 Brisson (2013) takes a sceptical stance towards the evidence and concludes that Archytas never solved the problem of the duplication of the cube. He argues that Plato would have mentioned a solution to the problem if one existed in his day and that the mathematics of the solution ascribed to Archytas is impossible for someone of his time, since it employs conic sections, which were not developed until the third century (2013: 220–1). However, while Plato does criticize the state of stereometry (solid geometry) in his day, he also affirms that there are people studying it and that some of their results have charm and beauty (Rep. 528c-d). There is no reason that Archytas’ duplication could not be included among these results. Moreover, the mathematics used in Archytas’ solution in no way relies on conic sections but relies on mathematics found in Euclid’s Elements Books 1, 3, 4, 6, and 11, which rely on geometry of the fourth century when Archytas was active (Heath 1921, Knorr 1986, Mueller 1997 and Menn 2015 all regard the mathematics as appropriate for Archytas). Menaechmus, who lived two generations after Archytas, is the first person to solve the problem using conic sections (see Menn 2015: 415–6). Brisson has to discount the explicit tradition that already in the fourth century Eudemus knew of Archytas’ solution and assume that the solution was developed by a compiler in the latter tradition, but it is implausible that such a compiler could have developed the sophisticated mathematics of the solution and that, if he were such an accomplished mathematician, he would ascribe it to Archytas.