Can I quantify the word "proof", so is it possible to write the phrase many proofs and if yes in which situation is this more appropriate than writing much proof?


Yes, proof can be quantifiable. One obvious context is the realm of mathematics, where there may be more than one proof of a theorem. So, for example, one could say:

There aren't many proofs for the four-colored map problem.
Many early proofs of Fermat's last theorem were found to contain errors.

On the other hand, proof is sometimes used in a way similar to evidence. (One might argue that evidence would be a better word to use in such situations, but the fact remains that proof is nevertheless used.) For example, in this science editorial, the author wrote:

There is much proof that Mars was once, if not a green planet, a planet that once held flowing water and possibly life.

Both can be used; it really depends on if you're talking about a body of evidence or individual proofs.

As a footnote, other usages of the word proof are clearly quantifiable, such as:

The photographer gave us nine proofs to choose from.

  • Good photo proof example -- I hadn't recalled the use "an advanced copy for checking." – JeremyDouglass Dec 13 '16 at 9:40
  • The author of the second citation should not have written "once" twice. Other trivium: a proof with an error is not a proof, so the "many early proofs" in the first citation were in fact none. – Marc van Leeuwen Dec 13 '16 at 14:31
  • @Marc - I considered putting "proofs" in scare quotes for that reason. (I debated it for a couple minutes, actually.) In the end, though, I opted for simplicity, as have many authors before me. – J.R. Dec 13 '16 at 15:28
  • I believe it is the four color theorem. The map problem is "how many colors?" The theorem is "four." Someone proves a theorem, not a problem: you could prove "P=NP", but cannot prove "the P vs. NP problem." Funny that we chose the same example. – JeremyDouglass Dec 13 '16 at 17:20
  • @JeremyD - I think it can be called either one. Perhaps some of us old geezers inadvertantly fall back on problem because we remember when it was still unproven :-) – J.R. Dec 13 '16 at 18:13

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