51¹ú²úÊÓƵ

Sudden breakthroughs long mythologised by mathematicians and scientists may not be as spontaneous as once thought ¨C a new study argues that ¡°eureka¡± moments can, in fact, be anticipated.

By video-recording six PhD-level mathematicians during problem-solving sessions, a team at the 51¹ú²úÊÓƵ of California, Merced have managed to identify signs that an individual was approaching an ¡°aha¡± moment.

Led by Shadab Tabatabaeian, who earned her PhD in cognitive and information sciences at the university, the team found that before gaining new insights, patterns in behaviour and reasoning became more unpredictable and showed signs of what they describe as ¡°critical slowing down¡±, a temporary loss of resilience in the cognitive system that hints that a dramatic shift is imminent.

The , published in?Proceedings of the National Academy of Sciences?(PNAS), recorded the mathematicians as they attempted notoriously difficult questions from the William Lowell Putnam Mathematical Competition, an annual exam where the median score is often just one point out of 120. Participants were filmed solving problems at blackboards in their own departments, with researchers cataloguing their speech, gestures and inscriptions.

Moments of breakthrough were marked not only by verbal exclamations but also by sudden shifts in movement, body language and the organisation of work on the board. These behavioural cues, the team argue, are akin to early-warning indicators observed in other systems approaching a tipping point, such as ecosystems nearing collapse or markets about to crash.

Mathematician Carl Gauss described such insights as ¡°a sudden of flash of lightning¡±, but the authors note, ¡°our findings suggest they emerge from detectable instabilities in the problem-solving process¡±.

The findings tie into a growing interdisciplinary literature on the predictability of sudden transitions. Research in complex systems has long documented how small perturbations can tip a fragile system into a new state once its resilience has eroded.?

The implications, the researchers suggest, extend beyond mathematics. Identifying early-warning signals of insight could inform teaching practices, cognitive training, and even the design of artificial intelligence systems intended to mimic creative reasoning.

Other researchers have noted that creative breakthroughs are rarely entirely sudden. Cognitive psychologists such as John Kounios and Mark Beeman have through neuroimaging that insight emerges from gradual subconscious processing before entering awareness.

The new study provides behavioural evidence of these dynamics in real-world expert practice but?the authors caution against overstatement. The behavioural signals they identified were small and context-dependent, and not every shift led to genuine insight.

¡°This is one of those discoveries that was possible only because we made connections between very different scientific disciplines,¡± Tyler Marghetis, UC Merced assistant professor of cognitive and information sciences and another of the authors, said.

¡°We took ideas from ecology and physics, added tools from information theory, and combined them with a century of work on the psychology of creativity. The resulting discovery belongs to all of those disciplines but also to none of them. It's its own thing.¡±