Explore the evolution and future directions of sparse computations in this comprehensive conference talk that examines how sparsity serves as a fundamental assumption enabling efficient computation and parsimonious solutions across science and engineering disciplines. Discover how sparsity manifests in basic sciences including physics, biology, and chemistry while learning about recent advances in sparse computational methods with particular emphasis on large-scale parallelism. Understand the unique challenges that sparsity presents and examine the computational techniques developed to overcome these obstacles. Gain insights into current trends shaping sparse computations, driven by evolving application requirements, increasing data sizes, and changing architectural forces that influence computational approaches in modern scientific computing.