Related papers: Ren{\'e} Thom: From mathematics to philosophy
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…
Here we review a kind of post-World-War-II "Nachtrag" to H. Weyl's philosophical comments on mathematics and the natural sciences published in the middle of the 1920s. In a talk given at Z\"urich in the late 1940s, Weyl discussed…
Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological…
"The mathematization of time has limits," writes Derrida in Ousia and Gramme. Taking this quote in all possible senses, this paper considers Derrida's definition of limit as gramme, trace, and aporia, and develops the mathematization of all…
In this paper we use theoretical frameworks from mathematics education and cognitive psychology to analyse Cauchy's ideas of function, continuity, limit and infinitesimal expressed in his Cours D'Analyse. Our analysis focuses on the…
For four decades it has been argued that we need to adopt a new conception of science called aim-oriented empiricism. This has far-reaching implications and repercussions for science, the philosophy of science, academic inquiry in general,…
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community.…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
Despite ongoing calls for inclusive and culturally responsive pedagogy in computing education, the teaching of algorithms remains largely decontextualized. Foundational computer science courses often present algorithmic thinking as purely…
Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced…
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…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
The purpose of this paper is to provide a confession of sorts from an economist to political science and philosophy. A confession of the weaknesses of the political position of the economist. It is intended as a guide for political…
I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…
As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…
This is a critical response to some arguments and general recommendations presented in a discussion paper Four Levels of Ethical Engagement [EiM Discussion Paper 1/2018 University of Cambridge Ethics in Mathematics Project,…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
In this essay, I argue that modern science is not the dichotomous pairing of theory and experiment that it is typically presented as, and I offer an alternative paradigm defined by its functions as a human endeavor. I also demonstrate how…