Many prominent mathematicians throughout history fit this pattern, but largely because they lived in different times. Mathematics builds on itself: 200-300 years ago, there was less mathematics to build on, so you could get to the frontiers a lot faster. Also, academic fields were less delineated--not only was Newton both a mathematician and a physicist at a time when the two weren't distinct fields and physics barely existed, but he also lived in a world where wasting the entire rest of his life studying Bible codes and nurturing personal feuds seemed like a reasonable idea.

There are also confirmation and sample biases involved. Everyone hears about Terence Tao because Terence Tao's story is remarkable. All the 38-year-old mathematicians who are making those research contributions are normal, and hence their stories aren't interesting.