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I remember reading that Jacobi once said:

If Cauchy says he proved something, you can be 50% sure that he actually did. If Gauss says he proved something, you can be mostly sure that he actually did. But if (insert name) says he proved something, then you can be 100% sure that he actually did.

Does someone remember the exact names and the exact quote? Thanks!

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I suppose that you have this quotation in mind:

“Dirichlet alone, not I, nor Cauchy, nor Gauss knows what a completely rigorous mathematical proof is. Rather we learn it first from him. When Gauss says that he has proved something, it is very clear; when Cauchy says it, one can wager as much pro as con; when Dirichlet says it, it is certain…”

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    $\begingroup$ Ironic, considering the story of the "Dirichlet principle". $\endgroup$ – Conifold Jan 12 '20 at 11:38
  • $\begingroup$ Yeah I meant this exact quote, thanks! $\endgroup$ – user600210 Jan 12 '20 at 11:41
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The original is in a letter from Jacobi to Alexander von Humboldt dated December 21, 1846:

Dirichlet allein, nicht ich, nicht Cauchy, nicht Gauß, weiß, was ein vollkommen strenger Beweis ist, sondern wir lernen es erst von ihm. Wenn Gauß sagt, er habe etwas bewiesen, so ist es mir sehr wahrscheinlich, wenn Cauchy es sagt, ist ebensoviel pro als contra zu wetten, wenn Dirichlet es sagt, ist es gewiß; ich lasse mich auf diese Delikatessen lieber gar nicht ein.

(Source: Laugwitz's book about Riemann, p. 63.)

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    $\begingroup$ It's interesting that Jacobi uses the word "wahrscheinlich" to describe Gauss' proofs. Jose Carlos Santos' answer has this translated as "very clear" but I think a better translation could be "very plausible", i.e. describing the strength of the logic, as opposed to the eloquence of the argument. Also, the last sentence that is missing from the English translation states "I prefer not to get involved in these delicate matters at all". $\endgroup$ – Jam Jan 13 '20 at 17:24

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