  Gentzen's last proof determined the “proof-theoretic  ordinal” of Peano arithmetic, namely the one that is needed to  prove consistency, with the property that nothing less would suffice. The work marked the beginning of ordinal proof theory. It was without doubt the most remarkable foundational achievement in arithmetic  after Gödel's incompleteness theorems, but is still largely  unknown—one can find many books about Gödel's theorems  that do not even mention Gentzen.