Related papers: Mathematics discovered, invented, and inherited
Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…
The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math…
Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of Burnside's Problem prior to its first publication. We present these letters as a whole to the public for the first time.…
The concept of infinity took centuries to achieve recognized status in the field of mathematics, despite the fact that it was implicitly present in nearly all mathematical endeavors. Here I explore the idea that a similar development might…
In a previous article we gave the general foundations of the theory of movement considered from a philosophical and mathematical point of view. Philosophical it meant to understand the opposition of the one and the multiple, mathematically…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
This paper presents mathematics as a general science of computation in a way different from the tradition. It is based on the radical philosophical standpoint according to which the content, meaning and justification of experience lies in…
In this paper, we propose that 'embodied mathematics' should be studied not only by reduction to the present individual bodily experience but in an historical context as well, as far as the origins of mathematics are concerned. Some early…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
Despite our familiarity with specific technologies, the origin of new technologies remains mysterious. Are new technologies made from scratch, or are they built up recursively from new combinations of existing technologies? To answer this,…
In point of fact the Indian tradition in mathematics is long and glorious. It dates back to earliest times, and indeed many of the Indian discoveries from 5000 years ago correspond rather naturally to modern mathematical results.
Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the…
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…
The evolution of theoretical physics in the XX century differs significantly from that in XVII-XIX centuries. While continuous progress is observed for theoretical physics in XVII-XIX centuries, modern physics contains many questions that…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…