Difference in nuance between 証明 and 証拠?

I know that both of these words mean "proof", but I can't figure out what the difference is, or if there's any at all. Can anyone explain to me the difference in nuance between these two words?

Answer

証明 is used for conceptual proof, e.g. in the mathematical sense.

証拠 is substantial proof in the sense of evidence, like evidence used in court, e.g. as in the phrase

証拠で裏付けられる
to be backed by evidence