We investigate the relationship between dust attenuation and stellar mass (
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Abstract M *) in star-forming galaxies over cosmic time. For this analysis, we compare measurements from the MOSFIRE Deep Evolution Field survey atz ∼ 2.3 and the Sloan Digital Sky Survey (SDSS) atz ∼ 0, augmenting the latter optical data set with both UV Galaxy Evolution Explorer (GALEX) and mid-infrared Wide-field Infrared Survey Explorer (WISE) photometry from the GALEX-SDSS-WISE Catalog. We quantify dust attenuation using both spectroscopic measurements of Hα and Hβ emission lines, and photometric measurements of the rest-UV stellar continuum. The Hα /Hβ ratio is used to determine the magnitude of attenuation at the wavelength of Hα ,A Hα . Rest-UV colors and spectral energy distribution fitting are used to estimateA 1600, the magnitude of attenuation at a rest wavelength of 1600 Å. As in previous work, we find a lack of significant evolution in the relation between dust attenuation andM *over the redshift rangez ∼ 0 toz ∼ 2.3. Folding in the latest estimates of the evolution ofM dust, (M dust/M gas), and gas surface density at fixedM *, we find that the expectedM dustand dust mass surface density are both significantly higher atz ∼ 2.3 than atz ∼ 0. These differences appear at odds with the lack of evolution in dust attenuation. To explain the striking constancy in attenuation versusM *, it is essential to determine the relationship between metallicity and (M dust/M gas), the dust mass absorption coefficient and dust geometry, and the evolution of these relations and quantities fromz ∼ 0 toz ∼ 2.3.