3201: Proof Without Content

2026-02-02T03:01:26Z

2A02:8071:5C20:40:C847:3E55:BD72:7D3F:

{{comic
| number = 3201
| date = January 30, 2026
| title = Proof Without Content
| image = proof_without_content_2x.png
| imagesize = 259x353px
| noexpand = true
| titletext = There's also a proof without content of a conjecture without content, but it's left as an exercise for the reader.
}}

==Explanation==
{{incomplete|This page was created as an exercise for the reader. Don't remove this notice too soon.}}

This comic refers to a {{w|Proof without words|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. Note that this conjecture cannot be generalized and the proof only proves this special case: the vast majority of all other conjectures cannot be proven without lack of content.

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 [https://ciencias.ulisboa.pt/sites/default/files/fcul/outros/Chemical-Free.pdf a comprehensive overview of chemical-free consumer products] – the point with that paper being that the {{wiktionary|chemical#Usage notes|lay meaning}} behind "chemical-free" can be considered technically nonsensical given that anything physical contains chemical elements, so no products can be free of them. (And, even in the various more vague senses that may be intended, it {{w|Appeal to nature#Examples|isn't necessarily}} as good a selling point as it may try to suggest.)

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 {{w|Proof by Intimidation|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==
{{incomplete transcript|Don't remove this notice too soon.}}

:[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.

{{comic discussion}}<noinclude>
[[Category:Math]]

explain xkcd - User contributions [en]

3201: Proof Without Content