Checking the math behind OpenAI and Anthropic’s latest headlines

2025-06-07 · Source: Marcus on AI · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Emerging Technologies & Innovation, Corporate Strategy & Leadership · Depth: Intermediate, medium

Summary

OpenAI recently announced a breakthrough in mathematics, disproving an 80-year-old conjecture by Paul Erdős regarding the planar unit distance problem. A new, unreleased reasoning model, utilizing "chain-of-thought" reasoning, identified a counterexample, which mathematicians then formalized into a proof. Cal Newport's analysis suggests the model's success stems from systematically exploring paths humans might dismiss, combining "superhuman levels of patience with familiarity with a vast array of technical machinery." However, he notes this might be more for marketing the model's power than advancing computer-aided math, given the niche market of academic mathematics. Separately, Anthropic projects its first profitable quarter, though this is attributed to a nonrecurring compute discount from SpaceX, raising questions about sustained profitability. Nvidia's financials also show concern, with approximately 95% of its operating cash flow absorbed by circular financing, up from 57% a year ago, leading to minimal cash growth.

Key takeaway

For AI Directors evaluating new model capabilities, you should view recent AI math breakthroughs with nuanced skepticism. While models like OpenAI's demonstrate systematic problem-solving, their real-world applicability beyond niche academic fields and the true cost of operation remain unclear. Scrutinize vendor claims, especially financial projections, for one-time benefits or circular financing that may obscure underlying economic realities. Focus on verifiable performance across diverse benchmarks relevant to your specific business needs.

Key insights

OpenAI's new reasoning model disproved an 80-year-old math conjecture by systematically exploring overlooked solution paths.

Principles

• LLMs excel at systematic, patient exploration.
• AI tools augment human capabilities, not replace them.
• Generalize AI math breakthroughs cautiously.

Method

OpenAI's unreleased reasoning model used "chain-of-thought" reasoning to generate a long transcript, from which mathematicians extracted and formalized a counterexample proof.

In practice

• Apply LLMs to systematically explore complex problem spaces.
• Combine AI with human expertise for rigorous validation.
• Scrutinize financial claims for nonrecurring factors.

Topics

• AI in Mathematics
• Large Language Models
• Chain-of-Thought Reasoning
• Financial Analysis
• OpenAI
• Anthropic

Best for: Research Scientist, AI Scientist, Director of AI/ML, Investor

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Editorial summary, takeaway, and curation by AIssential. Original article published by Marcus on AI.