 
Summary: Fields Institute Communications
Volume 00, 0000
Symplectization, Complexification and Mathematical
Trinities
V. I. Arnold
Steklov Mathematical Institute,
Gubkina st. 8, Moscow, 117966, Russia
and
CEREMADE, Universit'e Paris 9  Dauphine
75775 Paris, Cedex 16e, France
Abstract. This is the second of the series of three lectures given by
Vladimir Arnold in June 1997 at the meeting in the Fields Institute
dedicated to his 60th birthday.
Augury is not algebra. Human mind is not a prophet but
a guesser. It can see the general scheme of things and
draw from it deep conjectures, which are often borne out
by time.
A. S. Pushkin.
The goal of this lecture is to explain some mathematical dreams.
There are several parts of mathematics and they are considered as indepen
