The central scientific challenge of the 21st century is developing a mathematical theory of emergence that can explain and predict phenomena such as consciousness and self-awareness. The most successful research program of the 20th century, reductionism, which goes from the whole to parts, seems unable to address this challenge. This is because addressing this challenge inherently requires an opposite approach, going from parts to the whole. In addition, reductionism, by the very nature of its inquiry, typically does not concern itself with teleology or purposeful behavior. Modeling emergence, in contrast, requires the addressing of teleology. Together, these two requirements present a formidable challenge in developing a successful mathematical theory of emergence. In this article, I describe a new theory of emergence, called statistical teleodynamics, that addresses certain aspects of the general problem. Statistical teleodynamics is a mathematical framework that unifies three seemingly disparate domains purposefree entities in statistical Mechanics, human engineered teleological systems in systems engineering, and nature-evolved teleological systems in biology and sociology within the same conceptual formalism. This theory rests on several key conceptual insights, the most important one being the recognition that entropy mathematically models the concept of fairness in economics and philosophy and, equivalently, the concept of robustness in systems engineering. These insights help prove that the fairest inequality of income is a log-normal distribution, which Will emerge naturally at equilibrium in an ideal free market society. Similarly, the theory predicts the emergence of the three classes of network organization exponential, stale-free, and Poisson seen widely in a variety of domains. Statistical. teleodynamics is the natural generalization of statistical thermodynamics, the most successful parts-to-whole systems theory to date, but this generalization is Only a modest step toward a more comprehensive mathematical theory of emergence.