Related papers: On mathematics and knowledge
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…
A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…
The view of nature we adopt in the natural attitude is determined by common sense, without which we could not survive. Classical physics is modelled on this common-sense view of nature, and uses mathematics to formalise our natural…
In which a review of the concept of countability is done in mathematics, subjecting review some of the theorems so far accepted, showing their inconsistency and also taking concrete elements on the countability of all the powers of the set…
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays,…
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
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,…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
While philosophy of science is the study of problems of knowledge concerning science in general, there also exists - or should exist - a '' philosophy in science'' directed at finding out in what ways our actual scientific knowledge may…
The 75th anniversary of Turing's seminal paper and his centennial year anniversary occur in 2011 and 2012, respectively. It is natural to review and assess Turing's contributions in diverse fields in the light of new developments that his…
Quantum information theory represents a rich subject of discussion for those interested in the philosphical and foundational issues surrounding quantum mechanics for a simple reason: one can cast its central concerns in terms of a…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Many people are familiar with the physico-chemical properties of gene sequences. In this paper I present a mathematical perspective: how do mathematical principles such as information theory, coding theory, and combinatorics influence the…
The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Using an example from my own mathematical life, I argue that…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.