Within quantum theory it makes perfect sense to combine the numbers of curves of all degrees into a single elegant function. A string can be thought to probe all possible curves of every possible degree at the same time and is thus a super-efficient “Quantum calculator.” In the realm of quantum theory, they share many properties.
Mirror symmetry illustrates a powerful property of quantum theory called duality: Two classical models can become equivalent when considered as quantum systems, as if a magic wand is waved and all the differences suddenly disappear.
Dualities point to deep but often mysterious symmetries of the underlying quantum theory. The two sides of mirror symmetry offer dual and equally valid perspectives on “Quantum geometry.”
Quantum physics allows ideas to flow freely from one field to the other and provides an unexpected “Grand unification” of these two mathematical disciplines.