Does Math Make You Smarter? What Studying Mathematics Does to IQ

Studying math makes you better at math, and as part of a general education it probably contributes to the roughly 1 to 5 IQ points that each extra year of schooling adds. There is no good evidence that math raises intelligence more than other school subjects do, and the one study that followed students choosing math found a change in one narrow kind of logical reasoning and no extra gain on a matrix reasoning test.

The belief that mathematics trains the mind is very old. Educators once called it the "theory of formal discipline," the idea that hard subjects such as math and Latin strengthen thinking in general. This article covers what the best studies of schooling show, what happens when teenagers choose advanced math, why math training transfers so little, and why people who are good at math do score higher on IQ tests.

The strongest evidence that study can raise intelligence comes from research on years of education, not on any single subject.

• The meta-analysis: Stuart Ritchie and Elliot Tucker-Drob pooled 142 effect sizes from 42 data sets with more than 600,000 participants. They used only quasi-experimental designs, which are studies built to rule out the possibility that brighter people simply stay in school longer. One extra year of education raised scores by about 1.2 IQ points in studies that controlled for earlier intelligence, about 2.1 points in studies of school-leaving-age reforms, and about 5.2 points in studies comparing children just above and below a school-entry birthday cutoff. Across all three designs the average was about 3.4 points per year.

• The Norwegian reform: One of the clearest single studies used a 1960s Norwegian reform that raised compulsory schooling from 7 to 9 years. Using military test scores from about 107,000 men tested at age 19, Christian Brinch and Taryn Galloway estimated that one extra year of schooling raised IQ by 3.7 points.

These are effects of school as a whole, and every pupil in them studied math alongside many other subjects. Nobody has isolated how much of the gain came from math lessons. A further study points to a limit. In 1,091 Scottish adults tested at 11 and again at 70, the link between more education and higher scores ran through specific skills rather than through "general intelligence," the "g" factor that all cognitive tests share. Education seems to sharpen particular abilities more than it raises g itself, which is one reason the gains should be read carefully. For a broader look at what does and does not move scores, see the article on whether you can increase your IQ.

A handful of studies have looked at math itself. The best known tested the formal discipline idea directly.

• The A-level study: Nina Attridge and Matthew Inglis followed English 16- and 17-year-olds through their first year of post-compulsory study. Forty-four students taking A-level mathematics and 38 taking English literature (but no math) completed all tests at the start and end of the year. The math students changed how they handled "if...then" logic problems, rejecting more invalid inferences (effect sizes of about half a standard deviation), while the literature students did not change. The math syllabus contained almost no explicit logic, so the change seems to have come from doing math.

• What did not change: Both groups also took an 18-item version of Raven's Advanced Progressive Matrices, a nonverbal reasoning test. Both improved slightly over the year, and the math students did not improve more than the literature students. The math students also moved toward a "defective" reading of conditionals, which is not the textbook logical answer either. So the result is a shift in one style of reasoning. It is not evidence of higher intelligence.

• The brain chemistry study: George Zacharopoulos and colleagues scanned 87 A-level students and found that those who had dropped math had lower levels of the neurotransmitter GABA in a frontal brain region involved in reasoning. A second sample of 42 younger students suggested the difference was not there before the choice, and GABA levels predicted changes in mathematical reasoning about 19 months later. This was an observational study of brain chemistry and math attainment. It did not measure IQ, and students were not randomly assigned to drop math.

Taken together, these studies suggest that advanced math leaves a mark on how students reason about math-like problems. None shows a rise in general intelligence.

Psychologists separate "near transfer," improvement on tasks close to what you practised, from "far transfer," improvement on unrelated abilities such as general reasoning. Giovanni Sala and Fernand Gobet's meta-analyses are the clearest summary of how rarely far transfer happens. They examined chess, music and working memory training in children, with math and reading achievement among the outcomes, and found that apparent benefits shrank toward zero in the better-designed studies. For music instruction, the average effect was 0.25 standard deviations against passive control groups but only 0.03 against active control groups, which is about half an IQ point. None of their analyses treated math lessons themselves as the training, so they say more about whether other activities make children better at math than about whether math makes children smarter.

Mental arithmetic training shows the same pattern. In a three-year randomized trial with 204 children aged 5 to 7 at the start, David Barner and colleagues taught "mental abacus," a technique of calculating by picturing an abacus. The children became better at arithmetic than controls. Their basic cognitive abilities, including working memory, did not change. Children who started with stronger spatial working memory learned the technique better, so ability shaped the learning rather than the other way round.

