Learning is lovely, but without the advatage of being able to directly apply what you've learned toward actually improving your life, it's all just so much education porn.
You realize all the time you've spent whiling away so much time, imagining that it's all building up to something even better than yesterday's tide of serialized data streams, that your youth has faded, and you're still just staring at a lightbulb masked behind a screen of wires, listening to air disturbed by oscillating magnets, and nothing more.
But the worst part of this, is looking up, only to find a city full of similar people all still hopelessly enthralled by the discharge of so many lithium-ion batteries perturbed by some nearby electric coil.
Starting with mathematics, the a theoretical machine, augmented by a language hierarchy gleaned from linguistics, with models based in real biological and physical systems. Even today's hotness in machine learning with ANNs is founded in an attempt to understand intelligence based on the physical structure of the mind.
Perhaps much of this can be recreated without being exposed to mathematics, chemistry, physics, biology, philosophy, linguistics, and other fields. But I imagine the insights needed to develop the first ANN model, the first language designed around a CFG would've taken far longer to develop in that narrow worldview.