  From its early beginnings up to nowadays, algebraic number theory has evolved
in symbiosis with Galois theory: indeed, one could hold that it consists in the
very study of the absolute Galois group of the field of rational numbers.
  Nothing like that can be said of transcendental number theory. Nevertheless,
couldn't one associate conjugates and a Galois group to transcendental numbers
such as $\pi$? Beyond, can't one envision an appropriate Galois theory in the
field of transcendental number theory? In which role?
  The aim of this text is to indicate what Grothendieck's theory of motives has
to say, at least conjecturally, on these questions.
