I recently had an exhibition in a small alternative art gallery in Geneva (Le Labo), and I took the opportunity to show three abstract comics that I recently made in which I try to convey the ideas of a mathematical proof into a totally wordless comic. I had already posted such a comic here in 2009, as you might recall:
A lot of mathematical "proofs without words" do exist (there are even two books published containing the "best" ones), where mathematical results are proved using figures (single ones or a sequence), but there is almost always some kind of notation introduced into the figures to make the proof understandable. And of course, it is assumed that the reader has some kind of mathematical education, so as to understand the implicit steps of the proof.
My aim was to try to see whether the "intrinsic power of the sequence" (so to say) was enough to get rid of any kind of use of letters or typographical symbols, and to really break down the proofs in sufficiently many steps so that anybody, without mathematical education beyond "mandatory school" (I don't know how to call it, in Switzerland, it means roughly up to 15 years old), could in principle understand the proof. Of course you'd have to have some inclination towards abstract reasoning to really go through the whole story, but I tried to make it as self-contained as I could. But actually even my mathematicians friends had problems to really follow the reasoning, so I probably failed badly in my attempts.
Anyway, I thought it could be of some interest for the people here, so I post some pictures of these three pieces. I am really a terrible photographer and one of the pieces is like 2 meteres long, so it's impossible to really read anything, but at least it gives an idea of what I'm talking about.
The first piece is almost identical to my 2009 post and shows a proof of Pythagore's Theorem due to Thabit Ibn Qurra (826-901).
The second is a proof of an identity for sums of cubes:
And the third one is a comic rendering of a very nice proof of a theorem in "elementary" geometry that is due to Roger B. Nelsen. This theorem has the astonishing particularity of being both rather new (it was discovered in 2004) and quite simple (if you compare it with today's research).
By the way, I was inspired by an incredible book of 1847 recently re-edited by Taschen: The elements of Euclid by Oliver Byrne. Anyone interested in abstract comics and/or mathematics should at least have a look at it: