This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.

The 1990s could be called The Decade of Sociology in mathematics education. It was during those years that the sociology of mathematics became a core ingredient of discourse in mathematics education and the philosophy of mathematics and mathematics education. Unresolved questions and uncertainties have emerged out of this discourse that hinge on the key concept of social construction. More generally, what is at issue is the very idea of “the social”. Within the framework of the general problem of “the social”, (...) we want to open a discussion of boundaries and margins in mathematics and mathematics education. By theorizing the divisions of purity and danger, we will be able to better understand the intersection of logic, mathematics, and thinking with gender, race, and class, and morals, ethics, and values in the classroom. The process of transforming the sociology of mathematics and the sociology of mind into pedagogical tools for mathematics educators and philosophers of education has already begun. One of the tasks before us is the development of a more profound and at the same time more practical grasp of “the social”. Our objective in this paper is to move ourselves and our readers in the direction of just such a grasp of the social. (shrink)

In their publications during the 1820s, Jakob Steiner and Julius Plücker frequently derived the same results while claiming different methods. This paper focuses on two such results in order to compare their approaches to constructing figures, calculating with symbols, and representing geometric magnitudes. Underlying the repetitive display of similar problems and theorems, Steiner and Plücker redefined synthetic and analytic methods in distinctly personal practices.

: Half a century of political Marxism and Soviet social science deflected Marxist thought from its canonical sources. Communism and Marxism were so intertwined by events of the twentieth century that it is difficult to see what remains of the latter after the demise of the former. Specifically, three foundational principles--"being determines consciousness," the Asiatic Mode of Production, and "the ideas of the ruling class are the ruling ideas"--have been corrupted by heartfelt ideological commitments. A review of those principles against (...) the background of Marxist writing on the history of science stakes out research frontiers that remain to be reconnoitered. (shrink)

The author describes the Cartesian way of solving the problem of the universal method in mathematics, in particular, the problem of applying algebra in geometry when it comes to the convergence of a discrete number and a continuous quantity. The article shows that the solution to this problem proposed by F. Viète is imperfect, since it introduces vague pseudo-geometric objects, and the geometric quantity is still far from an algebraic number. The author proves that Descartes' solution to this problem through (...) the use of Eudoxus proportions is based on such Cartesian epistemological principles as: the requirement of clarity and expressiveness of thinking; the idea of the central role of a holistic mathematical science; the idea of the existence of a simple and obvious nature of length as a basis for comparing all extended things; the elevation of the concept of ratio to the rank of a single subject of mathematical disciplines. (shrink)

The increasing complexity of biological problems and the increase of mathematical means to handle them on the one hand, and the possibility of automatized computation at the other, necessitate a revaluation of the present interactions between biology and mathematics; in this connection interrelations occur which can be divided into three kinds: mathematical biology, biological mathematics, and general biomathematics or methodology of the biomathematical sciences, by which are meant those scientific branches which arise from the said interactions.

Mutual feedback between human-made environments and facets of thought throughout history has yielded two myths: the Garden and the Citadel. Both myths correspond to Jung’s feminine and masculine collective subconscious, as well as to Nietzsche’s premise of Apollonian and Dionysian impulses in art. Nietzsche’s premise suggests, furthermore, that the feminine myth of the Garden is time-bound whereas the masculine myth of the Citadel, or the Ideal City, constitutes a spatial deportment. Throughout history the two myths have continually molded the built (...) environment and thought, but the myth of the Ideal City – from Plato to Descartes to modernity – came to dominate city-form and ensuing aspects of contemplation. This relationship seems to have shifted during the twentieth century. Intellectual dispositions have begun to be largely nurtured by an incongruous city-form emerging from the gap between the incessant promise for an automated, well-functioning city, on the one hand, and looming alienation, coupled with the factual, malfunctioning city, on the other hand. Urban decay, a persisting and time-bound urban event that is a byproduct of this configuration, suggests the ascent of the Garden myth in post-modern city-form. (shrink)