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Brian Butterworth doesn’t look like a revolutionary. He is soft-spoken, precise, and occasionally amused by his own detours. But for decades at University College London—after an earlier stint at Cambridge—he has helped change a stubborn cultural reflex: the idea that struggling with maths is simply laziness, poor teaching, or lack of talent.
Butterworth argues something more unsettling and more humane: for some people, the difficulty is specific, biological, and often misread. It has a name—dyscalculia—and it is not the same as being “bad at maths”.
What does doing mathematics mean to you?
I had a poor mathematical education. Like many people, I didn’t like my maths teacher. So my maths has never been that good. But mathematics is diverse: you can be good at geometry and not good at numerical calculation, or the other way around. I’ve met people brilliant at advanced, abstract maths—tensor calculus—who struggle with simple calculation like 9 plus 6. Different parts of mathematics draw on different cognitive skills.
Why is it important to develop solid maths skills at school level?
The data are very clear across many countries: good maths is linked to better education, better jobs, better salaries. Poor maths tends to block those opportunities.
And it’s not only personal. It’s national. Napoleon understood this: a country’s mathematical competence relates to economic performance. OECD surveys show that when a country improves general maths education, the economy improves too. There’s evidence of a causal relationship.
You say dyscalculia is linked to an “innate number sense”. What is that?
Our theory is that we have an inherited mechanism for extracting numerical information from the environment. It’s called numerosity: the number of objects in a set. It can be visual objects, sounds, or both. The brain can respond to auditory and visual numerosities.
Is that ability unique to humans?
No. It’s important for many creatures. There’s a classic study of lions in the Serengeti: lions only attack invaders if they outnumber them. How do they know how many lions are invading when they can’t see them? They count the distinct roars. That’s cross-modal: comparing what they hear with what they see. Foraging is another example: more ripe fruit on one tree than another and choosing the better one. This has been tested in monkeys and other animals. Even creatures with small brains do it. Bees have around a million neurons, we have about 60 billion, yet bees can count landmarks to navigate back to the hive.
So we are born with number sense?
Yes. And like all innate abilities, it develops, and development can go normally or go wrong.
In the book Can fish count? you’ve studied numerical abilities in fish. Why fish?
Because they also make numerical choices. Small fish join shoals to reduce predation risk. If they have a choice, it makes sense to join the larger shoal. We noticed some fish were good at choosing the larger shoal, and some were not.
Could that be dyscalculia in fish?
We can’t say it’s the same condition. But it raises the question: are there individuals with weaker numerical discrimination? We did a simple experiment: put a fish who is bad at choosing the larger shoal with a fish who is good at it. The good fish goes to the larger shoal and the bad fish follows. That could simply reflect social following, but it’s very interesting. We’ve looked at genetics and found one anomaly that may suggest a mutation linked to poorer performance in that choice. I wouldn’t claim it more strongly than that.
When we say animals can count, do we mean they recite ‘one, two, three’?
“Counting,” in this context, means extracting numerical information from the environment.
So what changes when humans get counting words?
Counting words are tremendously useful because they let you communicate the result of a count, and remember it! You can link each number word to an internal representation. There’s this fascinating work by Mark Pagel using statistical methods to identify very old words across language families. One striking finding is that counting words appear among the oldest words, older than words like mother or fire in some analyses. And yet, there are still languages that lack counting words entirely.
Are some number-word systems better than others?
Yes. English is not very transparent. We have what we call: the “trouble with teens”: 11 and 12 don’t clearly signal “ten plus one” and “ten plus two.” In Chinese or Japanese, 11 is “ten-one,” 12 is “ten-two,” and so on. That transparency makes learning easier. German introduces a different complication (“one-and-twenty”), which can slow children down.
What is dyscalculia, then?
