Related papers: Math{\'e}matiques, musique et cosmologie : A parti…
Talk at the International Conference ``G\'eom\'etrie au vingti\`eme ci\`ecle: 1930--2000'', Paris, Institut Henri Poincar\'e, Sept. 2001. The title is a homage to Hans Rademacher and Otto Toeplitz whose book fascinated the author many years…
We briefly comment (in italian) on present relations between the traditional philosophy and modern positive sciences, in particular exact sciences.
The development of new statistical and computational methods is increasingly making it possible to bridge the gap between hard sciences and humanities. In this study, we propose an approach based on a quantitative evaluation of attributes…
There are growing uncertainties surrounding the classical model of computation established by G\"odel, Church, Kleene, Turing and others in the 1930s onwards. The mismatch between the Turing machine conception, and the experiences of those…
Are symmetries discovered or rather invented by humans ? The stand you may take firmly here reveals a lot of your epistemological position. Conversely, the arguments you may forge for answering to this question, or to one of its numerous…
Since the dawn of civilization, humanity has grappled with the big questions of existence and creation. Modern cosmology seeks to answer some of these questions using a combination of mathematics and measurement. The questions people hope…
In the period from about 1890 to 1915 an interdisciplinary and unifying research programme known as "cosmical physics" attracted much scientific and public attention. It typically included aspects of the earth sciences (such as magnetic…
In this paper, we discuss the associated family of harmonic maps $\mathcal{F}: M \rightarrow G/K$ from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type which are either algebraic or totally symmetric. These…
During the last three decades, there has been a growing realization among physicists and cosmologists that the relation between particle physics and cosmology may constitute yet another successful example of the unity of science. However,…
If there is a "platonic world" M of mathematical facts, what does M contain precisely? I observe that if M is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it…
Building over some ideas of Ren\'e Guitart, we provide a categorical framework towards some deviation notions in abstract logic.
We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…
The theory of cosmological perturbations is the main tool which connects theories of the early universe (based on new fundamental physics such as string theory) with cosmological observations. In these lectures, I will provide an…
In this paper we discuss the coupled dynamics, following from a suitable Lagrangian, of a harmonic or wave map $\phi$ and Einstein's gravitation described by a metric $g$. The main results concern energy conditions for wave maps, harmonic…
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…
We analyse the classical and quantum theory of a scalar field interacting with gravitation in two dimensions. We describe a class of analytic solutions to the Wheeler-DeWitt equation from which we are able to synthesise states that give…
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.
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,…
"Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which…