnoticed work of the second author in 1994 on quantum R-matrices at roots of unity obtained from solutions of the pentagon identity, and another one from…