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Think of the last time you concentrated deeply to solve a challenging problem. To solve a math puzzle or determine a chess move, for example, you might have had to screen through multiple strategies and approaches. But little by little, the conundrum would have come into focus. Numbers and symbols may have fallen into place. It might have even felt, at some point, like your problem effortlessly resolved itself on the blackboard of your mind.
In recent research, my colleagues and I set out to investigate the neural mechanisms underlying these experiences. Specifically, we wanted to understand what happens in the brain while a person engages in abstract and demanding thought—so we designed a study involving math expertise.
Mathematics relies on an ancient brain network located in the parietal regions at the top and center of the brain’s outer folded cortex. That network helps us process space, time, and numbers. Past studies on neurocognition in mathematics have focused on brain activity while considering problems that take a few seconds to solve. These studies have helped illuminate brain activity that supports focused attention and a special form of recall called working memory, which helps people keep numbers and other details top of mind in the short term.
But our study used longer, more complex math challenges that involve
multiple steps to solve. These problems are more akin to the tricky puzzles that mathematicians must tackle regularly. We found that people with more experience in mathematics enter a special state of deep concentration when thinking about challenging math problems. Understanding that state could help scientists to someday understand the power of concentration more broadly, as well as the possible trade-offs of off-loading our problem-solving to our devices.
For our experiment, we recruited 22 university students—at both the graduate and undergraduate level—who were in math and math-related programs, such as physics or engineering, along with 22 fellow students in disciplines with minimal to no quantitative emphasis, such as physiotherapy and arts. We determined each student’s verbal, spatial, and numerical intelligence quotient (IQ), as well as their level of math anxiety.
We asked the students to watch step-by-step presentations that explained how to solve several challenging math problems—such as proving a Fibonacci identity. Throughout this demonstration, students wore a cap covered with electrodes so that we could noninvasively track electrical activity in their brain. After each presentation, they had to report whether they thought they had understood the demonstrations and how engaged they felt during this experience. We also encouraged the participants to watch the demos carefully by telling them that they would have to explain the problem afterward.
We found that the students with greater math expertise showed markedly different brain activity than those with less. For example, the students whose coursework involved little mathematics showed more signs of complex activity in the prefrontal cortex, an area just behind the forehead that is engaged in all kinds of cognitive efforts. This finding may reflect how hard they were working to understand the various steps of the complex math demonstrations.
But things really got interesting when we turned to students who engaged in quantitative thinking regularly. We noted significant activity that appeared to link the frontal and parietal regions of their brain. More specifically, these areas exhibited a pattern of activity that neuroscientists describe as delta waves. These are very slow waves of electrical activity that are typically associated with states such as deep sleep. Of course, these students were wide awake and deeply engaged—so what was going on?
Some recent research suggests that these “sleepy” slower delta waves may play a crucial role in the cognitive processing that supports deep internal concentration and information transfer between distant brain regions. For example, recent studies show that large-scale delta oscillation emerges among experienced meditators when they enter meditative states. One reason that meditation, mathematical problem-solving and sleep resemble one another might be that, in each case, the brain needs to suppress irrelevant external information and unneeded thoughts to really focus and concentrate on the task at hand. (Indeed, even sleep can be a busy time for the brain. Sleep research has revealed deep sleep’s irreplaceable role in memory consolidation; slow-wave sleep retracts the neural patterns that were previously activated during a learning task.)
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