Related papers: Math{\'e}matiques, musique et cosmologie : A parti…
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a paper together, and I refereed an…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…
This text is based on an invited talk at the Dedekind Symposium at Braunschweig in October 2016. It summarizes views from my recent commented edition of Dedekinds two books on the foundations of mathematics.
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from…
To many people, music is a mystery. It is uniquely human, because no other species produces elaborate, well organized sound for no particular reason. It has been part of every known civilization on earth. It has become a very part of man's…
Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real,…
Gioseffo Zarlino reintroduced the Pythagorean paradigm into Renaissance musical theory. In a similar fashion, Nicolaus Copernicus, Galileo Galilei, Johannes Kepler, and Isaac Newton reinvigorated Pythagorean ideas in celestial mechanics;…
One of the aims of this paper is to better explain the philosophy behind the computations in [E.Bifet, C.De Concini,C.Procesi Cohomology of Regular Embeddings ] and to place them in a wider conceptual setting. Another aim of the paper is to…
The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general…
We propose the use of specific dynamical processes and more in general of ideas from Physics to model the evolution in time of musical structures. We apply this approach to two \'Etudes by F. Chopin, namely op.10 n.3 and op.25 n.1,…
This is an intrusion in the life and the mathematics of Norbert A'Campo, intended to be a tribute to him and an acknowledgement of his impact on those who know him and his work. The final version of this paper appears in the book ``Essays…
In this paper, we study the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of…
The state of our understanding of cosmology is reviewed from an astrophysical cosmologist point of view with a particular emphasis given to recent observations and their impact. Discussion is then presented on the implications for particle…
This paper is a short introduction to a special issue on philosophy of cosmology, published in the May 2014 issue of Studies in History and Philosophy of Modern Physics. I briefly introduce the philosophy of cosmology, and then provide a…
Can we use mathematics, and in particular the abstract branch of category theory, to describe some basics of dance, and to highlight structural similarities between music and dance? We first summarize recent studies between mathematics and…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
In a previous article, we discussed a paradox in Timaeus' cosmology: that there is no void inside the universe, even though it is entirely filled with polyhedra-a mathematical impossibility (Brisson-Ofman 2025). In the present article, we…
This review devoted to the centenary of Alexander Friedmann's prediction of the Universe expansion presents the results obtained by him in 1922 and 1924 and the sketch of their further developments. Special attention is paid to the role of…