  We use the Fox-Neuwirth cell structure for one-point compactifications of
configuration spaces as the starting point for understanding our recent
calculation of the mod-two cohomology of symmetric groups. We then use that
calculation to give short proofs of classical results on this cohomology due to
Nakaoka and to Madsen. v2. Added references, expanded exposition on the cochain
model and a mathematical correction in the final section. v3. Added references.
