We present an analytic calculation of the thermonuclear depletion of the light elements lithium, beryllium, and boron in fully convective, low-mass stars. Under the presumption that the pre--main-sequence star is always fully mixed during contraction, we find that the burning of these rare light elements can be computed analytically, even when the star is degenerate. Using the effective temperature as a free parameter, we constrain the properties of low-mass stars from observational data, independently of the uncertainties associated with modeling their atmospheres and convection. Our analytic solution explains the dependence of the age at a given level of elemental depletion on the stellar effective temperature, nuclear cross sections, and chemical composition. Most importantly, our results allow observers to translate lithium non-detections in young cluster members into a model-independent minimum age for that cluster. Using this procedure, we have found lower limits to the ages of the Pleiades (100 Myr) and Alpha Persei (60 Myr) clusters. Recent experimental work on the low energy resonance in the ^10B(p,alpha)^7Be reaction has greatly enhanced estimates of the destruction rate of ^10B, making it possible for stars with M>0.1 M_sun to deplete both ^10B and ^11B before reaching the main sequence. Moreover, there is an interesting range of masses, 0.085 M_sun < M < 0.13 M_sun, where boron depletion occurs on the main sequence in less than a Hubble time, providing a potential ``clock for dating low-mass stars.
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