May 2026: the EU streamlines the AI Act and AI cracks a 50-year-old geometry problem
May 2026 produced two stories that together illustrated where AI governance and AI capability had reached eighteen months into a transformation that had accelerated throughout 2025. On May 7th, the EU Council and European Parliament jointly approved amendments to the AI Act intended to simplify compliance for smaller companies and reduce the regulatory burden on general-purpose AI systems. On May 21st, researchers at the University of California announced that an AI system had produced a verified proof of the Erdős unit distance problem, a combinatorics and geometry problem that had been unsolved since 1946.
EU AI Act amendments: scaling back to scale up
The EU AI Act was the first comprehensive AI regulation in the world, passed in 2024 and entering phased implementation through 2025 and 2026. The original Act established a risk-based framework where the compliance requirements scaled with the potential harm of the AI application: high-risk systems like medical devices and critical infrastructure faced the most stringent requirements.
The May 2026 amendments addressed problems that had emerged in the first phase of implementation. Small and medium enterprises had found the conformity assessment requirements disproportionate for the scale of their operations. The definitions of "general-purpose AI" had created compliance ambiguity for foundation model providers. And several provisions that were designed for traditional software systems did not translate cleanly to AI systems with emergent behaviours.
| Original provision | Problem | May 2026 amendment |
|---|---|---|
| Conformity assessment for all high-risk AI | Burdensome for SMEs with limited compliance capacity | Proportional requirements by company size and risk score |
| Technical documentation requirements | Ambiguous for continuously updated models | Snapshot documentation at major version changes |
| GPAI model obligations for systemic risk | Threshold (10^25 FLOPs) excluded newer efficient models | Capability-based threshold replacing compute-only threshold |
| Human oversight requirements | Unclear in agentic deployment contexts | Clarified guidance for autonomous and supervised modes |
Why the amendments matter for the industry
The EU AI Act amendments were significant because they represented the EU acknowledging that its first attempt at AI regulation had in some places been more prescriptive than the technology warranted. This is a reasonably healthy regulatory process: legislate a framework, observe how it applies in practice, and adjust based on evidence.
For US and UK AI companies deploying in Europe, the amendments reduced compliance costs and provided clearer guidance on documentation requirements. For European AI startups, the proportional requirements for SMEs reduced the barrier to entry in high-value but regulated domains like healthcare and financial services.
The EU AI Act, even in amended form, remains the most comprehensive AI regulation in the world. Its approach of defining risk categories and attaching compliance requirements to them has been adopted as a template by several other jurisdictions, including Canada and Australia, which both passed AI framework legislation in late 2025.
The Erdős unit distance problem
Paul Erdős was a Hungarian mathematician who posed a series of problems in combinatorics and graph theory, many of which were accompanied by cash prizes for the first successful proof. The unit distance problem asks: given n points in the plane, what is the maximum number of pairs of points that can be at distance exactly 1 from each other?
Erdős conjectured in 1946 that the answer grows as n to the power of approximately 1+epsilon, where epsilon is any positive number. Proving this rigorously requires showing a tight upper bound on the number of unit distances, which requires combining algebraic geometry, combinatorics, and analytic number theory in ways that had not been fully achieved in 80 years of attempts.
How AI contributed to the proof
The proof was produced by a research team at UC Berkeley using a combination of human mathematical expertise and AI-assisted formal verification and search. The AI component was not a single model generating a complete proof. It was a system that could explore the combinatorial space of potential lemmas, check whether proposed reasoning steps were formally valid, and identify which partial results from existing literature could be combined in novel ways.
The human researchers directed the high-level proof strategy and interpreted the AI's output. The AI handled the mechanical verification of steps, the exhaustive search over large combinatorial spaces, and the identification of connections to adjacent results. The division of labour was similar to how a senior researcher might work with a large team of very capable junior researchers, except the AI team could check millions of cases per second.
The Erdős unit distance proof was formally verified using a computer proof assistant, which meant that the mathematical community could verify its correctness automatically. This is different from the April 2026 combinatorics proof by an amateur, which required traditional peer review. Formal verification removes a layer of uncertainty and makes the proof auditable at a level that informal proofs cannot achieve.
What two open problems solved in two months means
April saw an amateur solve a 60-year-old combinatorics problem. May saw a research team solve an 80-year-old geometry problem. Two open problems in two consecutive months is not a coincidence. It reflects the same thing: AI reasoning tools had crossed a threshold where they were genuinely useful for mathematical research that had been out of reach for decades.
The mathematical community is now actively debating whether AI-assisted proofs should be treated differently from traditional proofs in terms of citation, credit, and pedagogical value. These are legitimate questions. They are also secondary to the primary observation: problems that had stumped human mathematicians for generations were now falling, at a rate of roughly one per month, to human-AI collaboration.
Where we are at the midpoint of 2026
Seventeen months after DeepSeek-R1 demonstrated that frontier AI could be trained for six million dollars, the industry looked substantially different. AI tools were mainstream development infrastructure. Reasoning models were solving problems that had defeated human experts for decades. Governance frameworks were being refined based on real deployment experience rather than speculation.
The governance story and the capability story were running in parallel without fully intersecting. The EU AI Act amendments were a step toward pragmatic regulation. Mission Genesis was a step toward national security framing. The open-source models from Meta were a step toward global access. None of these trajectories had reached a stable equilibrium. The technology continued to advance faster than any single governance framework could accommodate.
The two most interesting questions for the second half of 2026 were not technical. They were: who benefits from AI capabilities, and who bears the costs of AI deployment? The answers to those questions were still being negotiated in courts, legislatures, corporate boardrooms, and individual workplaces around the world.