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." - Meaning and context.">
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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
“

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.

— André Weil

What It Means

This is a placeholder explanation generated by the low-overhead model. It interprets "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." in the context of "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" to mean that wisdom is timeless.

Source: Wikiquote: "André Weil" (Quotes) The 'What it means' explanation text was generated by Google Gemini Flash (accessed January 18, 2026). https://gemini.google.com/app

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André Weil

About André Weil

André Weil (6 May 1906 – 6 August 1998) was one of the greatest mathematicians of the 20th century, whether measured by his research work, its influence on future work, exposition or breadth. He is known for his foundational work in number theory and algebraic geometry. He was a founding member, and de facto the early leader, of the influential Bourbaki group. The philosopher Simone Weil was his sister.