This book is an unique and wonderful collection of papers presented at a conference honoring one of the most productive, influential and still young mathematicians of the 20th century, I. M. Gelfand. As the title suggests, the articles refer to the connections between several fields: geometry, physics, representation theory, algebraic geometry. It was published as number 244 in the Progress in Mathematics series.
The authors of the papers includes are some of the best mathematicians of present day: Michael Atiyah, Haim Brezis, and Alan Connes — just to name a few. Most of them emphasize the crucial contribution that Gelfand's work had in many different ways. For example, A. Connes writes: "Israel Gelfand is one of the handful of mathematicians who really shaped the mathematics of the twentieth century. Even among them he stands out by the fecundity of the concepts he created and the astonishing number of new fields he originated."
Of course, Gelfand himself gave a couple of talks on this occasion and said, among other things: "From my point of view, mathematics is a part of our culture, like music, poetry and philosophy… I was happy to find the following four common features: first, beauty; second, simplicity; third, exactness; fourth, crazy ideas." Later he expresses his gratitude to his teachers and answers the question "How can I work at my age?" by saying: "The answer is very simple. I am not a great mathematician. I speak seriously. I am just a student all my life. From the very beginning of my life I was trying to learn. And for example now, when listening to the talks and reading notes of this conference, I discover how much I still do not know and have to learn. Therefore, I am always learning."
The few quotes included here are attractive, but the papers are unique, very deep and very well written. Mathematicians and graduate students will find lots of connections, ideas and inspiration in this wonderful collection of papers.
Mihaela Poplicher is an assistant professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is Mihaela.Poplicher@uc.edu.
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