Opening lecture for the academic year 1993/1994 of the FME (UPC).
Delivered on September 30, 1993. Published by FME, 1993. 54 p.

Contents (chapter titles, with page range):

0. Preface (1-5)
1. Greek geometry: the origins (6-12)
2. Geometry in itself: Euler's circle (13-16)
3. The mysterious relationship mathematics−nature (16-21)
4. Analytical geometry (21-28)
5. Elementary geometry today (21-35)
6. Algebraic geometry (35-46)
7. Enumerataive geometry and string theory (46-49)
8. Acknowledgements (49)
9. References (49-54)

Dear friends:

I accepted the Dean's invitation to deliver this opening lecture because it looked to me as an excellent opportunity to share with you a few considerations on the mathematical activity.

According to my memories about what I thought when I had the age of those of you that today are at the beginning of a mathematical career, and taking into account the spirit of this new School of Mathematics and Statistics, I am convinced that the place I would like to be today, if I had eighteen years, would be right here with you.

The considerations that follow are, then, an attempt to formulate some of the thoughts that I had along the years which I would have liked to listen, or read, at the beginning of my university years, mostly about the significance of the mathematical work, and in particular of geometry, in the world of today.