Related papers: Modernism, Fiction and Mathematics
A revised version of the last appendix of the (previous) paper "Existence and Regularity for an Energy Maximization Problem in Two Dimensions" by S.Kamvissis and E.A.Rakhmanov, that appeared in the Journal of Mathematical Physics, v.46,…
This is a book review for Zhan's Matrix Theory (AMS, GSM 147, 2013).
This is a shortened version of "The Limits of Mathematics--Course Outline & Software" (IBM Research Report RC 19324, December 1993) in which all Mathematica code has either been deleted or, if absolutely necessary, replaced by C code. The…
This is a draft of a book about algorithms for performing arithmetic, and their implementation on modern computers. We are concerned with software more than hardware - we do not cover computer architecture or the design of computer…
This is a draft version of an invited article for a forthcoming book `The genesis of Langlands Program', eds. Julia Mueller and Freydoon Shahidi, which will be published in the London Mathematics Society Lecture Notes Series. It gives a…
This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of…
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
We provide an example of the application of quantitative techniques, tools, and topics from mathematics and data science to analyze the mathematics community itself in order to quantify and document inequity in our discipline. This work is…
This is a philosophy paper rather than mathematical physics work. I will publish it in some other place.
This document is an internet supplement to my book "Partially Observed Markov Decision Processes - From Filtering to Controlled Sensing" published by Cambridge University Press in 2016. This internet supplement contains exercises, examples…
In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…
To conduct a didactic analysis of the current modality of study of real numbers in the Bachelor's Degree in Mathematics, we rely on the notion of didactic paradigm and employ a novel research methodology within the framework of the…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.
Leibniz scholarship is currently an area of lively debate. We respond to some recent criticisms by Archibald et al.