The principal mathematical contributions attributed to Eudoxus are (1) sophisticated use of the Greek method of dealing rigourously with limits (called much later the method of exhaustion). This is necessary, for example, in proving that the formula found earlier for the volumes of tetrahedra and cones were correct; (2) establishing the theory of ratios on a rigourous foundation. The evidence for these attributions is weak, but it makes intrinsic sense, if only because both are very, very subtle, even in the light of modern mathematics.

Both points are to be found in Euclid's Elements (Books V, XII), but Euclid never mentions individuals. The treatment of ratios in Book V is fascinatingly close to Dedekind's treatment of real numbers in the nineteenth century, as the articles state. Neither article makes a serious attempt to explain the mathematics involved.