"Pure" mathematics sometimes has applications as well - number theory and cryptography, boolean algebra and circuits, etc. I do not think that Adams would argue

"Pure" mathematics sometimes has applications as well - number theory and cryptography, boolean algebra and circuits, etc. I do not think that Adams would argue that pure math is worthless, rather that it has applications that haven't shown how valuable it is or is not. Value is associated with utility as well. If Markov chains didn't help us describe things well, despite it seemingly being difficult to come up with, it would have little value. However, anything that stretches the limits of human understanding has value in that it increases our capacity reason and shows paths that do not bear much fruit.