Open Court began publishingThe Monistin 1890 as a journal“devotedto the philosophy of science”that regularly included mathematics. The audiencewas understood to be“cultured people who have not a technical mathematicaltraining”but nevertheless“have a mathematical penchant.”With these constraints,the mathematical content varied from recreations to logical foundations, but every-one had something to say about non-Euclidean geometry, in debates that rangedfrom psychology to semantics. The focus in this essay is on the contested value ofmathematical expertise in legitimating what should be considered as mathematics.While some mathematicians urgedThe (...) Monistto uphold disciplinary standards ofgeometrical reasoning, authors opposed tonon-Euclidean geometry aligned theirreasoning with practical applications, universal know-how, and nonhierarchicaldemocracy. As one contributorinquired,“How isthe professional expert betterfit-ted to see more lucidly in dealing with the elements of geometry than any otherperson of good geometric faculty?”. (shrink)

By 1870, non-Euclidean geometry had been established as a mathematical research field but was yet to be considered relevant to the real space inhabited by stars and nebulae. It was of much less interest to physicists and astronomers than to mathematicians and philosophers. Although most astronomers took the age-old Euclidean geometry for granted, during the following decades a few of them such as K. F. Zöllner, S. Newcomb and K. Schwarzschild followed in the footsteps of the pioneer N. I. Lobachevsky (...) by seriously considering the possibility that cosmic space might be curved. From the H. Poincaré’s conventionalist perspective the discussion was meaningless since there was no way in which observations or other empirical data could determine the geometry of space. Poincaré’s view was shared by a few astronomers, but its impact on astronomy was limited. The paper examines the question as it was discussed prior to the advent of the general theory of relativity. (shrink)