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Why the Legendary Erdős Problems Are Falling to AI
Reports that an AI model found a counterexample disproving a 1946 Erdős conjecture.
Quanta MagazineAug 2026
28 pieces that cleared seventy. Ordered by how far each sits from the centre of this catalogue.
Reports that an AI model found a counterexample disproving a 1946 Erdős conjecture.
Challenges the reflex to blame every problem on incentives, offering a counter-thesis and mechanism.
Asks whether AI 'reasoning' models reach correct answers through fundamentally flawed processes.
Argues that LLM capabilities stem mainly from imitative learning rather than reinforcement learning.
Explains how identifying the single highest-leverage question reframes complex problems.
Catalogs a personal set of recurring problem-solving techniques distilled from clever solutions.
Argues that second-order effects shape outcomes more than first-order ones and deserve deliberate attention.
Explains resulting bias, the tendency to judge decision quality by outcomes rather than the process.
Shares 88 questions written to encourage long-term thinking, used to shape the Long Now Foundation.
Explains why most advice fails, distinguishing generic bromides from guidance that's genuinely actionable.
Describes building a house by delaying decisions and adding only what turns out to be needed.
Extends an earlier argument that risk-taking and rule-breaking have declined since the 1990s.
Argues that new tools, not just ideas, have driven history's biggest leaps in scientific understanding.
Lays out the S.P.A.D.E. framework as a structured method for making and communicating decisions.
Continues a debate over whether liberalism failed to deliver happiness despite economic progress.
Traces the second-order and third-order consequences that follow from the shift to automobiles.
Weighs unresolved questions about the risks and benefits of releasing AI model weights openly.
Argues that AI-generated writing with no communicative intent produces prose nobody truly wants to read.
Catalogues common logical fallacies through illustrated examples of flawed argument patterns.
Recounts the 1954 Robbers Cave experiment and what it revealed about in-group and out-group conflict.
Lays out protopia, a mental framework for imagining plausible, desirable futures of small gains.
Revises an earlier framing of the replication crisis after readers pointed out a subtle error.
Explains the generation effect as a method for testing whether understanding is genuine.
Questions what people mean by 'root cause' and examines causality within systems thinking.
Connects small-world versus big-world intuitions across startups, trading and game theory.
Asks whether superforecasting has reached the top of institutions, and examines prediction markets.
Presents a decision-making framework for making hard technical calls that teams won't later regret.
Describes how an underground neutrino detector is helping scientists map the Earth's mantle.