It’s easy to be bad at maths for many reasons: poor education, poor home environment, poor nutrition, poor memory, general cognitive difficulties. Any of these can lead to low scores on standard maths tests. But that doesn’t make you dyscalculic. Dyscalculia is specific, like dyslexia is specific. Other cognitive abilities can be fine: intelligence, language, memory, reading. In our early studies, we selected children with good memory and language and reading, who were nevertheless very poor at simple number tasks. Those are the children we labeled dyscalculic.
Which areas does it affect most?
Basic number skills: addition and subtraction, and often multiplication and division. The tragedy is that curricula often block students from more advanced or more abstract mathematics if they struggle with these foundational number tasks, even though they may be capable of geometry or higher-level reasoning that doesn’t rely on rapid calculation. And there’s a second tragedy: the emotional one. If classmates can do something easily and you cannot, you become anxious, avoidant, and you practise less, creating a vicious circle.
How common is dyscalculia?
In a large study in Cuba, where the education and social systems are relatively uniform, we found around 3.5% to 4.5%. Other studies using different methods find estimates closer to 6% or 7%. The “ballpark” is roughly 3.5% to 7%.
Where can we find number sense in the brain?
In humans, the parietal lobes are key hubs for processing basic numerical information, which is the numerosity you extract from the environment, and for simple calculation. We know this from imaging studies and from brain damage cases. Damage to parts of the left parietal lobe can cause acquired dyscalculia, or acalculia: people who used to be good at arithmetic can no longer do simple calculations if their left parietal lobe is damaged. More complex mathematical reasoning also recruits other areas, including frontal lobes and language-related networks.
Is dyscalculia linked to differences in those parietal networks?
There is evidence that in dyscalculic teenagers these areas don’t activate in the same way as in typical peers. There’s some evidence of structural differences and differences in connectivity, but the research is still developing. Brains vary a lot, so detecting reliable structural differences is technically difficult.
How can we measure something as subtle as number sense?
You need tasks that target the proposed root: extracting numerosity efficiently. One approach is: show a display of dots and ask, “How many?” Measure speed and accuracy. But you have to ensure they’re responding to number, not just to “how much dottiness” (total area, density, etc.). And children also need to know what the word “five” means, which complicates interpretation. Other tasks reduce the language load: for instance, “Are there more dots on the left or the right?” Or discrimination tasks: “Which is closer—five vs six, or five vs eight?” The closer comparisons are harder. A method I particularly like is Match-to-Sample: show dots briefly, remove them, then show another set and ask “same number or different?” The brief exposure prevents counting, so you’re tapping that fast, approximate numerical representation. It’s been used in animal studies too, which is part of its appeal.
And once we have the diagnosis, can dyscalculia be trained?
This is an excellent question—and the honest answer is: we don’t yet have enough long-term evidence. The idea is to train the link between cultural tools (digits and number words) and numerosity (sets), and then train operations on sets: combining, splitting—so that addition and subtraction are grounded in meaning, not in rote. We have some evidence that training can help. We developed a simple home game called Number Beads. Children who played between 10 and 30 sessions (2-6 hours) improved on tasks, especially children identified as dyscalculic. But we still need long-term studies: do gains persist after training stops? Can someone move from dyscalculic performance to typical performance over time? That remains open.
Why does dyscalculia deserve more attention?
Because its impact can be severe. Some UK government work suggests dyscalculia may affect education and employment prospects even more than dyslexia. Dyslexia can sometimes be compensated by learning words through exposure. Mathematics is different: you can’t only memorise, you must understand what numbers represent and how operations work.
And what’s the big misunderstanding you want to correct?
Some people think dyscalculia is not a specific deficit but a “heterogeneous” mix. It’s true the presentation varies with home environment, teaching, numerical exposure, memory, working memory, spatial thinking. But that doesn’t mean the underlying cause is a random mix. Many lines of evidence, from human behaviour and brain studies to animal research, support the existence of an innate system for numerosity. Our claim is that dyscalculia is a deficit in that system, and that interventions must target the root, not merely rehearse procedures.