Practice builds skill and knowledge. Algebra and mental arithmetic are valuable in their own right, and the skills carry over to other quantitative work. They do not appear to raise the underlying ability that IQ tests measure.

The popular claim persists because the link between math and intelligence is real. It mostly runs from intelligence to math.

• Intelligence predicts math grades: Ian Deary and colleagues followed more than 70,000 English children from a cognitive ability test at 11 to national exams at 16. General intelligence accounted for 58.6% of the differences in math exam results, more than for any of the other 24 subjects. That corresponds to a correlation of about .77 (the square root of .586). The correlation between general intelligence and overall exam results was .81.

• Students who choose math start higher: In the Attridge and Inglis study, the math students already scored higher on Raven's matrices at the start of the year, 9.6 out of 18 compared with 6.9 for the literature students. That gap is roughly 0.8 standard deviations, which would be about 12 points on an IQ scale, although a short Raven's subset is not a full IQ test.

Math also overlaps with what IQ tests measure. Many tests include a "quantitative reasoning" section, and a quantitative reasoning test rewards both reasoning ability and arithmetic fluency. People who did more math may do better on those items partly because they practised similar problems. That is near transfer to the test, which is a different thing from higher intelligence.

The confounds here are serious. Students who take advanced math tend to have higher earlier ability and better prior grades, and they often have more educated parents. Unless a study controls for ability measured before the math, a gap between math students and others cannot be credited to the math.

Math makes you better at math, and schooling as a whole raises IQ by about 1 to 5 points per year. No study has shown that math raises intelligence more than other school subjects.

On average, yes. General intelligence measured at 11 explained about 59% of the differences in math exam results at 16, a correlation of about .77, mostly because more able students learn math more easily.

Not according to the best trial. Children trained in mental abacus for three years got better at arithmetic, but their working memory and other basic abilities did not improve.

In one study, a year of A-level math changed how students judged "if...then" statements. It did not improve their score on a matrix reasoning test more than studying literature did.

Study math for the knowledge and skills it brings. More education in general is linked with small IQ gains, but math is not a special shortcut.

Math sharpens math. A year in school raises IQ by a few points on average, and math is one part of that year, but research has not shown that math has any special power to raise intelligence. The strong link between math and IQ mostly reflects the fact that people with higher ability find math easier and choose more of it. If you want an accurate picture of your reasoning ability, including the quantitative side, take the RIOT IQ test.

1. Ritchie, S. J., & Tucker-Drob, E. M. (2018). How much does education improve intelligence? A meta-analysis. Psychological Science, 29(8), 1358-1369. [doi.org/10.1177/0956797618774253](. doi.org

2. Brinch, C. N., & Galloway, T. A. (2012). Schooling in adolescence raises IQ scores. Proceedings of the National Academy of Sciences, 109(2), 425-430. [doi.org/10.1073/pnas.1106077109](. doi.org

3. Ritchie, S. J., Bates, T. C., & Deary, I. J. (2015). Is education associated with improvements in general cognitive ability, or in specific skills? Developmental Psychology, 51(5), 573-582. [doi.org/10.1037/a0038981](. doi.org

4. Attridge, N., & Inglis, M. (2013). Advanced mathematical study and the development of conditional reasoning skills. PLoS ONE, 8(7), e69399. [doi.org/10.1371/journal.pone.0069399](. doi.org

5. Zacharopoulos, G., Sella, F., & Cohen Kadosh, R. (2021). The impact of a lack of mathematical education on brain development and future attainment. Proceedings of the National Academy of Sciences, 118(24), e2013155118. [doi.org/10.1073/pnas.2013155118](. doi.org

6. Sala, G., & Gobet, F. (2017). Does far transfer exist? Negative evidence from chess, music, and working memory training. Current Directions in Psychological Science, 26(6), 515-520. [doi.org/10.1177/0963721417712760](. doi.org

7. Barner, D., Alvarez, G., Sullivan, J., Brooks, N., Srinivasan, M., & Frank, M. C. (2016). Learning mathematics in a visuospatial format: A randomized, controlled trial of mental abacus instruction. Child Development, 87(4), 1146-1158. [doi.org/10.1111/cdev.12515](. doi.org

8. Deary, I. J., Strand, S., Smith, P., & Fernandes, C. (2007). Intelligence and educational achievement. Intelligence, 35(1), 13-21. [doi.org/10.1016/j.intell.2006.02.001](. doi.org

Hero image: Pure-mathematics-formulæ-blackboard, by Wallpoper, Public domain. Via Wikimedia Commons.