There is no... mathematician so expert in his science, as to place
entire confidence in any truth immediately upon his discovery of it... Every
time he runs over his proofs, his confidence encreases; but still more by
the approbation of his friends; and is raised to its utmost perfection by
the universal assent and applauses of the learned world.
---David Hume, 1739, A Treatise of Human Nature,
This article grew out of a talk I gave with the same title in a minisymposium at the 2011 SIAM CSE meeting in Reno, organized by Jarrod Millman, on Verifiable, Reproducible Research and Computational Science ... Slides from my talk and others
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