What Math Looks Like in the Mind

Humans are born to do math, and they have the brain infrastructure to prove it—including a cluster of specialized nerve cells for processing numbers.

Despite this dedicated cluster, mathematical concepts are often taught in a way that taps into the brain’s visual system. Children might be asked to count the apples in a picture, or to imagine two trains speeding away from one another at different speeds. But just how much does visual experience shape the way that people think about numbers?

To find out, researchers at Johns Hopkins compared brain activity among a group of congenitally blind individuals and a group of sighted individuals—asking all participants to solve a series of math problems and language comprehension tasks.

“Across all humans, numerical thinking is supported by similar areas in the brain,” said Shipra Kanjlia, a graduate student in psychological and brain sciences at Johns Hopkins University, and the lead author of a paper that resulted from the experiment. “Does this change in people who have dramatically different perceptual experience—like people who have been blind their whole lives and have never seen the number of people at a party or the number of flowers in a field?”

In both groups who participated in the study, the same parts of the brain were more active during the math task—a meaningful finding because it suggests that the ways in which humans process math concepts develop the same way regardless of visual experience.

But something even more surprising took place in the brains of blind participants as they performed math calculations: They were using a part of their brains for math that, among sighted people, is reserved for vision. And the more complex the math problem, the more active that region became. (Among sighted participants, this region of the brain was not active during the math task.) “These results suggest that experience can radically change the neurobiology of numerical thinking,” the researchers wrote in a paper that was published on Monday in the Proceedings of the National Academy of Sciences. In other words, some parts of the human brain are innately primed for mathematical thinking; whereas others flourish based on experience.

A natural next question is what this means for mathematical skill. If blind people, while processing numbers, are able to tap into a part of their brains that is reserved for visual thinking in sighted people, couldn’t that mean blind people are better—or at least advantaged—at math?

Maybe, but there’s no evidence to support that hypothesis just yet, “even though blind individuals have this whole extra chunk of brain devoted to the math task,” Kanjlia told me. In the meantime, though, the findings do at least challenge the commonly held idea of math necessarily being a “very visual process,” she says. The reality, instead, is that engaging in mathematic thinking is visual for some people and not for others.

Albert Einstein, for example, described his own thinking as partly “visual” and partly “muscular.” In one of his famous thought experiments, Einstein imagined what it would be like to chase a photon moving at the speed of light. But such an exercise doesn’t actually require a mental image. What a sighted person experiences as visual thinking might be characterized as “spatial,” by someone who is blind.

“Math, like everything else in my life, is something I interface with nonvisually,” said Scott Blanks, the senior director of programs for Lighthouse for the Blind and Visually Impaired. “I’m congenitally blind, totally blind from birth, so I have zero visual experience or memory.”

Blanks says that, for him, working out math problems in Braille—which is how he learned many mathematical concepts in school—is a key part of his numeric thinking. “It didn’t matter whether it was an algebraic equation, or a ‘a train traveling at...’ story problem, having the information under my fingers was key to maximum comprehension,” he said. “Real-world math is a different animal altogether. If I’m considering say, the distance between two points, or how many people are in a room, I do those things on the fly ... I might employ previous experiences to contribute to my answer, or weigh associated factors to come up with a number. For example, to the question of distances, I might consider how long it has taken me to walk the route in question, how many blocks are encompassed in that route, and so on.”

“There is rarely a tactile element in these situations,” he added. “Rather, my initial contact with the math scenario occurs auditorily.”

It’s surprisingly hard to articulate the experience of mathematical thinking, but it makes sense that people would rely on the senses—whether sight or sound—that shape their larger perceptions of the world. In informal conversation with several of my sighted colleagues, people described envisioning numbers as if they appeared on a chalkboard or a calculator in their mind. When I’m doing a quick calculation to alter the scale of a recipe, I sometimes picture measuring cups as I’m figuring it out.

Another study, published in the Proceedings of the National Academy of Sciences in April, found that mathematicians had “reduced activity in the visual areas of the brain involved in facial processing,” Jordana Cepelewicz wrote for Scientific American at the time. “This could mean that the neural resources required to grasp and work with certain math concepts may undercut—or ‘use up’—some of the brain’s other capacities.”

The latest findings, from Kanjlia and her colleagues, seem to complement that work. For instance, her team also found that blind individuals demonstrated “increased functional connectivity” between different regions that process numeric thinking.

“The big takeaway is that the brain is really flexible but also really resilient,” Kanjlia told me. “The things you wouldn’t necessarily think would change, do change.”