Related papers: Math{\'e}matiques, musique et cosmologie : A parti…
We study a pair p,e consisting of a projection p (an idempotent) and an effect e (an element between 0 and 1) in a synaptic algebra (a generalization of the self-adjoint part of a von Neumann algebra). We show that some of Halmos's theory…
Following the procedure proposed recently by Martin and Brandenberger we investigate the spectrum of the cosmological perturbations in the case when the ``trans-Plackian'' dispersion relations are motivated by the quantum…
This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at…
This text summarizes and expands the content of a general audience talk given in 2018 at the University of Mainz. Motivated by recent developments in dependent type theory and infinity category theory, it presents a history of ideas around…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a $\Psi$-epistemic quantum cosmology. We present a proposal that, if successfully implemented, would resolve the cosmological measurement…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical…
From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental role of geometric imagination in…
This is an article on the interaction between topology and physics which will appear in 1998 in a book called: A History of Topology, edited by Ioan James and published by Elsevier-North Holland.
Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…
Computational analysis of performed music is a key component of music information research, as performance shapes much of the music we hear. Music performance analysis studies the acoustic variations introduced by performers and how these…
This article is the first part of a study of the so-called 'mathematical part' of Plato's Theaetetus (147d-148b). The subject of this 'mathematical part' is the irrationality, one of the most important topics in early Greek mathematics. As…
This article, which grew out of my lecture at the conference "Analysis and Applications: A Conference in Honor of Elias M. Stein" in May 2011, is intended to give an overview on a collection of results which have been obtained jointly with…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
The purpose of the paper, of which this is part II, is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. Part II provides…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early…
We discuss a precise relation between the Veneziano amplitude of string theory, rewritten in terms of ratios of the Riemann zeta function, and two elementary criteria for the Riemann hypothesis formulated in terms of integrals of the…