Problems in the axiomatic foundation of geometry

We will present several problems in the axiomatic foundation of geometry. The first part of the talk will be connected with the Parallel Postulate, and will involve Aristotle's axiom and the Lotschnittaxiom (including results not yet published). Beside results, there will be open problems. The second part will be devoted to the axiomatic foundation of ordered geometry and to the question whether the Pasch axiom is the simplest possible axiom. Here there is one result and a mjor open problem. A third part, if time permits, will be on the axiomatics of the arithmetic of the even and the odd, and the question whether one can prove by even and odd considerations that the square root of 17 is irrational. This goes back to a problem Theodorus of Cyrene had, as reported by Plato in his dialogue Theaetetus.

The subject matter of the talk is deceptively elementary.

The aim of the talk is to show that fundamental questions, that are easily stated, are still open in the foundations of mathematics, that the times

when you could answer elementary fundamental questions is not irrevocably past, after the discoveries of the 1930s and 1960s. My hope is that someone in the audience will take up the challenge to solve some open questions.

The written part will be in English, the spoken part in Armenian.

Զեկուցող՝ Victor Pambuccian (Arizona State University, USA, Victor V. Pambuccian (asu.edu))

Ամսաթիվը՝ ապրիլի 3

Ժամը՝ 18:00

Վայրը՝ Zoom, 923 2614 5848

Գաղտնաբառը՝ mteq

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