I think it's important to remember that the Millennium Prize problems were chosen partly because they would drive the development of new mathematics (it’s not as though the Poincare conjecture or Fermat’s last theorem are useful things). Ideally, when someone solved one of these problems, they would train a new generation of mathematicians with their toolbox. Gromov benefitted from this - his work was built using technology that people had spent their entire careers exploring and clarifying. Perelman didn’t really do anything like that, so it’s fair someone like Gromov would feel Perelman didn't pay it forward.
Of course, this whole debacle could have been avoided if Princeton had given Perelman tenure after he proved the Soul Conjecture. To an extent, I agree with Perelman’s opinions of the mathematics community, I just felt Gromov’s opinion was a bit more defensible than you were giving it credit for.
Yes, of course I read your comment. I have read it again now. I still don't see how it is about mathematics being an end unto itself.
What I mean by mathematics being an end unto itself is that mathematical results have intrinsic value. That is, they have value in and of themselves, regardless of how they may or may not be used.
Perhaps you thought I meant that mathematical results could be used to discover more mathematical results? No, that is not what I meant.
So, I think the point you’re missing is that how results are proved is just as important as the existence of a proof (in fact, I’d say it’s often more important). That’s why people are often excited about new proofs of old theorems, and why the Simon’s foundation chose certain problems to be “Millennium Problems” - the techniques developed to solve the problem would, ideally, drive progress in that area of mathematics.
The Poincaré conjecture is interesting because it was a simple statement that ended up being very hard to prove. How someone proved it, and understanding why such an innocuous statement is so difficult to prove, is far more interesting than knowing that the obviously-true-sounding statement is true.
Of course, this whole debacle could have been avoided if Princeton had given Perelman tenure after he proved the Soul Conjecture. To an extent, I agree with Perelman’s opinions of the mathematics community, I just felt Gromov’s opinion was a bit more defensible than you were giving it credit for.