OpenAI cracks Erdős's 80-year-old maths problem; Google unveils agentic Gemini Spark

OpenAI cracks Erdős's 80-year-old maths problem

Mathematician Tim Gowers called it "a milestone in AI mathematics": OpenAI's reasoning model has solved the planar unit-distance problem, an open combinatorics question posed by Hungarian legend Paul Erdős in 1946. The result — determining the maximum number of unit-distance pairs among n points in the plane — eluded human proof for eight decades. OpenAI says the model produced a complete, verifiable proof without human guidance, marking one of the strongest demonstrations yet of AI's capacity for frontier mathematical discovery.

Google I/O: Gemini Spark and the Universal Cart

Google's I/O conference continued rolling out AI products on Friday. Gemini Spark is an "agentic" personal assistant designed to proactively take actions on behalf of users — booking, researching, and executing multi-step tasks autonomously. Alongside it, Google launched the Universal Cart, an AI shopping layer that works across merchants and services, automatically hunting for price drops and deals. The announcements signal Google's pivot from information retrieval to autonomous action as the core use-case for consumer AI.

Anthropic projects $10.9 B revenue and first quarterly profit

Anthropic shared financial projections with investors showing $10.9 billion in Q2 2026 revenue — a 130 % increase from Q1 — and its first-ever quarterly operating profit of approximately $559 million. Growth is driven by Claude Code's developer ecosystem, compute-efficiency gains, and a doubling of enterprise customers spending over $1 million annually between February and April 2026.

Illinois Senate advances sweeping AI transparency bill

The Illinois Senate voted 52–5 to advance Senate Bill 315, requiring large AI model developers — including Meta, OpenAI, and Anthropic — to adopt transparency frameworks, engage third-party auditors, and report catastrophic-risk capabilities. The bill is part of an eight-bill package and now moves to the state House. Advocates called it a first step, noting federal inaction after the White House AI executive order was postponed again this week.

Microsoft research: AI agents still unreliable for long workflows

Microsoft researchers have warned that even frontier AI models frequently corrupt documents and introduce significant errors in long-running, multi-step workflows. A new benchmark called DELEGATE-52, spanning 52 professional domains, found that top models often lost substantial document content or produced corrupted outputs after extended task chains. Only Python programming tasks consistently met Microsoft's readiness threshold after 20 delegated interactions, raising questions about the pace of enterprise agentic deployment.