F. Schleiermacher’s Influence on H. Grassmann’s Mathematics
In this paper I would like to summarize my account of the nature of the influence of Schleiermacher on Grassmann’s mathematics and to make same comparisons between this and the role of W. R. Hamilton’s metaphysics in Hamilton’s quaternions. There are two questions that might be asked about Schleiermacher’s influence: 1) How did Schleiermacher influence Grassmann’s mathematics? and 2) Did this influence affect the acceptance of Grassmann’s work in the mathematical community and, if so, how? Historians of other aspects of nineteenth-century mathematics may have an interest in the matter of the lack of contemporary acceptance of Grassmann’s Ausdehnungslehre of 1844 since the reasons for this would say something about the mathematical community of his time. Parallels might be drawn with the reception given to Bolyai, Bolzano, Galois, and even Gauss (at least in his anticipation of a negative reception which kept him from publishing on non-Euclidean geanetry). As D. Struik pictures it for us in this volume, it was the best of times in many ways for new, revolutionary, ideas in mathematics, while also the worst of times from the point of view of the reception, propagation and growth of some of these ideas.
KeywordsMathematical Community Abstract Science Transcendental Philosophy Protestant Theology Foundational Program
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