November 13, 2024
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The mathematical mind gives neuroscientists a masterclass in concentration
Expertise increases the brain’s ability to think deeply, and this skill can potentially be applied across tasks
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Think about the last time you focused deeply to solve a difficult problem. For example, solving a math puzzle or determining a chess move may have required sifting through multiple strategies and approaches. However, little by little, the challenges are becoming clearer. Numbers and symbols may be placed in appropriate positions. At some point, you may even feel as if your problems were effortlessly solved on your mental blackboard.
In recent research, my colleagues and I set out to investigate the neural mechanisms underlying these experiences. Specifically, he wanted to understand what happens in the brain when people engage in abstract and demanding thinking, and he designed a study that leveraged his expertise in mathematics.
Mathematics relies on an ancient brain network located in the parietal region at the top and center of the brain’s outer folded cortex. This network helps us process space, time, and numbers. Previous research on neurocognition in mathematics has focused on brain activity when considering problems that take several seconds to solve. These studies reveal brain activity that supports focused attention and a specialized form of recall called working memory that helps people keep numbers and other details in mind in the short term. It was helpful.
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However, our study used longer and more complex math tasks that required multiple steps to solve. These problems are similar to difficult puzzles that mathematicians have to grapple with on a regular basis. It turns out that people with a lot of math experience go into a special deep state of concentration when thinking about difficult math problems. Understanding that state could one day help scientists understand the power of concentration and the possible tradeoffs of offloading problem-solving to devices.
Our experiment involved 22 undergraduate students enrolled in mathematics and mathematics-related programs, such as physics and engineering, at both graduate and undergraduate levels, with minimal or no quantitative emphasis, including: We recruited 22 students in the field. Physical therapy and art. We measured each student’s verbal, spatial, and numerical intelligence quotient (IQ) and level of math anxiety.
We had students watch a step-by-step presentation explaining how to solve some difficult math problems, such as proving the Fibonacci identities. During this demonstration, students wore hats covered with electrodes. This made it possible to non-invasively track electrical activity in students’ brains. After each presentation, they were required to report whether they thought they understood the demonstration and how engaged they felt during this experience. He also urged participants to watch the demonstration carefully, saying, “I’ll explain the issues later.”
They found that students with strong math expertise showed significantly different brain activity compared to those with less math expertise. For example, students whose classes included little math showed signs of more complex activity in the prefrontal cortex, the area just behind the forehead that engages in all kinds of cognitive effort. This finding may reflect how engaged they were in understanding the various steps of complex mathematics demonstrations.
But things got really interesting when we looked at students who regularly engaged in quantitative thinking. We noted significant activity that appeared to connect the frontal and parietal regions of their brains. More specifically, these regions exhibited a pattern of activity that neuroscientists describe as delta waves. These are very slow waves of electrical activity and are usually associated with states such as deep sleep. Of course, these students were wide awake and deeply engaged, so what is going on?
Recent research suggests that these “sleepy” slow delta waves may play an important role in cognitive processing that supports deep internal focus and the transfer of information between distant brain regions. For example, recent research has shown that experienced meditators exhibit large-scale delta oscillations when they enter a meditative state. One of the reasons why meditation, mathematical problem solving, and sleep are similar to each other is that in each case, the brain cuts out irrelevant external information and unnecessary thoughts in order to truly focus and focus on the task at hand. Maybe it’s because we need to suppress it. (In fact, even when you’re sleeping, it can be a busy time for your brain. Sleep research has revealed the irreplaceable role of deep sleep in memory consolidation. regressing neural patterns previously activated during the task).
Indeed, we suspect that the long-range delta oscillations we observed may play a central role when people are immersed in complex problem-solving in context. For example, dancers and musicians were found to exhibit similar delta waves when watching dance or listening to music. This suggests that engaging brain networks in this way may be useful for many tasks that require concentration. When someone with extensive experience in a task is deeply engaged in that task, similar slow delta waves may be involved, even if the specific brain networks are different. It’s also possible that this deep state of concentration is generalizable, although more research is needed to be sure. Whether you’re working on trigonometry or playing the violin, developing this idea in one area can help you in others. .
Although our experiments involved students rather than, say, champion mathematicians or Nobel Prize winners, the differences in brain activity we observed are still evidence of the power of practice in expertise. For example, there were no significant differences in the participating students’ IQ or math anxiety levels. Rather, repetition and planned or intentional learning helped some graduate and undergraduate students master quantitative thinking more effectively.
By the same logic, these findings suggest trade-offs that people should keep in mind, especially as artificial intelligence and other tools offer attractive shortcuts to various forms of problem solving. Every time we leave a problem to a calculator or ask ChatGPT to summarize an essay for us, we are missing out on an opportunity to improve our own skills and practice deep concentration on our own. To be clear, technology can make us more efficient in important ways, but our seemingly “inefficient” efforts can also have powerful effects.
When I think about how eagerly we switch tasks in our high-speed society and how eagerly we externalize creativity and complex problem solving to artificial intelligence, I personally wonder: What will happen in the future if we teach ourselves not to use deep concentration? After all, such ways of thinking may be needed today more than ever to solve increasingly complex technological, environmental, and political problems.
Are you a scientist specializing in neuroscience, cognitive science, or psychology? And have you read any recent peer-reviewed papers you’d like to write about? Submit your proposal scientific americanDaisy Yuhas, editor of Mind Matters dyuhas@sciam.com.
This is an opinion and analysis article and the views expressed by the author are not necessarily those of the author. scientific american.
