"An important point is that the p-adic field, or respectively the real or complex field, corresponding to a prime ideal, plays exactly the role, in arithmetic, that the field of power series in the neighborhood of a point plays in the theory of functions: that is why one calls it a local field."
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as translated by Martin H. Krieger "A 1940 letter of André Weil on analogy in mathematics." Notices of the AMS 52, no. 3 (2005) pp. 334–341, quote on p. 340
https://en.wikiquote.org/wiki/Andr%C3%A9_Weil
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André Weil
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