86 - Serafina Cuomo on Ancient Mathematics

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How did the mathematics of figures like Euclid and Archimides relate to ancient philosophy? Peter finds out in an interview with Serafina Cuomo.



Further Reading

• S. Cuomo, Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge: 2000).

S. Cuomo, Ancient Mathematics (London: 2001).

• S. Cuomo, Technology and Culture in Greek and Roman Antiquity (Cambridge: 2007).


Graham White on 1 April 2020

Mathematical Objects

Very interesting talk, and I particularly enjoyed the connections between ancient mathematics and practical activities. One thing that came up here was the problem of mathematical ontology -- whether there are such things as independently existing mathematical objects and so on -- and Cuomo's response to this was that mathematical objects were then thought of as being much more physical than we think of them now. But even back then, things weren't so simple: if we take square numbers, then we can think of them as groups of physical objects arranged in squares. But still: we know that, for example, every other square number is even. And we can exhibit that by taking the physical objects in a suitable square number and rearranging them in two lines, with objects in one line corresponding to objects in the other line. So, if we really want to say that "ancient mathematics is all about collections of objects, suitably arranged", we also have to say that we are allowed to rearrange the collections. So we are really saying that "ancient mathematics is all about collections of objects, up to rearrangement". (And if you think that this argument sounds familiar, it's a rerun of Benacerraf's paper "What Numbers Could Not Be", where he argues that numbers cannot be identified with sets with a certain structure: rather they are sets with a certain structure up to suitable rearrangement of the structures.)  

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