The Gromov-Hausdorff distance is a notion of dissimilarity between two datasets or between two metric spaces. It is an important tool in geometry, but notoriously difficult to compute. I will show how to provide new lower bounds on the Gromov-Hausdorff distance between unit spheres of different dimensions by combining Borsuk-Ulam theorems with Vietoris-Rips complexes. This joint work with 15 coauthors is available at https://arxiv.org/abs/2301.00246. Many questions remain open!