Bernhard Riemann's published 1860 paper on compressible gas dynamics failed to conserve energy across a shock front because it assumed reversible adiabatic compression instead of entropy-producing jump conditions:

Auditing 12,000 pages of handwritten Nachlass manuscripts by Gauss, Riemann, Hilbert, and Grothendieck at Göttingen with Opus 5.5 agents uncovered 2 unpublished Riemann sheets that derive the exact Rankine-Hugoniot shock conditions in his own notation 10–20 years before William Rankine (1870) and Pierre-Henri Hugoniot (1887), alongside shock-wave relations conventionally dated to 1906–1937.