Google is completely inadequate at mathematical search. But here is a concrete problem that no search seems to handle: given some complicated integral (say, some contour integral involving a K-Bessel function), find where it appears in the literature.

Most search will totally fail, because this is made of math symbols. Embedding-based search will give various related things involving, say, integrals and Bessel functions. But then I end up opening Gradshteyn and Ryzhik and trying to find where in this book the relevant terrible integrals appear.

This is a common experience for analytic number theorists. And it's a lousy experience.