"Now I Get It!": Eureka Experiences During the Acquisition of Mathematical Concepts

Many famous scientists have reported anecdotes where a new understanding occurred to them suddenly, in an unexpected flash. Do people generally experience such "Eureka" moments when learning science concepts? And if so, do these episodes truly vehicle sudden insights, or is this impression illusory? To address these questions, we developed a paradigm where participants were taught the mathematical concept of geodesic, which generalizes the common notion of straight line to straight trajectories drawn on curved surfaces. After studying lessons introducing this concept on the sphere, participants (N = 56) were tested on their understanding of geodesics on the sphere and on other surfaces. Our findings indicate that Eureka experiences are common when learning mathematics, with reports by 34 (61%) participants. Moreover, Eureka experiences proved an accurate description of participants' learning, in two respects. First, Eureka experiences were associated with learning and generalization: the participants who reported experiencing Eurekas performed better at identifying counterintuitive geodesics on new surfaces. Second, and in line with the firstperson experience of a sudden insight, our findings suggest that the learning mechanisms responsible for Eureka experiences are inaccessible to reflective introspection. Specifically, reports of Eureka experiences and of participants' confidence in their own understanding were associated with different profiles of performance, indicating that the mechanisms bringing about Eureka experiences and those informing reflective confidence were at least partially dissociated. Learning mathematical concepts thus appears to involve mechanisms that operate unconsciously, except when a key computational step is reached and a sudden insight breaks into consciousness.

Insight Problem Solving Ability Predicts Reduced Susceptibility to Fake News, Bullshit, and Overclaiming

The information humans are exposed to has grown exponentially. This has placed increased demands upon our information selection strategies resulting in reduced fact-checking and critical-thinking time. Prior research shows that problem solving (traditionally measured using the Cognitive Reflection Test-CRT) negatively correlates with believing in false information. We argue that this result is specifically related to insight problem solving. Solutions via insight are the result of parallel processing, characterized by filtering external noise, and, unlike cognitively controlled thinking, it does not suffer from the cognitive overload associated with processing multiple sources of information. We administered the Compound Remote Associate Test (problems used to investigate insight problem solving) as well as the CRT, 20 fake and real news headlines, the bullshit, and overclaiming scales to a sample of 61 participants. Results show that insight problem solving predicts better identification of fake news and bullshit (over and above traditional measures i.e., the CRT), and is associated with reduced overclaiming. These results have implications for understanding individual differences in susceptibility to believing false information.