> Just consider volume: it's estimated that around a quarter of a million theorems are proved every year. That's real, measurable, progress; what's the metaphys

> Just consider volume: it's estimated that around a quarter of a million theorems are proved every year. That's real, measurable, progress; what's the metaphysics equivalent? I'm not sure I disagree with your overall argument, but this point here is silly. First, I'd like to know where you got that number. (I must admit it sounds rather high to me, but I'm sure it depends how you count.) But more importantly, measuring mathematical progress by number of theorems proved is absurd. I can write a computer program to prove theorems; it will almost surely prove more than a quarter-million a day (though eventually it will have to slow down). But they will not be _useful_ theorems. Nobody will read them, nobody will use them, nobody will build on them, nobody will find them beautiful, nobody will apply them to any practical problem. "Number of theorems proven" may be measurable, but it is not "real progress".