Overview

• Researchers video-recorded six Ph.D.-level mathematicians tackling Putnam problems and coded over 4,600 blackboard interactions in a study published in PNAS.
• Information-theoretic metrics showed behavioral unpredictability ramping up roughly two minutes before a spoken insight, peaking about one minute after, then returning to baseline.
• The authors frame sudden insights as critical transitions in complex systems, drawing on concepts from statistical physics and theoretical ecology to interpret early-warning signals.
• Insight moments were identified by verbal exclamations such as “Oh, I see!”, which may miss unspoken realizations and reflect a small, expert sample that requires broader testing.
• The team suggests similar early-warning signatures could be sought in domains where thinking leaves observable traces, including chemistry, design, and art.