Perhaps like Erdos, he could be called more of a problem solver than a theory builder. In contrast to a figure like Cantor, Galois, or Grothendieck whose work has more fundamental ramifications. I think this raises interesting questions about the continued viability of the "great man" theory of methematical/scientific progress going forward. As Tao and Gowers exemplify, the trend is towards increasing collaboration on problems as they became ever more complex and individual mathematicians become ever more specialized. Could the age of the great theory builders one day come to an end? Is it already over?

Not that I'm trying to downplay Tao's achievements. How overrated can a Fields medalist really be? They don't hand it out for nothing.

This seems like a thoroughly detestable use of HN: a gratuitous, mean, and almost certainly uninformed (you spelled his name incorrectly) judgement of another human being as "overrated" or "underrated". Why not use your time to do something worthwhile?

He received the Fields in 2006 due in no small part to the paper “The primes contain arbitrarily long arithmetic progressions”. I would call that work groundbreaking.

Can you define groundbreaking? In a proper historical context, one might say the same about the likes of Newton, Euler etc. Mathematical ideas don't just happen out of nowhere. Everyone is inspired by something that was done before. So truly groundbreaking things are mostly a myth. The closest it gets is when someone takes ideas from one field and unexpectedly applied it to solve ab important problem in another field. Like Poincare's work on three body problem and celestial mechanics.

If you want to argue it, please do so in depth. But don’t post shallow dismissals here.

A lot of people would have said that of Erdős as well...

Define ‘overrated.’ He did get awarded a prestigious prize, didn’t he? (On the other hand, there may be little that’s left to be discovered in mathematics which one could call groundbreaking and which the human mind could comprehend without a life-time effort...)

Overrated or not, I’d give my right arm to have Terry Tao’s brain.

Cheapskate. How about getting Hawking’s body or Galois’ short life.

Either this comment, or its parent, is a joke.

They're not groundbreaking to you because they don't fit the mold of popular science which requires something to be cool and easily digestible in order for most to consider it ground breaking.