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Václav Hlavatý on intuition in Riemannian space

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Abstract We present a historical commentary together with an English translation of a mathematical-philosophical paper by the Czech differential geometer and later proponent of a geometrized unified field theory Vaclav Hlavatý (1894–1969). The paper was published in 1924 at the height of interpretational debates about recent advancements in differential geometry triggered by the advent of Einstein's general theory of relativity. In the paper he argued against a naive generalization of analogical reasoning valid for curves and surfaces in three-dimensional Euclidean space to the case of higher-dimensional curved Riemannian spaces. Instead, he claimed, the only secure ground to arrive at results is analytical calculation. We briefly discuss the biographical circumstances of the composition of the paper and characterize its publication venue the journal Ruch filosofický. We also give a discussion of the mathematical background for Hlavatý's argument.