ArticleProceedings of the National Academy of Sciences of the United States of America2025
An information-theoretic foreshadowing of mathematicians' sudden insights.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
1 citing paper in PubMed.
- An information-theoretic foreshadowing of mathematicians' sudden insights.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
4 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The "eureka" insights that drive progress in science and mathematics remain shrouded in mystery. Sudden, unexpected, appearing like "flashes of lightning", these insights have the hallmarks of critical transitions in complex systems. Here, zooming in on mathematicians working on proofs in their own departments, we show that sudden insights are anticipated by a system-agnostic, information-theoretic early warning signal. Using dense behavioral recordings of mathematicians' moment-to-moment activity, we find that their blackboard interactions (e.g., writing, gesturing; [Formula: see text]) became increasingly unpredictable before an insight, analogous to the critical fluctuations that anticipate transitions in physical and ecological systems. We explore analytically when this early warning signal applies to varied systems with discrete, symbolic dynamics. While bibliometric analyses offer a zoomed-out perspective on innovation, publications are a coarse-grained record of individuals' insights. Explaining the sudden insights of innovators, from scientists to sculptors, requires attending to the local, distributed systems of their intellectual activity.
Indexed as
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.