Publications de Alain Bernard

 Abstract: The 4th century AD mathematician Theon of Alexandria is the well known commentator on Ptolemy’s Almagest, which was written two centuries before him. It is often presupposed that Theon taught mathematics and astronomy to his own students, as the preface to his commentary strongly suggests. But we have no real mean, on the basis of the contents of his commentary alone and in the absence of any biographical data on him, to determine if this was indeed the case and how he might have proceeded with his students. Nevertheless, it is possible and interesting to define precisely the nature of the project presented in the preface as well as its coherency with the core of the commentary itself. In this paper, we propose to define the sense in which Theon’s project might be called ‘pedagogical’, in spite of our ignorance of his actual practice as a teacher.

For this purpose, we propose to examine three fundamental elements of ‘context’: (1) the nature and structure of Ptolemy’s Almagest itself, which can be rightly described as ethical in purpose and ‘protreptic’ in structure; (2) the sociological context, namely the fact that Theon’s students were in all probability advanced astrologers; (3) the ancient situation, in which classical texts were studied and commented upon, on the background of rhetorical practice.

On this basis, we show that these elements largely explain the nature of Theon’s project and how it is coherently reflected in the structure of the commentary itself. We finally explain how it results in a conception of mathematics and mathematical practice which is very different from Ptolemy’s, in spite of the fact that the commentary follows the model of the Almagest.


Ptolemy was a self-identified philosopher who examined a number of the most pressing philosophical questions of his time, commented on the (lack of) success of previous philosophical theories, appropriated the philosophical concepts of contemporary schools, and, moreover, propounded philosophical ideas unprecedented in the history of ancient Greek philosophy.  Ptolemy, however, was not a typical philosopher. He neither affiliated himself with a specific school nor did he proclaim himself an eclectic, as did his contemporary Galen.  Ptolemy’s texts, in fact, reveal him to be a Platonist empiricist. He adopts Platonic, Aristotelian, and, to a lesser extent, Stoic ideas, but the manner in which he mixes these philosophical influences depends heavily on contemporary Platonic concerns. While Ptolemy does not identify himself as a Platonist in his texts, the ideas he promulgates reveal a substantial Platonic influence on his philosophy. He adapts these Platonic ideas to his theory of knowledge, which is best described by the anachronistic term ‘empiricism’, and he bases this so-called empiricism on an ontology that is distinctively Aristotelian. Yet, what proves most striking in Ptolemy’s philosophy is an emphasis which results from his Platonic empiricism. This emphasis is on the role of mathematics, not only in its practice, but in its epistemic and ethical contributions as well. According to Ptolemy, only the mathematician produces knowledge and attains a virtuous state.  This claim proved immensely influential, as evidenced by the subsequent work in the ancient exact sciences by Ammonios, Theon of Alexandria, Hypatia, Proclus, and Olympiodoros, among others

Abstract: This chapter focuses on Hypatia of Alexandria and the school of thought she represented in 4th cent. CE Alexandria. Defining what was Hypatia’s doctrine is rendered very difficult by the facts that we have no single source that can be attributed with certainty to her and that the only works she is reputed to have written bear on (apparently) ‘strictly mathematical’ topics. These are frustrating facts, given that various sources emphasize her considerable reputation both as a philosopher and as a local political figure. It is often taken for granted that Hypatia was a Platonist. But this presupposition relies on such disputable evidence that it is in fact no more than one possibility among many others. Amore plausible possibility is that she basically was a Ptolemist, i.e., a dedicated follower of this original and composite philosophy elaborated by Ptolemy in the 2nd cent. CE (see ch. Ptol). One major reason for thinking so is that this philosophy had probably been already followed by her father Theon of Alexandria in the mid 4th cent CE, as well as by his predecessor Pappus of Alexandria at the beginning of the same century. Hypatia, Theon and Pappus obviously shared a deep interest in the study of Ptolemy’s Almagest, the two last having left influential commentaries on it. It is highly plausible (though not entirely provable, as we shall see) that this interest came along with the cultivation of the same kind of Ptolemism, derived from the philosophical commitment advocated by Ptolemy himself in his introduction to the Almagest, which gives to the study of  mathematics a central role. There are, on the other hand, two major aspects of Ptolemy’s philosophy that Theon and Pappus do not seem to have followed. This first is Ptolemy’s broad definition of mathematics, which encompasses theory and instrumented observations. The second is Ptolemy’s association of astronomy with astrology and physics.


ABSTRACT: The paper explores the historical reasons why Ptolemy’s Almagest was cultivated in Antiquity as a legitimate part of ancient culture. It tries to elucidate first the precise nature of Ptolemy’s project in the Almagest, its relation to ethics as well as to the particular conception that Ptolemy had of mathematics. It then proposes an explanation for the fact that this treatise, both in Ptolemy’s period and afterwards, was studied within the milieu of ancient astrologers.




Article paru dans le n° 26 de la revue Tréma (IUFM de Montpellier), où sont publiés les actes du colloque Histoire des Sciences : formations et recherches en IUFM organisé à Montpellier en mai 2005, pp.59-86.   Voir le texte intégral de l’article sur le site ‘’.