Time and periodicity from Ptolemy to Schrödinger: paradigm shifts vs continuity 
in history of mathematics

Manin, Yuri I.

doi:10.1007/978-3-030-13609-3_3

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Time and periodicity from Ptolemy to Schrödinger: paradigm shifts vs continuity in history of mathematics

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Manin, Yuri I.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/978-3-030-13609-3_3
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arXiv:1812.00364.pdf
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Citation

Manin, Y. I. (2019). Time and periodicity from Ptolemy to Schrödinger: paradigm shifts vs continuity in history of mathematics. In S. Dani, & A. Papadopoulos (Eds.), Geometry in history (pp. 129-138). Cham: Springer.

Cite as: https://hdl.handle.net/21.11116/0000-0007-8D5D-3

Abstract

I briefly consider the Kuhnian notion of "paradigm shifts" applied to the
history of mathematics and argue that the succession and intergenerational
continuity of mathematical thought was undeservedly neglected in the historical
studies. To this end, I focus on the history of mathematical theory of time and
periodicity, from Ptolemy's epicycles to Schroedinger's quantum amplitudes
interference and contemporary cosmological models.