Related papers: Modernism, Fiction and Mathematics
A review of progress in NMR quantum computing and a brief survey of the literature
Abraham Robinson's philosophical stance has been the subject of several recent studies. Erhardt following Gaifman claims that Robinson was a finitist, and that there is a tension between his philosophical position and his actual…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
The goal of this book is to provide an introduction to the mathematical theory of Kinetically constrained models developed in the last twenty years, intended for both mathematicians and physicists.
The paper "Is Complexity an Illusion?" (Bennett, 2024) provides a formalism for complexity, learning, inference, and generalization, and introduces a formal definition for a "policy". This reply shows that correct policies do not exist for…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…
We expand upon some topics reviewed and sketched in a book to appear with more details, embellishments, and some new material of a speculative nature.
University level mathematics in a number of countries is under pressure to `decolonise the curriculum'. This paper considers, as a test case, a possible `decolonisation' of linear algebra. This is a representative case, since linear algebra…
Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…
These are reminiscences of I.M.Gelfand's mathematical seminar of 1970s-1980s. The essay will appear in the March 2016 issue of Notices of the AMS.
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…
We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of…
This paper provides some reflections on the field of mathematical software on the occasion of John Rice's 65th birthday. I describe some of the common themes of research in this field and recall some significant events in its evolution.…
The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a…
This study concerns the use of e-learning in the mathematics education system, shedding the light on its advantages and disadvantages, analyzing its applicability either partially or totally, and discussing the ways of improvement. From…
Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by…
This is part two of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
This paper is a criticism on "A Mathematician's Apology" by G. H. Hardy.