Mathematical Conversations

Understanding the mechanics of crumpling, i.e. of isotropically compressing thin elastic sheets, is a challenging problem of theoretical and applied interest. We will present an interesting conjecture on the order of magnitude of the elastic energy per unit thickness needed to achieve crumpling. Half of the conjecture has been solved by drawing inspiration from the observation of the creases appearing on real-world crumpled sheets of paper. The other half is considered totally open, and several clues indicate that its solution will require finding new, original ideas, and, indeed, many real-world sheets of paper have been crumpled in their search.