| Meaning | The branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness. |
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| Narrower | algebra | The mathematics of generalized arithmetical operations |
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| arithmetic | The branch of pure mathematics dealing with the theory of numerical calculations |
| calculus, infinitesimal calculus | The branch of mathematics that is concerned with limits and with the differentiation and integration of functions |
| geometry | The pure mathematics of points and lines and curves and surfaces |
| group theory | The branch of mathematics dealing with groups |
| metamathematics | The logical analysis of mathematical reasoning |
| numerical analysis | (mathematics) the branch of mathematics that studies algorithms for approximating solutions to problems in the infinitesimal calculus |
| set theory | The branch of pure mathematics that deals with the nature and relations of sets |
| topology, analysis situs | The branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions |
| trigonometry, trig | The mathematics of triangles and trigonometric functions |
| Broader | mathematics, math, maths | A science (or group of related sciences) dealing with the logic / logic of quantity and shape and arrangement |
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| Catalan | matemàtica pura |
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