Before revision:  It was thought in the numerical linear algebra community that to obtain nearly-optimal bounds for various problems such as rank computation, finding a maximal linearly independent subset of columns, regression, low rank approximation, maximum matching on general graphs and linear matroid union, that one would need to resolve the main open question of Cohen (SODA, 2016 ) regarding the logarithmic factors in existing oblivious subspace embeddings.
After revision:  It was thought in the numerical linear algebra community that to obtain nearly-optimal bounds for various problems such as rank computation, finding a maximal linearly independent subset of columns, regression, low rank approximation, maximum matching on general graphs and linear matroid union, that one would need to resolve the main open question of Nelson and Nguyen (FOCS, 2013 ) regarding the logarithmic factors in existing oblivious subspace embeddings.