  This paper is dedicated to the memory of Professor K. Alex Muller. After
describing our personal and scientific encounters since 1974, I concentrate on
the many puzzles whinch appeared in our discussions and collaborations,
involving the interplay between theory and experiments on the critical behavior
of cubic perovskites which undergo (second or first) order transitions to a
lower symmetry phases (trigonal or tetragonal). The conclusion, reached only
very recently, is that (although beginning with the same cubic symmetry) the
two types of transitions belong to two distinct universality classes: under
[100] stress, the cubic to trigonal transition exhibits a tetracritical phase
diagram, with cubic exponents, while the cubic to tetragonal transition exhibit
an intermediate bicritical phase diagram, but asymptotically the bicritical
point turns into a triple point, with three first order lines. To test these
conclusions, it is suggested to measure the effective critical exponents as the
temperature approaches criticality.
