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Spin glasses are the most basic examples of disordered systems ofÌýstatistical mechanics with mean-fieldÌýinteractions. The infinite-volumeÌýlimit of their free energies are described by the celebrated Parisi formula.ÌýI will describe a connection between this result and certain Hamilton-JacobiÌýequations. The talk will then mostly focus on a simpler setting arising fromÌýthe problem of infering a large rank-one matrix, in which the correspondingÌýHamilton-Jacobi equation is posed in a finite-dimensional space.