Peter Riedlberger, Minerva fellow, Tel Aviv University, Mathematics and the philosophers of Late Antiquity

 

 

 

Monday, 19.3.2012, 18:00

Gilman Building, room 449

  

In Late Antiquity, a basic training in the mathematical subjects (including arithmetic and geometry) was part of the lectures philosophical schools offered. A clear commitment to mathematics was typical for philosophers then. Significantly, the first attestations of the spurious inscription which was allegedly displayed at the entrance of Plato’s academy - ἀγεωμέτρητος μηδεὶς εἰσίτω, “Nobody without geometric knowledge may enter” – belong only to this period. While budding philosophers delved into mathematics, hardly anyone else did: Our comprehensive evidence seems to exclude a universal liberal arts education which included mathematics, and even practical professions requiring some mathematical knowledge (such as engineering, architecture, land-surveying) had to cope with very limited training.

It was, hence, the late antique philosophers (whom we are wont to call ‘Neoplatonists’) who preserved and, in some cases, expanded the inherited mathematical knowledge. Their importance in the history of mathematics can hardly be overrated. In my paper, I want to focus on the seeming contradiction between their competence in, and appraisal of, mathematics in the sense of deductive reasoning (“common mathematics”), and their further interests in the mystical properties attached to numbers (“theological mathematics”). How could ‘common mathematics’, based on reasoning, be understood as gateway to more speculative approaches? How could mathematics as deductive disciple thrive despite an intellectual climate which subordinated “common mathematics”, perceived as beginners’ subject, to “theological mathematics”? Did those philosophers notice any contradictions involved, or is the question a notional anachronism?

     פרופ' יוסי שוורץ, יו"ר

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