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We report the discovery of 1.97 ms period gamma-ray pulsations from the 75 minute orbital-period binary pulsar now named PSR J1653-0158. The associated Fermi Large Area Telescope gamma-ray source 4FGL J1653.6-0158 has long been expected to harbor a binary millisecond pulsar. Despite the pulsar-like gamma-ray spectrum and candidate optical/X-ray associations -- whose periodic brightness modulations suggested an orbit -- no radio pulsations had been found in many searches. The pulsar was discovered by directly searching the gamma-ray data using the GPU-accelerated Einstein@Home distributed volunteer computing system. The multi-dimensional parameter space was bounded by positional and orbital constraints obtained from the optical counterpart. More sensitive analyses of archival and new radio data using knowledge of the pulsar timing solution yield very stringent upper limits on radio emission. Any radio emission is thus either exceptionally weak, or eclipsed for a large fraction of the time. The pulsar has one of the three lowest inferred surface magnetic-field strengths of any known pulsar with $B_{\rm surf} \approx 4 \times 10^{7}\,$G. The resulting mass function, combined with models of the companion star's optical light curve and spectra, suggests a pulsar mass $\gtrsim 2\,M_{\odot}$. The companion is light-weight with mass $\sim 0.01\,M_{\odot}$, and the orbital period is the shortest known for any rotation-powered binary pulsar. This discovery demonstrates the Fermi Large Area Telescope's potential to discover extreme pulsars that would otherwise remain undetected.