Къде е грешката в решението ми? ─ разговор пред бялата дъска с Олег Мушкаров

Abstract

The article is dedicated to the 70th anniversary of Prof. Oleg Mushkarov – a full professor at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (IMI-BAS) and a corresponding member of BAS. Currently, he is the Head of the Analysis, Geometry and Topology Department and Deputy Director of IMI-BAS. His main research interests are in the areas of Complex Analysis, Complex Differential Geometry, and Twistor theory. Another important aspect of Oleg’s professional involvements is his work with mathematically gifted high school students. He himself benefited from the Bulgarian system of identifying mathematical talents at an early age leading to his participation in IMO’1969, Romania. Since then, he has been involved in numerous activities dealing with nurturing and developing young mathematical talents. We present a conversation with him illustrating what his favorite problems are and why. Unlike the traditional situations in which the professor expects the students to come to a solution (possibly with his help), he presents a solution containing mistakes to a well-defined problem and “throw the gauntlet down” for them: Find the mistakes in the solution! We provide a specific example in support of his conviction that such problems are crucial in math education (since everyone, even a professional mathematician, makes errors on an everyday basis). The phases the talk in front of the white board went through were: To feel that something is wrong in his original solution. To discover where the mistake is. Finally, to find a correct solution to the problem. The very process of starting with a wrong idea, becoming aware of the error in reasoning, and finally, succeeding to correct it, which Oleg Mushkarov has kept reproducing when teaching a course on extracurricular math activities to his undergraduate students, reveals his dedication and talents to teaching in addition to his research achievements.