The exceptionally delicate electronic structure of plutonium metal, a subject of decades of intense study, drives properties that are not captured by even the very best modern theories. Magnetism, valence fluctuations, thermodynamic stability and more, have all been tried. But radiation-induced complications, the need for gallium to stabilize the most important phase to ambient temperatures, and the safety and security issues surrounding the most available isotope, ²³⁹Pu, cloak the route to a fundamental understanding, something increasingly important for nuclear energy as well as nuclear weapons. Recent advances in precision thermodynamic measurements, including elastic moduli and heat capacity, have quantified essential properties that are not captured by today’s theories of the metal but must be for those theories to be valid. We describe this ongoing work and its implications.