Researchers observe mathematicians, describe unpredictability prior to 'eureka' moment

New Delhi, Aug 19 (PTI) Minutes before a mathematician had a breakthrough 'eureka' moment, researchers saw subtle changes in their behaviour that notably became less predictable -- findings offer a new window into understanding human creativity, they said.

Derived from the ancient Greek language, the word is famously known to have first uttered by the mathematician and inventor Archimedes, when he discovered the principle of bouyancy while taking a bath and ran naked down the streets shouting 'Eureka!'.

However, how these sudden 'eureka' moments -- that drive progress in science and mathematics -- happen remains shrouded in mystery, the researchers from the US' universities of California Merced and Indiana said in the study published in the journal Proceedings of the National Academy of Sciences.

The team videographed six PhD-level mathematicians as they worked out "notoriously tough problems" from the William Lowell Putnam Mathematical Competition -- considered a premiere one at the university level -- on a blackboard.

Analysing more than 4,600 moment-to-moment interactions with blackboard "inscriptions" that included writing, pointing, erasing and shifting attention, the researchers observed that the mathematicians' behaviour became measurably less predictable in the minutes before suddenly exclaiming 'aha!' or 'I see it!'.

Familiar patterns of moving between ideas gave way to novel, unprecedented connections, the team said.

"Using naturalistic video recordings of mathematicians working on proofs 'in the wild' (i.e., in their own offices and seminar rooms), we show that insights that appear to come out of nowhere are actually prefigured by changes in how mathematicians are writing and gesturing," the authors wrote.

They used analytical methods from statistical physics and theoretical ecology to understand the onset of 'eureka' moments.

Using information theory -- a mathematical analysis of concepts, parameters and rules that influence how a message is conveyed -- the researchers quantified the unpredictability prior to the 'eureka' moment and found that it reliably ramped up before insights were verbalised.

"This is one of those discoveries that was possible only because we made connections between very different scientific disciplines," senior author Tyler Marghetis, Assistant Professor of Cognitive and Information Sciences, University of California Merced, 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," Marghetis said.

The authors added that even though the study focussed on expert mathematicians, the methodology can be applied in any field where thinking unfolds in observable steps, such as a chemist sketching molecular bonds, or an artist exploring new forms.

The study's approach could help scientists better understand the micro-dynamics of creativity and, perhaps, even predict breakthroughs before they happen, the authors said.

"Our method for inferring when mathematicians are on the cusp of a breakthrough is quite general, so it may apply to other systems that generate a time series of discrete, symbolic events," they wrote. PTI KRS KRS KSS KSS