July 29, 2026
Prime drama, composite chaos
Theo Conjecture solves 35-year-old math problem, finds a term no one predicted
AI cracks an ancient math puzzle, but the comments section is having a meltdown
TLDR: Theo-Conjecture reportedly solved a decades-old number puzzle and uncovered an unexpected extra term, a big moment for human-plus-AI math work. But the community fixated on a different battle: whether the result is real and whether the article explaining it was unreadable AI mush.
A math story that should have been a clean victory lap turned into a full-on comments-section cage match. The big news: a tool called Theo-Conjecture, working with a human mathematician, reportedly solved a question that had been hanging around since the 1980s and even found an extra piece in the answer that nobody saw coming. In plain English, it looked at a number puzzle about which numbers can sit together without sharing factors, and linked that to counting prime numbers — those indivisible numbers kids meet in school and forget they’ll one day cause internet drama.
But readers were less busy celebrating the breakthrough than dragging the article itself. One of the loudest reactions? “This article appears to be AI-written slop,” a blunt opener that set the mood fast. Another commenter wondered if the whole thing had already face-planted: was this actually just a bug in the solver? Others piled on the writing, saying the explanation was somehow both overstuffed and impossible to follow. Ouch.
Still, not everyone came to boo. A few math-history nerds were delighted to hear about Graffiti, the old program that first posed the question decades ago, and its modern cousin TxGraffiti. And the funniest summary of the whole saga came from one deadpan commenter: “One program makes up questions, another one solves them.” Honestly? That’s either the future of mathematics or the plot of a very niche buddy comedy.
Key Points
- •The article says Theo-Conjecture, an automated discovery system supported by a large language model, was used to revisit a graph-theory question first posed by Graffiti in the 1980s.
- •It states that Theo-Conjecture produced a proof of the answer previously conjectured by Paul Erdős and collaborators, plus an unexpected extra term.
- •The mathematical setup uses a graph on integers 2 through n, connecting numbers that share a factor greater than one.
- •In that graph, the article explains that the largest independent set has size equal to the number of primes up to n, expressed as α(Gₙ) = π(n).
- •The article introduces the residue R(G), computed by the Havel-Hakimi procedure from degree information alone, as a fast lower bound on the independence number and as the basis for the deeper question under study.