That also presumes that knowledge depends on computation, which is not necessarily true.

Two interesting things are going on right now. First, we've come to a crossroads in cosmology [0] where some heavy hitters are rebelling and saying time is real and mathematics is a too-comfortable approximation. Second is a new foundation for mathematics that moves away from set theory to a fusion of type theory and homotopy theory called univalence [1].

It is these kinds of events that permit the scales to fall from our eyes and show us more of the things we didn't know we didn't know. Our meta-ignorance may soon be reduced, just a bit. But back to the point, it may likely also become true that these pull many subjects into the realm of the computable.

  [0] Unger, Smolen http://www.amazon.com/gp/product/1107074061
  [1] https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/