Logical-mathematical intelligence is the ability to reason logically, work with numbers and abstract relationships, and investigate problems systematically. It is one of the original seven intelligences in Howard Gardner’s theory of multiple intelligences, often called being “number smart” or “logic smart”. Of all Gardner’s intelligences it is the one closest to what IQ tests measure — and when it was tested directly, it turned out to be largely general intelligence under another name.

Where the idea comes from

Gardner described logical-mathematical intelligence in Frames of Mind (1983) as the capacity to study problems analytically, carry out mathematical operations and conduct scientific investigations. His examples are the mathematician, the logician and the scientist. For this intelligence he leaned on Jean Piaget’s account of how children’s logical thinking develops, from handling objects to reasoning about abstractions — see our guide to Piaget’s stages.

Gardner has also argued that schools and IQ tests value this intelligence and linguistic intelligence above the others. How it sits next to the rest of his list is covered in our guide to types of intelligence.

Signs and examples of logical-mathematical intelligence

These illustrate the definition; they are not a diagnostic checklist:

  • Enjoying number and logic puzzles. Sudoku, riddles, brain teasers, strategy games.
  • Spotting patterns and rules. Seeing the sequence or the rule behind a set of examples quickly.
  • Asking why. Wanting to know how something works and testing explanations.
  • Mental arithmetic. Estimating and calculating comfortably in your head.
  • Thinking in steps and categories. Breaking a problem into parts, ordering and classifying.
  • Liking evidence. Preferring data, experiments and clear arguments to impressions.

What happened when it was tested

The most direct test of Gardner’s theory is a 2006 study by Beth Visser, Michael Ashton and Philip Vernon in the journal Intelligence. They gave 200 adults two tests for each of Gardner’s eight intelligences plus a standard test of general mental ability, the Wonderlic Personnel Test. To cover both sides of logical-mathematical intelligence they chose a reasoning test and a speed test: Necessary Arithmetic Operations (30 word problems in 10 minutes, where you decide which operations are needed without doing the calculation) and Subtraction and Multiplication (120 simple sums in four minutes). The results, from the full data in Visser’s thesis:

  • The reasoning test was almost pure general intelligence. Necessary Arithmetic Operations had a loading of .70 or more on the general factor that ran through all the reasoning tests — the g factor — and the highest correlation of any test with the general ability test. Visser expected this, since mathematical reasoning is generally assumed to be closely tied to general intelligence.
  • The speed test much less so. Subtraction and Multiplication loaded only between .20 and .39 on the general factor. In Visser’s review of John Carroll’s 1993 survey, fast simple arithmetic is a less g-loaded ability, linked to working memory and perceptual speed.
  • Only a little left over. After the general factor was removed, the two arithmetic tests still correlated .15 — statistically significant, but about half the figure for the two word tests (.29). The reasoning test also correlated as much or more with four tests from other intelligences as it did with its own partner.
  • People knew their maths ability. Self-ratings of logical-mathematical ability were significantly related to both tests. Visser suggested this is one of the areas where people get plenty of feedback — from school marks, for example.

So the evidence supports a real mathematical ability, but not one that is independent of general intelligence, as Gardner’s theory claims. Mathematical reasoning sits close to the centre of g; quick calculation is a narrower skill.

Logic, maths and IQ tests

This is the intelligence IQ tests overlap with most. Number series, arithmetic word problems and logical deductions appear in many tests, and pattern-reasoning items such as Raven’s matrices test the rule-finding side without numbers at all. Our guide to deductive and inductive reasoning covers the two kinds of logic involved.

That overlap is also why critics say this intelligence adds little to the older picture of intelligence: mathematical reasoning was a standard part of intelligence research decades before Gardner, and the 2006 data show it is hard to separate from general ability.

Is maths a language?

Gardner treated logic and maths as separate from language, and brain research has supported him. In a 2016 study, Marie Amalric and Stanislas Dehaene scanned professional mathematicians while they judged advanced statements in algebra, analysis, geometry and topology. The mathematical statements activated a network in the frontal, parietal and lower temporal areas of both hemispheres and spared the areas involved in language. The same areas respond when non-mathematicians recognise numbers and formulas.

Patients point the same way. A 2016 review by Evelina Fedorenko and Rosemary Varley reported that people with global aphasia, who have almost no ability to understand or produce language, could still add and subtract and solve logic problems. Mathematical thinking does not run on words — even though, in healthy people, mathematical and verbal ability tend to go together.

Is it really an intelligence?

Nobody doubts that mathematical ability is real; the dispute is about independence. Critics such as Lynn Waterhouse argued in 2006 that multiple intelligences theory lacks adequate empirical support; Gardner and Seana Moran replied that the critique misreads it. For logical-mathematical intelligence specifically, the evidence supports a distinct brain system for number and maths, but a test of mathematical reasoning behaves like a test of general intelligence.

Careers that use it

Gardner’s own examples are mathematicians, logicians and scientists. Career lists add engineer, programmer, data analyst, accountant, actuary, economist and doctor. Treat these as illustrations of work that depends on reasoning with numbers and rules, not research findings. For a structured look at work that fits you, try our career test.

How to develop logical and mathematical skills

  • Learn more maths. Knowledge builds on knowledge; working through problems is still the most direct route.
  • Explain your reasoning. Writing out each step shows where an argument breaks down.
  • Practise estimating. Rough mental checks catch errors and build number sense.
  • Learn to code or play strategy games. Both train thinking in rules and steps — though our article on whether chess makes you smarter explains why the benefits rarely spread beyond the game.

Expect these to improve the skills you practise. There is no good evidence that logic games, puzzles or brain-training apps raise general intelligence.

What an IQ test measures here

IQ tests capture a large part of what Gardner calls logical-mathematical intelligence: number series, quantitative reasoning and finding rules in patterns. They do not measure mathematical knowledge, creativity in mathematics or scientific skill. Our test measures reasoning with patterns, numbers and words; for examples of item types, see our guide to IQ test questions.

Trust and scope notes

This page summarises published research for general information. The 2006 findings are reported from the full data in the author’s thesis, including its review of earlier research; the brain-imaging and aphasia findings are reported from the published papers. Nothing on this page assesses dyscalculia, a learning difficulty or any medical condition — concerns about a child’s or an adult’s difficulties with numbers are a question for a doctor, a teacher or an educational psychologist. The IQ Revealed test is an online reasoning test of 40 original items for adults aged 18 and over; it is not a clinical assessment.

IQ Revealed is not affiliated with, endorsed by or connected to Howard Gardner, the Educational Testing Service (publisher of the two arithmetic tests), the publisher of the Wonderlic Personnel Test, the publishers of Raven’s Progressive Matrices or the other researchers, universities, journals and publications named on this page.