  The real Ginibre ensemble refers to the family of $n\times n$ matrices in
which each entry is an independent Gaussian random variable of mean zero and
variance one. Our main result is that the appropriately scaled spectral radius
converges in law to a Gumbel distribution as $n\rightarrow\infty$. This fact
has been known to hold in the complex and quaternion analogues of the ensemble
for some time, with simpler proofs. Along the way we establish a new form for
the limit law of the largest real eigenvalue.
