We present Hubble Space Telescope UV spectra of the 4.6 h period double white dwarf SDSS J125733.63+542850.5. Combined with Sloan Digital Sky Survey optical data, these reveal that the massive white dwarf (secondary) has an effective temperature T 2 = 13030 ± 70 ± 150 K and a surface gravity log g 2 = 8.73 ± 0.05 ± 0.05 (statistical and systematic uncertainties respectively), leading to a mass of M 2 = 1.06 M ⊙ . The temperature of the extremely low-mass white dwarf (primary) is substantially lower at T 1 = 6400 ± 37 ± 50 K, while its surface gravity is poorly constrained by the data. The relative flux contribution of the two white dwarfs across the spectrum provides a radius ratio of R 1 /R 2 ≃ 4.2, which, together with evolutionary models, allows us to calculate the cooling ages. The secondary massive white dwarf has a cooling age of ∼ 1 Gyr, while that of the primary low-mass white dwarf is likely to be much longer, possibly 5 Gyrs, depending on its mass and the strength of chemical diffusion. These results unexpectedly suggest that the low-mass white dwarf formed long before the massive white dwarf, a puzzling discovery which poses a paradox for binary evolution.