I graduated from the mathematical High school #134 in Baku, capital of Azerbaijan (USSR) in 1972 where had been the first student in the class both in math and physics. From 1969 to 1972 I annually won the first prizes on all Regional Mathematics Olympiads, however, was prohibited from admission to the USSR Mathematics Olympiads and, accordingly, to the International Mathematics Olympiads due to the restrictions imposed on Jews in USSR.

In 1977 I graduated with honour from Applied Math Department of Azerbaijan State University

My research in math started back in the High school in 1971 when inspired by the article "The architecture of mathematics" by N. Bourbaki, I started to work on the theory of the basic mathematical constructs ("structures").

Later, I have been investigating the fenomenon of duality in various fields of mathematics (working on the general theory of duality) and in the course of this work discovered that


(more information on the subject is contained in my (unpublished) book "This dual, dual, dual world". The publishers are welcome to bid: karasik@sympatico.ca)

I have also been working on non-classical logics. In particular, I proposed a new logic without the excluded middle, which formalizes some aspects of the inventive thinking (see Y. B. Karasik, "The logic of inventors' thinking", Proceedings of the Eleventh European Meeting on Cybernetics and Systems Research EMCSR'92, Vienna, Austria, 1992, pp. 591-598)