The understanding of natural forms and their classications attracted
natural scientists and mathematicians since antiquity.
The presentation asks whether there can be a well-dened mathematical
point of view, a clear system of classication that is useful
for science and can say something new. The classication we propose
is based on the static equilibrium points that are comprehensible also
as the singularities of the gradient of the distance from the centre of
gravity. The number of equilibria and the topology of the integral
curves connecting them (the so-called Morse{Smale complex) create
our proposed classication the completeness of which is a mathematical
question of equal interest to search for suitable natural phenomena
that can be described by this classication.
The presentation discusses the main mathematical issues and the
geological, biological, palaeontological and astrophysical applications.