Related papers: Ren{\'e} Thom: From mathematics to philosophy
We describe a mainstream "universalist" approach to the understanding of mathematics. We then conduct a systematic (but not exhaustive) review of the academic literature on the decolonisation of mathematics and identify how this challenges…
Henri Poincare's work on mathematical features of the Lorentz transformations was an important precursor to the development of special relativity. In this paper I compare the approaches taken by Poincare and Einstein, aiming to come to an…
An opiniated essay on what pure mathematics is and why the adjective "pure" in "pure mathematics" is not a good choice.
This paper examines the intellectual legacy of Philip E. Agre by situating his work at the intersection of artificial intelligence, philosophy, and critical theory. It reconstructs Agre's proposal of a critical technical practice, according…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
I discuss three connections between Dummett's writings about time and philosophical aspects of physics. The first connection (Section 2) arises from remarks of Dummett's about the different relations of observation to time and to space. The…
Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and…
In the last years the debate on complexity has been developing and developing in transdisciplinary way to meet the need of explanation for highly organized collective behaviors and sophisticated hierarchical arrangements in physical,…
Feyerabend frequently discussed physics. He also referred to the history of the subject when motivating his philosophy of science. Alas, as some examples show, his understanding of physics remained superficial. In this respect, Feyerabend…
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…
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical…
This paper reconstructs the derivations underlying the kinematical part of Einstein's 1905 special relativity paper, emphasizing their operational clarity and minimalist use of mathematics. Einstein employed modest tools-algebraic…
Beginning in the 1970s, statistician-cum-logician Per Martin-L\"of wrote a series of papers developing what became Martin-L\"of type theory, realizing a system where the distinction between mathematics and programming disappears. Inspired…
Economic theory is a mathematically rich field in which there are opportunities for the formal analysis of singularities and catastrophes. This article looks at the historical context of singularities through the work of two eminent…
The theoretical biologist Robert Rosen developed a highly original approach for investigating the question "What is life?", the most fundamental problem of biology. Considering that Rosen made extensive use of mathematics it might seem…
In the last decades, several objects such as grammars, economical agents, laws of physics... have been defined as algorithms. In particular, after Brouwer, Heyting, and Kolomogorov, mathematical proofs have been defined as algorithms. In…
We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as `bridges' for…
While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of…
Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Klein. Some of Mehrtens' conclusions have been picked up by…