[umanwizard]

But pi is also "constructed", in the sense that you can write down a constructive definition for it, for example \sqrt{6 \times \sum_{k=1}^\infty \frac{1}{k^2}}.

So I suppose maybe OP meant we haven't proven any number to be normal (or not) that is not designed to be normal (or not) ?

[pocksuppet]

That's what it means.