Ruehle and collaborators took up the old problem of approximating Calabi-Yau metrics. Anderson and others also revitalized their earlier attempts to overcome step 2. The physicists found that neural networks provided the speed and flexibility that earlier techniques had lacked. The algorithms were able to guess a metric, check the curvature at many thousands of points in 6D space, and repeatedly adjust the guess until the curvature vanished all over the manifold. All the researchers had to do wa...