The Memo - Special edition - First ASI indicators achieved (#4 & #5 mathematics) - 20/May/2026
Items #4 & #5 (‘First major new mathematical proof’ & ‘First major mathematical conjecture resolved’)
To: US Govt, major govts, Microsoft, Apple, NVIDIA, Alphabet, Amazon, Meta, Tesla, Citi, Tencent, IBM, & 10,000+ more recipients…
From: Dr Alan D. Thompson <LifeArchitect.ai>
Sent: 20/May/2026
Subject: The Memo - AI that matters, as it happens, in plain English
AGI: 97%
ASI: 2/50OpenAI internal model checks first ASI checklist items
Today, we have witnessed a general large language model provide a new mathematical proof resolving a long-standing, major, open problem. I’m marking these indicators (new proof, resolved conjecture) as the first full achievements on Alan’s ASI checklist.
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 (UoT):
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 announce, 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 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.
Here is how OpenAI’s achievement satisfies each of those specific milestones:
#4: First major new mathematical proof. The OpenAI reasoning model autonomously generated a rigorous, novel mathematical proof that was thoroughly vetted and verified by leading external mathematicians, including Fields Medalist Prof Tim Gowers. The model constructed a complex logical argument that holds together from beginning to end.
#5: First major mathematical conjecture resolved. The AI successfully resolved the planar unit distance problem, a famous open problem in combinatorial geometry first posed by Paul Erdős in 1946. For decades, mathematicians widely believed and conjectured that the maximum number of unit-distance pairs followed a specific upper bound tied to a square grid. The model decisively disproved this 80-year-old conjecture by finding an infinite family of counterexamples that yield a polynomial improvement.
Read Alan’s ASI checklist: https://lifearchitect.ai/asi/
View the ASI checklist sheet.
All my very best,
Alan
LifeArchitect.ai