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OpenAI says its model solved an 80-year-old geometry problem; “tokenmaxxing” spreads at tech firms

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13

Why it matters

OpenAI's internal reasoning model has produced a proof that resolves an open geometry conjecture posed by Paul Erdős in 1946. Human mathematicians have since verified the result. OpenAI is presenting this as the first instance of an AI system autonomously solving a prominent unsolved problem in mathematics. The previous best-known upper bound on the conjecture dated to 1984.

The verification status of the proof and the identity of the mathematicians who confirmed it remain unclear. The technical details of the filing have not yet been made public.

For practitioners, this development cuts two ways. On one hand, it signals a genuine capability frontier—AI systems may now contribute original, peer-verifiable research to fields where human progress has stalled. On the other hand, the result arrives amid a broader industry reckoning with "tokenmaxxing," the practice of measuring AI adoption by token consumption rather than business outcomes. Some firms are already scaling back employee access to third-party AI agents after weak returns on investment. Attorneys advising tech companies should watch whether this mathematical breakthrough shifts the conversation around AI ROI, or whether it remains an outlier in a landscape where token volume continues to diverge from actual productivity gains.

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