By experimentation, do you mean people running randomized controlled trials on Bitcoin or otherwise empirically testing hypotheses on the software?

Not really - by experimentation I meant proving a concept by implementing it and then observing whether the implementation works or not, as contrasted to the pure math/theory approach where you attempt to prove something abstractly on paper.

For context, I was responding to your statement:

But first, this isn't obviously true... mathematicians, for instance, have found theoretical approaches to be more powerful. (I'd guess that the developer of Bitcoin took a theoretical rather than an empirical approach to creating a secure cryptocurrency, for instance.)

Bitcoin is an example of typical technological development, which is driven largely by experimentation/engineering rather than math/theory. Theory is important mainly as a means to generate ideas for experimentation.