# Iamblichus, "On the General Science of Mathematics"

*Iamblichus: On the General Science of Mathematics*, translated by John Dillon and J. O. Urmson, Ancient Commentators on Aristotle, Bloomsbury Academic, 2020

p. 44, Chapter 5:

Further, as for what looks to the firmness and constancy of mathematical science, which does not change from time to time, nor depart from its own essential nature, nor is conceived first in one way and then in another, this too is embraced by the common subject-matter of mathematical science within its reasoning. But one should not think of these common features as supervening on, but as being prior to, the particular studies; nor should they be thought of as included in the particular and having their being with them, but as having already a being which is prior to them and more fundamental, and not as dwelling in them but as set in place before the special objects of each mathematical science. For this reason knowledge of them is common to all and fundamental, more basic than that of the particular ones, and giving a general overview of all, arranging together all theorems of mathematics from a single beginning to a single end, surveying their kinship and likeness to each other, while taking account also of what is dissimilar and different in them, collecting together their primary kinds and their species, and distinguishing them. Also it surveys their common agreements, their prime hypotheses, their definitions, their postulates, their divisions and compositions, their aggregations and separations, their excesses and deficiencies and comparisons, throughout all the kinds of mathematical entities. It gives a unified account and not one separately of each, distinguishing what is possible in them and what impossible, what necessary and what not, the true and the false, and also their differences, their number and character, conducting a most accurate investigation.

p. 48, Chapter 6:

One should study mathematics also for the sake of knowledge; for the soul is in this way strongly led upwards, and it compels us to discourse about realities themselves, in no way tolerating it if someone, in discussion of them, brings to the fore visible or tangible bodies. For it speaks about those things about which reasoning alone is possible, it being not possible to deal with them in any other way. So mathematics is, it would seem, indispensable, since it can be seen to compel the soul to make use of intellect itself on the road to truth. Also, indeed, it makes people excel themselves in acuity, and further it provides much labour for him who studies and practises it.

*Iamblichi De communi mathematica scientia liber*, edited by Nicola Festa and Ulrich Klein, Bibliotheca scriptorum Graecorum et Romanorum Teubneriana, B. G. Teubner, Stuttgart, 1975^{1}

pp. 19-20, Chapter 5

p. 26, Chapter 6