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Did you seriously not read the rest of my comment, which was about how mathematics is practiced as an ends unto itself?

• garbagetime 5y ago
  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.
  • catgary 5y ago
    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.