For a profinite group G and a prime number p, let C?(G, Fp) be the differential graded algebra of continuous cochains on G with Fp-coefficients. If G = GF is the absolute Galois group of a field F which contains a primitive pth root of unity, the structure of the associated cohomology algebra H?(GF , Fp) is described in elementary terms by the celebrated Norm Residue Theorem of Rost and Voevodsky. One may then ask whether C?(GF , Fp) itself can be described in elementary terms as well. For example, one may ask whether C?(GF , Fp) is formal, i.e., is quasiisomorphic as a differential graded algebra to its cohomology algebra. Formality is a rather strong property and implies, for example, the vanishing of all Massey products. While there are many examples of non-vanishing Massey products in arithmetic, Hopkins and Wickelgren showed that all triple Massey products of degree one classes in the mod 2-Galois cohomology of global fields of characteristic different from 2 vanish whenever they are defined. They therefore asked whether the mod 2-cohomology algebra of such fields is formal. Min´a?c and T?an then showed the vanishing of mod 2-triple Massey products for all fields and formulated the Massey vanishing conjecture. This conjecture has inspired a lot of activity in recent years, and it is now known to be true in many cases. The Hopkins?Wickelgren formality question, however, has a negative answer in general, as Positselski showed that there are local fields which provide counterexamples. In my talk, I will report on joint work with Ambrus P´al in which we describe the first nontrivial family of absolute Galois groups for which C?(GF , Fp) is indeed formal. In fact, we prove that the mod p-cohomology algebra H?(G, Fp) of any real projective profinite group G is intrinsically formal for all primes p. By the work of Haran and Jarden, real projective profinite groups can be characterized as the absolute Galois groups of fields F with virtual cohomological dimension at most one.