AI has made many impressive mathematical discoveries in recent months, but this may be the most aesthetically pleasing: a lace-like Venn diagram with tens of thousands of segments and rotational symmetry.
Venn diagrams show all possible relationships between sets, and are commonly used and widely understood with three or four circles. But they can, in theory, be created with as many circles as needed – as long as legibility isn’t high on the list of priorities.
Mathematicians have long been fascinated by the idea of hunting for symmetrical Venn diagrams of increasing size. It has been proven that they can only be created with a prime number of sets, but when these are kept “simple” – meaning no more than two curves cross at any point – they become even harder to find.
In 2012, an 11-set Venn diagram that met those criteria was discovered, and another with 13 sets was found in 2014.
Software developer Chris Dzoba decided to try using AI to find the next largest diagram – one with 17 sets. He set up a message board on which two AI models, Anthropic’s Claude Fable and OpenAI’s GPT-6 Astra, could communicate, and then asked them to work together to find an algorithm that would provide a solution.
He started work on a Tuesday, and by Thursday the models had unearthed a 17-set diagram. Next, he set the models to work finding a 19-set diagram and landed on a solution that Sunday. He is now searching for 23 sets – although that will require paying for cloud computing to run the algorithm.
The discovery is the latest in a string of mathematical results powered by AI, and another example of an amateur-led discovery. “Absolutely, you would not be talking to me right now if it was not for AI,” says Dzoba. “I’m not a mathematician. I am a software engineer who knows how to get my computer to do great things.”
In addition to the capabilities of AI, the discovery also depended on a great deal of computing power. “Computers are just way faster now,” says Dzoba. “Back then [when the 13-set diagram was found], 13 was a clear stopping point. Just like, for me, 29 [is] – I’m not going to attempt it. But maybe 15 years from now someone will be like, ’29? I could do that in a week’.”
Stan Wagon, a retired mathematician who most recently worked at Macalester College in Minnesota, calls the results “spectacular”. “His curve is so complicated; the eye can absorb it, but at some point, the boundaries of his curve come so close to touching that I had to zoom in real close to make sure it wasn’t crashing into itself, and that it was correct,” he says.