Related papers: Desperately seeking mathematical truth
Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore,…
In this paper of "The Epistemology of Contemporary Physics" series we investigate the epistemological significance and sensibility (and hence interpretability and interpretation) of classical mechanics in its Newtonian and non-Newtonian…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.
This paper has been withdrawn by the author. In this article I review W\"ust's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in…
Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…
Scientific fact-checking aims to determine the veracity of scientific claims by retrieving and analysing evidence from research literature. The problem is inherently more complex than general fact-checking since it must accommodate the…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
The concept of infinity took centuries to achieve recognized status in the field of mathematics, despite the fact that it was implicitly present in nearly all mathematical endeavors. Here I explore the idea that a similar development might…
A conceptual foundation for approximation of belief functions is proposed and investigated. It is based on the requirements of consistency and closeness. An optimal approximation is studied. Unfortunately, the computation of the optimal…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…
We report on an exploratory analysis of the forms of plagiarism observable in mathematical publications, which we identified by investigating editorial notes from zbMATH. While most cases we encountered were simple copies of earlier work,…
The authors discuss various objections and rejoinders in the collected responses [math.HO/9404229,math.HO/9404236] to their original article on the relationship between mathematics and theoretical physics [math.HO/9307227].
This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…
One main goal of argumentation theory is to evaluate arguments and to determine whether they should be accepted or rejected. When there is no clear answer, a third option, being undecided, has to be taken into account. Indecision is often…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
Experimental mathematics is an experimental approach to mathematics in which programming and symbolic computation are used to investigate mathematical objects, identify properties and patterns, discover facts and formulas and even…
Deficiencies in Kauffman's proposal regarding a new way for building scientific theories are pointed out. A suggestion to overcome them, and in fact, independently construct mathematical theories which are beyond the reach of Goedel's…
Modern science developed within a culture of Judeo-Christian theism, and science and theism have generally supported each other. However, there are certainly areas in both science and religion that puzzle me. Here I outline some puzzles…