Let F be the free graded Lie algebra generated by one generator e_i in rank i for each odd i greater than or equal to 3. A graded Lie algebra appears naturally in four different mathematical contexts: Galois actions, Grothendieck-Teichmuller group, mixed Tate motives and multizeta values. Conjecturally, the Lie algebras in all four cases are isomorphic to F and thus to each other. This provides several specific and fascinating links between these subjects. In particular we will present Furusho's fascinating recent result relating GT to multizeta values.