The Value of Ideas
What a curious post.  Pure mathematics is nothing but ideas - often very deep ones that very few people are capable of originating.  If you take Adams literally, then mathematics is worthless.  Is the idea of the Ricci flow, which Perelman used to prove the Poincare conjecture, really useless?<p>The problem Adams is addressing, so far as I can see, is that many people think trivial, easy-to-have ideas are somehow valuable.  Of course, that's false, as Adams says.  Value is associated to scarcity.  Easy-to-have ideas aren't valuable, simply because they're not scarce.  An idea like the Ricci flow is valuable, because very few people are capable of having it.<p>Ditto the ideas behind deep algorithms.  PageRank had value in large part because relatively few people had the depth of insight required to come up with it.<p>Come to think of it, the Turing machine was an idea that Turing invented to formalize Hilbert's intuitive notion of an effective computation.  And I think that idea turned out to have some value.