Nine patients did simple calculations in their heads while researchers recorded their brain activity. Sure enough, in the data, Nieder and Mormann saw neurons firing for their preferred numbers — the first time number neurons had been identified in the human brain. They published their findings in Neuron in 2018.

Neuroscientists are of course driven to understand their own mind, Nieder said, and so “finding such neurons in the human brain is extremely rewarding.”

A Numeric Threshold

To continue their quest, Nieder and Mormann launched a new study to find out how the neurons represent odd and even numbers. The researchers recruited 17 epilepsy patients and showed them flashes of dots, ranging in number from one to nine, on computer screens. The participants indicated whether they saw an odd or even number while electrodes recorded their brain activity.

Over the next few months, as Esther Kutter, a graduate student studying with Nieder, analyzed the resulting data, she saw a clear pattern emerge — right around the number 4.

The data, which comprised 801 recordings of single neurons firing, showed two distinct neural signatures: one for small numbers and one for large. Above the number 4, the neurons’ firing for their preferred number grew progressively less precise, and they erroneously fired for numbers close to the preferred one. But for 4 and below, the neurons fired precisely — with the same small amount of error whether firing for one, two, three or four objects. The misfiring in response to other numbers was largely absent.

This surprised Nieder. He hadn’t previously seen this boundary in his animal studies: Those experiments had included numbers only up to 5. He hadn’t set out to probe Jevons’ observation, nor did he expect to see a neural boundary confirm what behavioral studies had found. Up until that point he had been convinced that the brain had just one mechanism for judging numbers — a continuum that got fuzzier the higher the numbers climbed.

The new data changed that for him. “This boundary popped out in different ways,” Nieder said. The neural patterns suggested that there is an additional mechanism that suppresses smaller-number neurons from firing for the wrong numbers.

Piantadosi and Serge Dumoulin, the director of the Spinoza Center for Neuroimaging in Amsterdam, had both previously published papers supporting the idea that only one mechanism manages the neuronal interpretation of numbers. Yet they were struck by Nieder and Mormann’s new data showing that there are in fact two separate mechanisms.

It’s “real validation that large and small numbers have different neural signatures,” Piantadosi said. But he cautioned that two signatures can emerge from a single process; whether it should be described as one mechanism or two is still up for debate.

“This is just beautiful,” Dumoulin said. “This type of data wasn’t available and certainly not in humans.”

However, one more major uncertainty remains. The researchers didn’t study the prefrontal or parietal cortices, where the majority of number neurons are located in monkeys. Instead, because of where the patients’ electrodes were inserted, the study focused on the medial temporal lobe, which is involved in memory. It isn’t the first place in the human brain you’d investigate to understand numbers, Nieder said. “On the other hand, the medial temporal lobe is also not the worst place to look for such neurons.”

That’s because the medial temporal lobe is linked to number sense. It’s active when children learn calculations and multiplication tables, and it’s intimately connected to regions where number neurons are thought to lie, Nieder said.

It’s not clear why number neurons are present in this region, Butterworth said. “The things that we thought were specific to the parietal lobe seem to be reflected also in parts of the medial temporal lobe.”

One possibility is that these aren’t number neurons at all. Pedro Pinheiro-Chagas, an assistant professor of neurology at the University of California, San Francisco, thinks these could instead be concept neurons, which are located in the medial temporal lobe and are each linked to specific concepts. For example, one famous study found a concept neuron that responded directly and specifically to images of the actor Jennifer Aniston. “Maybe they are not finding the mechanisms of the number sense. … Maybe they’re finding concept cells that are also applied to numbers,” Pinheiro-Chagas said. “As you have the concept of ‘Jennifer Aniston,’ you could have the concept of ‘three.’”

The level of analysis is “just really outstanding,” said Marinella Cappelletti, a cognitive neuroscientist at Goldsmiths, University of London. The researchers provide “compelling evidence” for dual mechanisms in the medial temporal lobe. She thinks it would be valuable, however, to see whether these mechanisms operate in other brain regions as well, if the opportunity presents.

“I see these findings as looking into a window,” Cappelletti said. “It would be nice to open it up a bit more and tell us more about the rest of the brain.”

There’s Something About 4

The new findings have clear parallels to the limitations of working memory. People can hold only a certain number of objects in their awareness, or working memory, at one time. Experiments show that number is also 4.

The agreement between the boundary of number sense and that of working memory is “hard to ignore,” Cappelletti said.

It’s possible that the mechanisms are related. In previous studies of number sense, when a participant stopped paying attention, they lost their ability to precisely judge the true value of numbers 4 and below. That suggests that the small-number system, which suppresses adjacent misfirings with small numbers, might be intimately tied to attention.

Nieder now hypothesizes that the small-number system turns on only when you’re paying attention to what’s in front of you. He’s hoping to test this idea in monkeys, in addition to looking for a neural boundary at 4 that their experiments haven’t yet captured.

The new research “seems to be the beginning of a new leap” in our understanding of number perception, Pinheiro-Chagas said, which could have useful applications. He hopes it will be fodder for discussions in math education and even artificial intelligence, which struggles with numerosity perception. Large language models are “pretty bad at counting. They are pretty bad at understanding quantities,” he said.

Better characterizing number neurons can also help us understand who we are. Next to the language system, number representation is humans’ second-biggest symbol system. People use numbers frequently and in a variety of ways, and we and our ancestors have used math to describe the world for millennia. In that sense, math is a fundamental part of being human.

And, as this study starts to show, this calculation prowess might all stem from a finely tuned network of neurons in the brain.

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