Do Geometric Points Actually Exist?

The fundamental object in Euclidean geometry is the "point," but it's unclear exactly what a point is. Our intuitive notions of points don't work within Euclidean geometry, so some thinkers have posited different definitions. Some mathematicians treat "points" as pairs of numbers - coordinates in a Cartesian plane. But is this correct? Is geometry about numbers, or is it about objects that take up space?

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