While we can read a book one letter at a time, biologists still lack the ability to read a DNA sequence one nucleotide at a time. Instead, they can identify short fragments (approximately 100 nucleotides long) called reads; however, they do not know where these reads are located within the genome. Thus, assembling a genome from reads is like putting together a giant puzzle with a billion pieces, a formidable mathematical problem. We introduce some of the fascinating history underlying both the mathematical and the biological sides of DNA sequencing.