I will report on some recent work on multiple zeta values. I will sketch the definition of motivic multiple zeta values, which can be viewed as a prototype of a Galois theory for certain transcendental numbers, and then explain how they were used to prove a conjecture due to Hoffman giving a generating family for multiple zeta values, and a conjecture of Deligne and Ihara on the fundamental group of the projective line minus 3 points.

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