Dear mathematicians, What is the most practically useless mathematical truth you know of? Background to this question: I am evaluating an epistemological hypothesis called "confirmational holism" (http://en.wikipedia.org/wiki/Confirmation_holism). It (roughly) states that: (i) empirical evidence only ever confirms/falsifies the conjunction of ALL of our beliefs at once (ii) when falsification occurs we hold fixed certain conjuncts and revise others (iii) mathematical (and logical) beliefs are typically held fixed in this process (iv) mathematical (and logical) beliefs attain justification only by their successful role in being the conjuncts typically held fixed (v) mathematical (and logical) truths are not justified a priori, but empirically. I'm thinking that if there are mathematical propositions that intuitively we ahve justification for believing, that have little to no significance to physics or the empirical sciences more generally, then it could be used to problematise (iv). Very interested in your suggestions.