Amir, ArielLemeshko, MikhailTokieda, Tadashi2017-11-032016Ariel Amir, Mikhail Lemeshko, and Tadashi Tokieda. 2016. “Surprises in Numerical Expressions of Physical Constants.” The American Mathematical Monthly 123 (6): 609. doi:10.4169/amer.math.monthly.123.6.609.0002-9890http://nrs.harvard.edu/urn-3:HUL.InstRepos:34325474In science, as in life, ‘surprises’ can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of mathematical constants like π or e. The inverse problem also arises, whereby the measured value of a physical constant admits a ‘surprisingly’ simple approximation in terms of well-known mathematical constants. Can we estimate the probability for this to be a mere coincidence, rather than an inkling of some theory? We answer the question in the most naive form.en-USJournal Article2017-11-0310.4169/amer.math.monthly.123.6.609