Related papers: Intuitionism: an inspiration?
This is an introductory article to the theory of multiple gaps.
This chapter sets the stage for the rest of the book by exploring the role of intuition as a tool to deepen understanding in Einsteinian physics. Drawing on examples from the history of general relativity, we argue that the development of…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…
In this article we determine the implicational fragments of most of the known subintuitionistic logics.
This is an introduction to some of the most probabilistic aspects of free probability theory.
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
This book is a short introduction into dyadic analysis with applications to classical weighted norm inequalities.
{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has two objectives. The first is to reconcile the way of…
This paper is a very brief introduction to idempotent mathematics and related topics.
In this paper we show that an intuitionistic theory for fixed points is conservative over the Heyting arithmetic with respect to a certain class of formulas. This extends partly the result of mine. The proof is inspired by the quick…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
Planning to explore the beginning of the Universe? A lightweight introductory guide to the theory of Inflation.
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
Inductive inference is a recursion-theoretic theory of learning, first developed by E. M. Gold (1967). This paper surveys developments in probabilistic inductive inference. We mainly focus on finite inference of recursive functions, since…
This survey article is an introduction to Diophantine Geometry at a basic undergraduate level. It focuses on Diophantine Equations and the qualitative description of their solutions rather than detailed proofs.
The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the…
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
We introduce relationalism and discuss how it is useful for interpreting probability theory and quantum mechanics. This paper is written in relatively lay terms and presumes no prior knowledge of quantum theory.
This article is part introduction and part survey to the mathematical area centered around local cohomology.