Related papers: Joseph Carter Corbin: Arkansas's "Profound Mathema…
Moore introduced a method for graduate mathematics instruction that consisted primarily of individual student work on challenging proofs (Jones, 1977). Cohen (1982) described an adaptation with less explicit competition suitable for…
This is the paper "Niels Henrik Abel and the birth of fractional calculus", Podlubny, I., Magin, R. L., Trymorush I., Fractional Calculus and Applied Analysis, vol.20, no.5, pp.1068-1075, 2017 (https://doi.org/10.1515/fca-2017-0057) with…
This paper starts with a biographical sketch of the life of Josef Meixner. Then his motivations to work on orthogonal polynomials and special functions are reviewed. Meixner's 1934 paper introducing the Meixner and Meixner-Pollaczek…
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…
Professor Alan Selman has been a giant in the field of computational complexity for the past forty years. This article is an appreciation, on the occasion of his retirement, of some of the most lovely concepts and results that Alan has…
This article is a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn [math.HO/9307227]. The authors discuss the role of rigor in mathematics and the relation between…
The information-theoretic point of view proposed by Leibniz in 1686 and developed by algorithmic information theory (AIT) suggests that mathematics and physics are not that different. This will be a first-person account of some doubts and…
This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010…
Whether racial disparities in enrollment in advanced high school coursework can be attributed to differences in prior academic preparation is a central question in sociological research and education policy. However, previous investigations…
Scientometrics is the field of quantitative studies of scholarly activity. It has been used for systematic studies of the fundamentals of scholarly practice as well as for evaluation purposes. Although advocated from the very beginning the…
This book covers the history of probability up to Kolmogorov with essential additional coverage of statistics up to Fisher. Based on my work of ca. 50 years, it is the only suchlike book. Gorrochurn (2016) is similar but his study of events…
Decisions about how the population of the United States should be divided into legislative districts have powerful and not fully understood effects on the outcomes of elections. The problem of understanding what we might mean by "fair…
The century of complexity has come. The face of science has changed. Surprisingly, when we start asking about the essence of these changes and then critically analyse the answers, the result are mostly discouraging. Most of the answers are…
"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…
The following is an exposition of a course of algebra that Prof. Aleksandr Aleksandrovich Zykov (1922-2013) distributed among the participants of his seminar in graph theory not far away from Odessa, Ukraine, on September, 1991. It is a…
Jacobi is one of the most famous mathematicians of his century. His name is attached to many results in various fields of mathematics and his complete works in seven volumes have been available since the end of the XIXth century and are…
This paper presents an updated biography of Samgamagr\=ama M\=adhava incorporating viewpoints expounded by scholars in the recent past and collecting together in one place more details about his works culled from recent researches into his…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
This article reflects on the life and mathematical contributions of Pierre Cartier, a distinguished figure in 20th- and 21st-century mathematics. As a key member of the Bourbaki collective, Cartier played a pivotal role in the formalization…