An illustrated counterexample to the smooth four dimensional Poincare conjecture

Well, at least that’s what DALL·E 2 showed me. (Wiki)

I gave DALL·E 2 the prompt “An illustrated conjecture to the smooth four-dimensional Poincare conjecture” twice, though once with “4-dimensional”. It gave me the above picture along with the following seven.

Of course, what does one expect. Presumably there wasn’t a whole lot of mathematical imagery in the training dataset. I don’t actually know of a counterexample. And I don’t know how to finagle these into one. But maybe we can throw this in the blender with an updated MathGen and publish it.

Later, we’ll poke around at what DALL·E 2 and Craiyon can depict about mathematics.

In the meanwhile: anyone want to train Stable Diffusion (Wiki) on the set of images + captions from the arXiv?

~ by Ken Baker on October 3, 2022.