Abstract
‘What is progress in mathematics?’ The answer, at least a partial answer, seems easy: ‘I make mathematical progress when I solve a problem I wanted to solve or prove a theorem I wanted to prove.’ Now there’s surely something right about this, but the issue that brings us here isn’t my mathematical development or lack thereof; what we want to know is how mathematics as a discipline progresses. Does mathematics as a discipline progress when someone solves a problem she wanted to solve or proves a theorem she wanted to prove? Well, not if the problem had already been solved or the theorem had already been proved by someone else, at least as long as that previous solution or proof is well known to the mathematical community. But the shortcomings of the easy answer go deeper than this.
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Maddy, P. (2000). Mathematical Progress. In: Grosholz, E., Breger, H. (eds) The Growth of Mathematical Knowledge. Synthese Library, vol 289. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9558-2_23
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DOI: https://doi.org/10.1007/978-94-015-9558-2_23
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