Artificial Super Intelligence.
China: 90 million empty or unfinished apartments.
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An internal general OpenAI model has autonomously disproved Paul Erdős’ planar unit distance conjecture (1946), an 80-year-old central open problem in combinatorial geometry. The model constructed an infinite family of point sets achieving n^(1+δ) unit-distance pairs (Will Sawin later showed δ=0.014), overturning the long-held belief that rescaled square grids were essentially optimal. The proof bridges algebraic number theory (infinite class field towers, Golod–Shafarevich theory) to elementary geometry. Verified by external mathematicians including Fields medalist Tim Gowers, who called it ‘a milestone in AI mathematics.’ According to leading number theorist Prof Arul Shankar (University of Toronto):
In my opinion this paper demonstrates that current AI models go beyond just helpers to human mathematicians – they are capable of having original ingenious ideas, and then carrying them out to fruition.
Read the OpenAI announcement, read the proof, read the companion paper.
No one wants to say it, so I will. While definitions keep shifting and goalposts move again and again, the evidence is clear: when a system outthinks our brightest human minds on problems human experts couldn’t solve, we’ve entered ASI (Artificial Super Intelligence) territory.
OpenAI’s internal model represents early ASI capabilities, though the truly transformative superintelligence systems are still ahead. History will mark this moment (20 May 2026) as the first publicly visible ASI achievement. (Sources: openai.com, lifearchitect.substack.com, substack.com, ams.org, ias.edu )
2. Interesting Engineering:
Thomas Bloom, one of the mathematicians involved in the companion work, said the discovery suggests deep number theory may hold answers to several unsolved questions in discrete geometry. He added that many mathematicians will likely revisit older problems using these newly revealed connections.
The result also highlights how rapidly AI reasoning systems are evolving. Unlike specialized theorem-proving software, OpenAI said this proof came from a general-purpose reasoning model. Engineers did not specifically train it on the unit distance problem or build dedicated search tools for this task.
That detail matters because it hints at broader scientific applications. Researchers believe systems capable of managing long chains of reasoning could eventually assist in fields such as physics, biology, engineering, and medicine.
For now, the unit distance breakthrough stands as a landmark moment. A problem that resisted human effort for nearly eight decades fell to an AI system that approached geometry from an entirely unexpected direction. (Sources: thomasbloom.org, interestingengineering.com)
3. Chris McGuire:
Artificial intelligence (AI) policy will be the most important issue in the 2028 U.S. presidential election. To most Americans, that statement probably seems absurd. AI policy was a total nonfactor in the 2024 presidential election. It does not even appear on Gallup’s latest tracking poll of the most important issues to American voters.
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