We discuss the history of finding quasicrystals, those arrays of atoms that are like crystals--but aren't quite crystals. These are rarely talked about in undergraduate classes. We start with a purely mathematical question by David Hilbert, and move forward through the 1960s and 1970s, till actual quasicrystals were discovered in the 1980s. Then we reach the point where natural quasicrystals were found. Then we hear about some of their potential uses.Support the show Support my podcast at https://www.patreon.com/thehistoryofchemistry Tell me how your life relates to chemistry! E-mail me at steve@historyofchem.com Get my book, O Mg! How Chemistry Came to Be, from World Scientific Publishing, https://www.worldscientific.com/worldscibooks/10.1142/12670#t=aboutBook