The database research community has been building methods to store, access, and update data for more than four decades. Throughout the evolution of the structures and techniques used to access data, access methods adapt to the ever changing hardware and workload requirements. Today, even small changes in the workload or the hardware lead to a redesign of access methods. The need for new designs has been increasing as data generation and workload diversification grow exponentially, and hardware advances introduce increased complexity. New workload requirements are introduced by the emergence of new applications, and data is managed by large systems composed of more and more complex and heterogeneous hardware. As a result, it is increasingly important to develop application-aware and hardware-aware access methods. The fundamental challenges that every researcher, systems architect, or designer faces when designing a new access method are how to minimize, i) read times (R), ii) update cost (U), and iii) memory (or storage) overhead (M). In this paper, we conjecture that when optimizing the read-update-memory overheads, optimizing in any two areas negatively impacts the third. We present a simple model of the RUM overheads, and we articulate the RUM Conjecture. We show how the RUM Conjecture manifests in stateof-the-art access methods, and we envision a trend toward RUM-aware access methods for future data systems.