No, but the average educated person (and by educated I don't mean "has a degree," I mean educated as in "has reached the basic social expectations of education") knows rudimentary chemistry, mathematics, engineering, astronomy, and physics. In a world where knowing how things work = exerting some level of control over them, basic book learning would logically afford a minor capacity for spellcasting.
And, related to my above rejection of "The Special," no I don't buy that a first level wizard has the equivalent of a doctorate, let alone a PhD. Being a wizard is well within the capacity of races with lifespans significantly shorter (and intellects objectively dimmer, so it's not a raw talent thing) than humans, so it's not like it takes 30-odd years to learn how to cast cantrips (unless you're an elf, in which case it takes that long to get toilet trained).