Comment by lhd1

Tao is not the one who needs to worry, but it bears pointing out that Tao is probably one of the most famous archetypal "problem solving" mathematicians in history (though at that echelon all mathematicians are both problem solvers and theory builders, in the same way that Chess Super GMs are all universalists).

Tao only changed the heading of his blog to that quote in the last month, which is part of my point. Somehow despite this framework for viewing the field of mathematics having been beautifully described by one of our greatest leaders over 30 years ago, Terence Tao who has spent the last 5 years thinking about this has only just come around to it. Perhaps it has something psychologically to do with his greatest skills being those most under attack (though of course I'm not actually implying anything about Tao, he is obviously an honest and good-natured contributor to the community).

The people who need to read On Proof and Progress are the undergraduates and PhD students who have ended up down an academic pathway without looking up because they've always been good at proof and understanding mathematics, without ever pausing to ask why.