We call a real number computable if there is an algorithm that can compute it to arbitrarily high precision. So e and pi have always been computable.

I think in this case it's Reals that are too general. What is the virtue of these uncomputable numbers? If we can't compute/express them then what can we do with them?

Was pi ever really uncomputable? You can draw a really big circle and measure it in multiple ways.

And when e was defined as a symbol, it was with a computation, (1 + 1/n)^n