Theories didn't make transistors. People did at Bell Labs with trial and error. Predictions had nothing to do with it. Math had nothing to do with it.

I'm sorry, but historically speaking, this just isn't true. See this page for details. Basically:

This idea that particles could only contain lumps of energy in certain sizes moved into other areas of physics as well. Over the next decade, Niels Bohr pulled it into his description of how an atom worked. He said that electrons traveling around a nucleus couldn't have arbitrarily small or arbitrarily large amounts of energy, they could only have multiples of a standard "quantum" of energy.

Eventually scientists realized this explained why some materials are conductors of electricity and some aren't since atoms with differing energy electron orbits conduct electricity differently. This understanding was crucial to building a transistor, since the crystal at its core is made by mixing materials with varying amounts of conductivity... Electrons acting like a wave can sometimes burrow right through a barrier. Understanding this odd behavior of electrons was necessary as scientists tried to control how current flowed through the first transistors.

It was people in the lab who created transistors, using trial and error to get just the correct mix of elements in the semiconductor crystal, but they knew it was remotely possible because the math of quantum mechanics predicted (and this was already verified in experiment) that electrons could 'tunnel through' an apparently non-conductive barrier–thus 'semiconductor'. According to classical understanding of the atom, this wouldn't happen, and so no one would try making something like a transistor, by trial and error or by theoretical prediction or whatever.