# When to say "a proof", "the proof" and just "proof"?

I think Asimov is proof that being prolific is at least as valuable as being talented.

He writes simply is proof. Did he write correctly without an article? In which case would one write is a proof or is the proof?

I've probably seen all three forms of this but I don't know what the meaning of each one of them is. Can anyone explain?

• Mar 2, 2015 at 11:54
• @DanBron I don't believe this is a duplicate, as "a/the proof" is usually used to refer to an entirely different concept from the usage in the OP's example. Mar 2, 2015 at 15:05
• In my experience, I've only ever heard "a proof" in maths. Mar 2, 2015 at 22:14
• For reference, proof is often used as "uncountable", so it is normal to NOT have any "a/an" macmillandictionary.com/dictionary/british/proof_1 Dec 10, 2019 at 10:03

Your friend's sentence is both grammatically and idiomatically correct.

In the sentence you quote, "is proof" is closer in meaning to the verb "proves" than it is to "is {a / the} proof".

In this sense it is a fairly rare type of usage, but "is proof" with the meaning "proves" is a normal expression.

Normally, 'a / one proof' is used where it is acknowledged that there are different sufficient proofs (ie a count noun usage):

One proof of Pythagoras's Theorem uses constructions and congruent triangles. A proof that is easier for many to understand uses tessellations.

'The' can be used with both count (when it makes sense to single out that proof) and non-count usages:

The proof using congruent triangles was the one most usually taught fifty years ago in schools.

The proof of Fermat's Last Theorem is considerably more difficult.

Article-less 'proof' is again a non-count usage, used in more general contexts:

Proof is necessary for a theory to be fully accepted.

His fingerprints in the room are proof that he is lying.

• I think the issue is more using 'proof' to mean 'evidence' than whether or not different 'proofs' are possible. Certainly, additional evidence could be cited in the OP's example case aside from just Asimov (or else the OP's friend's conclusion is extremely weak.) Mar 2, 2015 at 15:22
• The proof = evidence meaning is the primary sense given in all the 6 online dictionaries I've checked in. Thus Collins has: proof n 1. any evidence that establishes or helps to establish the truth, validity, quality, etc, of something. There are many senses besides the 'evidence' and the mathematical 'series of steps to prove' (RHK Webster's gives 13 nounal senses). I've just illustrated count vs non-count examples. Mar 2, 2015 at 15:42
• Yes, I'm just saying that the difference in usage for whether the article is used or not in common usage has more to do with which sense is being used than whether or not multiple 'proofs' are possible. Again, multiple 'proofs' (pieces of evidence) are certainly possible in the case of the OP's example, however, when used in that sense, it still seems more common to exclude the article. Mar 2, 2015 at 15:48
• The issue seems to be whether "proof" must refer to a complete proof (as in mathematics), i.e. something that absolutely establishes the truth of something. In general usage it doesn't always have so strong a meaning, and can refer to a partial proof or evidence towards something. Jun 19, 2022 at 11:59
• "Stuart F Here, it's not the only issue; 'a proof' and 'the proof' both seem to virtually force the more rigorous meaning. Jun 19, 2022 at 15:51

"A/the proof" is most commonly used to refer to an actual formal mathematical construction, i.e. a proof of a mathematical theorem.

As Erik noted, your friend's sentence is correct, but it is the more informal use of the word 'proof,' meaning 'evidence.' When used in this sense, the article is usually excluded.

Really, the word 'evidence' would have been a better choice here, but 'evidence' and 'proof' have unfortunately become conflated in modern usage. I say it is unfortunate because the formal usage actually refers to a related but quite different concept. With a proof (in the formal sense of the word,) if the proof is constructed correctly, it is not possible for the conclusion to be false if the premises on which it is based are true.

Proofs require either deductive reasoning or exhaustive induction to be used. Evidence, on the other hand, can be interpreted to suggest a conclusion, but doesn't actually prove that conclusion to be necessarily true. Such a conclusion is reached via inductive reasoning. This seems to be the case with your friend's assertion.

• " '[T]he proof' is most commonly used to refer to an actual formal mathematical construction ..." Your evidence for this is? I hope you're not speaking as a mathematician, because that may well have obscured your perceptions. The first two pages of results for a Google search don't give supporting evidence for your claim. 'The proof of the pudding is in the eating', for instance, doesn't involve the formal mathematical process. In OP's example, he quite possibly chose 'proof' as a stronger alternative to 'evidence'. He'd already hedged with 'I think'. Mar 2, 2015 at 15:52
• @EdwinAshworth Well, for starters, all of the examples in your answer seem to follow this pattern (using the article when using the formal meaning and excluding it for the informal 'evidence' meaning.) Mar 2, 2015 at 15:57
• 'The proof of the pudding ...' is hardly your 'formal' meaning. 'Now here is the living proof that old Wordsworth was perfectly right.- (Internet) is obviously the 'evidence' sense. Mar 2, 2015 at 17:04
• @EdwinAshworth I agree that that idiom would be a counter-example. More generally, the informal meaning could be used as "the proof" to mean "all of the evidence," but, at least in my experience, that doesn't seem to be a terribly common usage. My experience is with U.S. English usage, though, so perhaps U.K. usage is different from what I'm used to (though the most recent comment on the question would suggest that it is not.) Mar 2, 2015 at 22:18