3201: Proof Without Content
| Proof Without Content |
 Title text: There's also a proof without content of a conjecture without content, but it's left as an exercise for the reader. |
Explanation
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This is one of 61 incomplete explanations: This page was created as an exercise for the reader. Don't remove this notice too soon. If you can fix this issue, edit the page! |
This comic refers to a proofs without words, which rely on images or other geometric tools to visually demonstrate a concept without further explanation. The comic gives an example of a proof without any content at all, which proves its own existence.
This proof requires the conjecture to be stated, which could be construed as content.
This can also be a parody on scientists doing empty papers sometimes as an inside joke, such as a comprehensive overview of chemical-free consumer products.
The title text refers to another proof without content, that a conjecture without content could exist. This would imply a conjecture-proof pair with no content whatsoever. This could only be discussed indirectly, which is why it is mentioned and left as an exercise for the reader. Alternatively, the exercise could be forming the conjecture and proof itself if the comic is interpreted as a blank sheet of paper.
Transcript
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This is one of 41 incomplete transcripts: Don't remove this notice too soon. If you can fix this issue, edit the page! |
- [Within a panel, two boxes stacked vertically. Each one has a label above it.]
- Conjecture:
- [Within the box]
- It's possible to construct a convincing proof without words, pictures, or content of any kind.
- [The next label]
- Proof:
- [The box underneath this label is empty.]
- [Caption under the panel]
- Proofs without words are cool, but we can go further.
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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
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.
- 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)
- You must be very smart. 2600:1700:2120:5880:C885:5DAF:EFD8:EADF 22:12, 30 January 2026 (UTC)
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)
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)
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