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Index structures are a building block of query processing and computer science in general. Since the dawn of computer technology there have been index structures. And since then, a myriad of index structures are being invented and published each and every year. In this paper we argue that the very idea of "inventing an index" is a misleading concept in the first place. It is the analogue of "inventing a physical query plan". This paper is a paradigm shift in which we propose to drop the idea to handcraft index structures (as done for binary search trees over B-trees to any form of learned index) altogether. We present a new automatic index breeding framework coined Genetic Generic Generation of Index Structures (GENE). It is based on the observation that almost all index structures are assembled along three principal dimensions: (1) structural building blocks, e.g., a B-tree is assembled from two different structural node types (inner and leaf nodes), (2) a couple of invariants, e.g., for a B-tree all paths have the same length, and (3) decisions on the internal layout of nodes (row or column layout, etc.). We propose a generic indexing framework that can mimic many existing index structures along those dimensions. Based on that framework we propose a generic genetic index generation algorithm that, given a workload and an optimization goal, can automatically assemble and mutate, in other words 'breed' new index structure 'species'. In our experiments we follow multiple goals. We reexamine some good old wisdom from database technology. Given a specific workload, will GENE even breed an index that is equivalent to what our textbooks and papers currently recommend for such a workload? Or can we do even more? Our initial results strongly indicate that generated indexes are the next step in designing index structures.