This book contains the problems and solutions of the Youth Mathematical Olympiad named after Prof. Gillis, held in the years 1983-1996. In addition, the book contains the problems and solutions of the Israel-Hungary math competitions, held in 1990-1996. The book is dedicated to the memory of Prof. Gillis who died in 1993. Prof. Gillis was a great scientist and educator and was the living spirit in the world of mathematical competitions in Israel.

One of Professor Kleiner's main areas of interest is the history of mathematics and its use in teaching mathematics. Four of his articles in this field have been translated into Hebrew and appear in this collection. For the article "The Evolution of Group Theory - A Brief Survey" he received the Allendoerfer Prize from the Mathematical Association of America in 1986. In 1989, the same association awarded him the George Pólya Prize for his article "Evolution of the Function Concept: A Brief Survey". In 1991 he again won the Allendoerfer Prize, this time for "Rigor and Proof in Mathematics: A Historical Perspective". The reasons of the award committees appear verbatim before each article in this collection.

The first part of the book includes classic minimum and maximum problems, solved for decades by some of the world's greatest mathematicians. The second part presents general methods for solving minimum and maximum problems in the fields of variation mathematics, linear and non-linear planning, and more.

A paradox is the mathematician's best joke. Like a good joke, the paradox develops easily, in a logical and seemingly plausible manner, until it reaches the punch line, which is an unbelievable, completely surprising error, which gleefully mocks simple logic. Some paradoxes are easily explained because they rely on the incorrect use of a well-known basic rule. Some believe that such mistakes should not be called paradoxes at all, but only erroneous arguments. This book is a collection of paradoxes, fallacies and thinking challenges which are suitable for integration into mathematics studies in high school. Each of the activities in this book will encourage students to see familiar mathematical concepts in a new light and deepen their understanding of these concepts.

In 1931, Kurt Gdöel published a revolutionary article - an article that challenged some basic assumptions on which a significant part of the research in mathematics and logic was based until then. The unknown land Terra Incognita that he discovered is recognized today as one of the greatest contributions to the development of scientific thinking. This is the first book to present to the enlightened reader who is not an expert a readable explanation of the main ideas and extensive history of Gödel's Proof. It offers every cultured person, who has a sympathetic approach to logic and philosophy, an opportunity to satisfy the intellectual curiosity regarding the subject that has been blocked from him until now.