Benjamin Peirce on Euler’s Identity

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I love this quotation from Benjamin Peirce (1809-1880):

“It is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth.”

— Benjamin Peirce (after proving Euler’s Identity in a lecture)

It gets to the heart of mathematical epistemology: that there is a certainty in mathematical truths that exceeds the certainty of most other kinds of knowledge, even when the results are mysterious to us.

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