Talk:3201: Proof Without Content

First. Would be funny to have an explanation along the lines of "It is possible to give an explanation with no content. Here's how:" R128 (talk) 17:44, 30 January 2026 (UTC)

Proof without Content seems to be a play of words for [1]Proof without Words 2001:16b8:b583:2500:4d66:4f4e:17e2:34f1 (talk) 17:50, 30 January 2026 (UTC) (please sign your comments with ~~~~)

The comic pokes fun at a common situation found in mathematics books. The students sees a statement with a very short proof that doesn't make sense since it's been summarized in a way that is helpful for people already familiar with the theorem. For instance: "prime numbers larger than 2 are odd". Proof: "even numbers are divisible by 2". The student is expected to know that a number divisible by 2 is not prime, but that's most likely something that comes up later in the same book, or sometimes not explained at all. In the comic the "short" proof is taken to the absurd level of being completely empty. What mathematical statement can be proven with a completely empty proof? The fact that there exists comics which have statements with empty proofs. It is both a joke about difficult to understand proof in math books and also a meta-mathematics joke as the proof is talking about itself. The title text pokes even more fun at maths books where many important theorems are stated and are given to the students as useful facts but with no proof, stating that demonstrating the truth of the statement is so easy it is "left as an exercise for the reader". This common scenario frustrates students because in some cases the "exercise" is extremely difficult to do. The only "proof without content of a conjecture without content" is a blank page altogether, which clearly exists, so the statement is true, even if meaningless. 104.28.199.245 (talk) 17:58, 30 January 2026 (UTC) (please sign your comments with ~~~~)

I really do not get that title text. I put an attempt at understanding it down but it may have gone over my head R128 (talk) 17:58, 30 January 2026 (UTC)

I don't recall that problem with such a proof. Usually the statement about primes being odd comes after giving the definition of prime and composite numbers. From that, being divisible by 2 clearly makes a number composite. Barmar (talk) 19:31, 30 January 2026 (UTC)

A number being divisible by two proves that a number that is not two is composite. You still have to prove that the number you first thought of is not two.76.180.39.133 05:02, 1 February 2026 (UTC)

You must be very smart. 2600:1700:2120:5880:C885:5DAF:EFD8:EADF 22:12, 30 January 2026 (UTC)

The comic demonstrates a proof without content, but is it a convincing proof? Barmar (talk) 19:33, 30 January 2026 (UTC)

If it is, then yes. QED. ;) 81.179.199.253 21:14, 30 January 2026 (UTC)

I think the tautological nature of the proof could be better explained. If the blank image is interpreted as a correct proof, it proves the notion that a blank image can prove a conjecture. 2600:4041:2E5:B900:6C41:5AFB:89D1:F216 22:11, 30 January 2026 (UTC)

Isn't this proof using circular reasoning? The proof is only convincing if the conjecture that an empty proof can be convincing is correct. 73.222.207.213 23:26, 30 January 2026 (UTC)

Yeah, it is a circular argument. Maybe that’s part of the joke? Logalex8369 (talk) 01:39, 31 January 2026 (UTC)

I say it's only circular reasoning if it's circular reasoning. 81.179.199.253 02:01, 31 January 2026 (UTC)

Yes, it really begs the question... 136.47.216.1 03:42, 31 January 2026 (UTC)

This space provably left blank Hcs (talk) 09:13, 31 January 2026 (UTC)

I see what you didn't there. Martin (talk) 21:21, 1 February 2026 (UTC)

The only problem I see here is that the "conjecture" should be called "theorem". In a mathematical paper, statements for which you are about to present a proof are called "theorems," not "conjectures." Conjectures are statements made without proof which the author expects to be true and provable. I would expect something like "Theorem 1.1. There is an empty proof of a non-vacuous theorem." Then it would be followed by an empty line, then "Proof." another empty line, and finally nothing. (That said, this isn't really a proof of anything. If I assert that it is not a proof, how can you demonstrate that I am wrong? Only if I accept that it is a proof does it become a proof. It's one of those natural language paradoxes like "this statement is true.") EebstertheGreat (talk) 22:31, 31 January 2026 (UTC)

I am not convinced. Commercialegg (talk) 18:51, 1 February 2026 (UTC)

If the empty box (or just it’s empty content) is a proof in the first place, then it is a convincing proof of the conjecture that a proof can have no content, and hence, since it is a convincing proof, and it has no content, it is a proof of the conjecture that a convincing proof can have no content. But is it a proof in the first place? Well, maybe it is a proof that something with no content -- the purported proof -- can be referred to! Gorzog63 (talk) 06:30, 3 February 2026 (UTC)