At its core, an emergent property is a phenomenon that arises from simpler interactions but is not predictable or deducible from the sum of its parts alone. In the context of equations, one could argue that the relationship described by the equation is the emergent property, arising from the interaction of its variables.
Take, for instance, the equation for kinetic energy:
KE = ½mv2
The kinetic energy of an object isn't something that is inherent in its mass or its velocity alone. Instead, it emerges when you consider both the mass and the velocity squared in the context of this equation. The equation provides a framework for understanding how these variables interact to produce a new concept: kinetic energy.
However, it's also worth noting that equations are human constructs. They are tools we've developed to describe and predict the behavior of the universe around us. In this sense, the "emergence" is not so much a property of the universe, but rather a product of our understanding and description of it.
While it's not traditional to describe equations as emergent properties, your perspective offers a fresh lens through which we can appreciate the intricate dance of variables and the relationships they form. It's a reminder that mathematics, at its heart, is a language we've crafted to describe the complex symphony of interactions in the universe.