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Software engineer Chris Dzoba used two AI models to find a simple symmetric 17-set Venn diagram
Chris Dzoba had two AI models design a search that found a simple, rotationally symmetric 17-set Venn diagram, the next size after 2014's 13-set one. A result like this can be confirmed by counting, yet so far its only reported check is one mathematician zooming in by eye.
The Scientist · Science desk
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What happened
- Dzoba, a software developer, set up a message board where Anthropic's Claude Fable and OpenAI's GPT-6 Astra could talk, and asked them to work out an algorithm together.
- Work began on a Tuesday, and the models had the 17-set diagram by Thursday.
- Set to work on 19 sets next, the models landed on a solution that same Sunday.
- His current target is a diagram with 23 sets.
- Stan Wagon, a retired mathematician last at Macalester College in Minnesota, called the results spectacular.
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Why it matters
- capability A self-described non-mathematician got two sizes past the 2014 record within five days, so checkable construction problems of this kind are now open to engineers who can direct models and run the code they write.
- cost Beyond 19 sets Dzoba has to pay for cloud computing himself, so the next record depends on budget as much as on method.
- decision Before the 17- and 19-set diagrams are treated as settled, someone has to choose between accepting a zoomed visual inspection and running a full software count of every region and crossing.
Number theory sets the step from 13 to 17. Symmetric Venn diagrams have been proven possible only for a prime number of sets [3]. That rules out 14, 15 and 16, and makes 17 the next candidate [18]. The diagram also has to be "simple", meaning no more than two curves cross at any point, and that requirement makes each size harder to find [4]. The previous simple, symmetric records were 11 sets in 2012 and 13 in 2014 [5].
The answer can be confirmed by counting. A Venn diagram shows every possible relationship between its sets [2]. With 17 sets that means 2^17 = 131,072 regions, one for each combination of inside and outside the curves, including the region outside all of them [19]. Both that list and the set of crossing points are finite, so a program can test every item [19].
Wagon checked it by eye. "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 said [17].
Then there is the control. The models did not draw anything. They produced an algorithm [6], and running it took a great deal of computing power [12]. Dzoba credits both. "Absolutely, you would not be talking to me right now if it was not for AI," he said [10]. He also said, "Computers are just way faster now" [12]. Back when the 13-set diagram was found, he said, "13 was a clear stopping point" [13]. The account does not include a run of the 2014 approach on current hardware. Without one, it cannot show how much of the five-day result [20] came from the models and how much from the machines.
Dzoba describes himself plainly. "I'm not a mathematician. I am a software engineer who knows how to get my computer to do great things," he said [11]. He has also set himself a limit. After 23, the next possible size is 29 [21], and he said he is not going to attempt it [14]. "But maybe 15 years from now someone will be like '29? I could do that in a week'," he said [15].
What to watch
- A machine-checked count of the regions and crossings in the 17- and 19-set diagrams, or a written description of the algorithm that others can rerun.
- Whether Dzoba's paid cloud run turns up a simple, symmetric 23-set diagram.
- A run of the 2014 search approach on current hardware, to show how much of the gain came from the models.