Think of the last time you concentrated deeply to solve a challenging problem. To crack a math puzzle or determine a chess move, for example, you might have had to screen multiple strategies and approaches. But little by little, the answer to the conundrum came 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 investigated 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.
Mathematical thinking relies on an ancient brain network located in the parietal regions, at the top and center of the brain’s outer folded cortex. This network helps us process space, time and numbers. Previous studies on neurocognition in mathematics focused on what happens in the brain while people consider 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 the brain uses to keep numbers and other details top of mind in the short term.
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In our work, we used longer, more complex math challenges that had to be solved in multiple steps. 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 hard math problems. Understanding that state could someday help scientists understand the power of concentration more broadly, as well as the possible trade-offs of off-loading our problem-solving to our devices.
Very slow delta brain waves are typically associated with deep sleep, not with intense concentration. So what was going on?
For our experiment, we recruited 22 university students—at both the graduate and the undergraduate level—who were in math or math-related programs, such as physics or engineering, along with 22 students in disciplines with minimal to no quantitative emphasis, such as physiotherapy or the arts. We determined each student’s verbal, spatial and numerical intelligence quotient (IQ), as well as their level of math anxiety.
The students watched step-by-step presentations that explained how to solve several challenging math problems. Throughout this demonstration, the subjects wore caps covered with electrodes so we could track the electrical activity in their brains. After each presentation, they reported whether they thought they had understood the information and how engaged they felt during the experience. We also encouraged the participants to watch the demos carefully by telling them 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, those 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 these participants 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 call delta waves. These very slow waves of electrical activity 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 these “sleepy” 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, some studies show that large-scale delta oscillation emerges among experienced meditators when they enter meditative states. One reason that brain-activity patterns during 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 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 retraces the neural patterns that were previously activated during a learning task.)
In fact, we suspect that the long-distance delta oscillation we observed may play a central role whenever people are immersed in contextual and complex problem-solving. For instance, we have found that dancers and musicians show similar delta waves when watching dance or listening to music, which suggests that engaging brain networks in this way could be useful for many tasks involving concentration. Most likely when people who have extensive experience in a task are profoundly engaged in that effort, these same slow delta waves are involved, even if the specific brain networks vary. It’s also possible that this state of immersive concentration is generalizable: develop this way of thinking in one domain, whether it’s tackling trigonometry or playing the violin, and it could help you in others. We’ll need to investigate this idea further to be sure.
Although our experiments involved students and not, say, champion mathematicians or Nobel laureates, the differences in brain activity that we observed are still a testament to the power of practice in expertise. Our student participants did not significantly differ in their IQ or level of math anxiety, for example. Instead repetition and deliberate or intentional study helped some of these graduate and undergraduate students become more efficient masters of quantitative thinking.
By the same logic, these findings hint at a trade-off that people should keep in mind—particularly as artificial intelligence and other tools offer tantalizing shortcuts for various forms of problem-solving. Each time we off-load a problem to a calculator or ask ChatGPT to summarize an essay, we are losing an opportunity to improve our own skills and practice deep concentration for ourselves. To be clear, technologies can boost our efficiency in important ways, but the seemingly “inefficient” hard work we do can be powerful, too.
When I consider how frenetically people switch between tasks and how eagerly we outsource creativity and problem-solving to AI in our high-speed society, I personally am left with a question: What happens to our human ability to solve complex problems in the future if we teach ourselves not to use deep concentration? After all, we may need that mode of thought more than ever to tackle increasingly convoluted technological, environmental and political challenges.
Are you a scientist who specializes in neuroscience, cognitive science or psychology? And have you read a recent peer-reviewed paper that you would like to write about for Mind Matters? Please send suggestions to Scientific American’s Mind Matters editor Daisy Yuhas at dyuhas@sciam.com.
This is an opinion and analysis article, and the views expressed by the author or authors are not necessarily those of Scientific American.