Феномен провинции (очерк истории математики в Нижнем Новгороде)
Sketch of history of mathematics in Nizhny Novgorod
In his reasoning concerning the relationship between surface or visible superficies (understood as the boundary or the limit of a body) and color (De sensu 439a19–b17), Aristotle asserts that the Pythagoreans called the surface (ἐπιφάνεια) color (χροιά), i.e. that they made no terminological difference between the former and the latter. In the scholarship on early Pythagoreans, this passage has been usually used as an indirect proof for the inaccuracy of attribution to the early Pythagoreans (1) of the abstract notion of surface (as found in Plato and Euclid), and thereby (2) of various forms of “derivation theory”. We argue that the colour-surface-limit doctrine has great significance for the understanding of the early Pythagorean concept of a number, since they articulated it, in various ways, precisely through the notion of a limit.
Аbout approaches to the definition of a subject of mathematics and about a periodization of its history
Materials for the International Conference Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017)
The scientific publication presents the materials of the International Scientific Conference "Analytical and Computational Methods in Probability Theory and Its Applications" in the following main areas:
- Analytical methods in probability theory and its applications;
- Computational methods in probability theory and its applications;
- Asymptotic methods in analysis;
- History of Mathematics
The collection is intended for scientists and specialists in the field of probability theory and its applications.
The study is based on a dataset formed on the basis of the Encyclopaedia of Ancient Natural Scientists (London, 2008) with significant revisions and modifications. The selection criteria, problems of demarkation of sciences (mathemata) from natural philosophy (physike) and practical arts (technai) are discussed. The dataset includes entries on 415 persons, pseudonyms and anonymous treatises associated with at least one of the six mathematical "disciplines": mathematics, astronomy, geography, harmonics, optics, and mechanics. Five phases of the population dynamics of sciences of the antiquity were identified: the rapid growth phase (600–350 BCE), first plateau at the level of 60–70 contemporaries (350–50 BCE), decline (from 50 BCE through the beiginning of the current Era), second plateau at the level of 25–40 contemporaries (0–500 CE), final decline (500–600 CE). The growth and decline phases are characterised by a concerted rise or decline of most populated disciplines, while the plateaus are composed of fluctuations of the different disciplinary communities counterbalancing each other. Patterns of population dynamics of different disciplines are discussed separately.
The significance of the education in the field of philosophy of mathematics as the part of both philosohpy and mathematics at the universities is the subject of the article.