The modern era of human genomics began ten years ago with the launch of the HapMap project following the publication of the first draft of the human genome. Although the sequencing of the genome was a major scientific achievement, it has become clear that naive analysis of sequence will not be sufficient to address the fundamental challenge in genomics: determination of the function of genes and the prediction of their regulatory dynamics. We will discuss modern "Star-Seq" technologies that leverage cheap sequencing technology to enable high-throughput molecular biology and that are revealing, for the first time, the complexities of the genome and its dynamics at full resolution. The development, analysis and interpretation of the assays is based on a number of computational, statistical and mathematical primitives that we will survey. The sequencing of the first vertebrate genomes coincided with the founding of the Mathematical Biosciences Institute, and we will highlight the huge impact that the marriage of mathematics and genomics has had on biology, with a view towards the exciting possibilities in the decade ahead.