BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Victor Pambuccian (Arizona State University\, USA) DTSTART:20210403T140000Z DTEND:20210403T150000Z DTSTAMP:20260423T035818Z UID:YMC/24 DESCRIPTION:Title: Pro blems in the axiomatic foundation of geometry\nby Victor Pambuccian (A rizona State University\, USA) as part of Yerevan Mathematical Colloquium\ n\n\nAbstract\nWe will present several problems in the axiomatic foundatio n of geometry. The first part of the talk will be connected with the Paral lel Postulate\, and will involve Aristotle's axiom and the Lotschnittaxiom (including results not yet published). Beside results\, there will be ope n problems. The second part will be devoted to the axiomatic foundation of ordered geometry and to the question whether the Pasch axiom is the simpl est possible axiom. Here there is one result and a mjor open problem. A th ird part\, if time permits\, will be on the axiomatics of the arithmetic o f the even and the odd\, and the question whether one can prove by even an d odd considerations that the square root of 17 is irrational. This goes b ack to a problem Theodorus of Cyrene had\, as reported by Plato in his dia logue Theaetetus.\n\n  The subject matter of the talk is deceptively ele mentary. The aim of the talk is to show that fundamental questions\, that are easily stated\, are still open in the foundations of mathematics\, tha t the times when you could answer elementary fundamental questions is not irrevocably past\, after the discoveries of the 1930s and 1960s. My hope i s that someone in the audience will take up the challenge to solve some op en questions.\n\n  The written part will be in English\, the spoken part in Armenian.\n LOCATION:https://researchseminars.org/talk/YMC/24/ END:VEVENT END:VCALENDAR