Many people don't believe it. But it's true. The Galois group Gal(R/Q) is trivial.
And here is the proof.
Click here to download the proof in PDF
Click here to download the proof in PS
For those of you, who don't know what a Galois-Group is, here a brief explanation:
For a field extension L/K the Galois-Group Gal(L/K) is the set of automorphisms of L which fix K.