In the tiling of wallpaper and bathroom floors, collective repeated patterns often emerge. Mathematicians have long tried to find a tiling shape that never repeats in this way. In 2023, they lauded an unexpected amateur victor. That discovery of the elusive aperiodic monotile propelled the field into new dimensions.

The study of tessellation is much more than a fun thought exercise: Peculiar, rare tiling formations can sometimes seem to tell us something about the natural world, from the structure of minerals to the organization of the cosmos. In this episode, Janna Levin speaks with mathematician Natalie Priebe Frank about these complex geometric combinations, and where they may pop up unexpectedly. Specifically, they explore her research into quasicrystals — crystals that, like aperiodic tiles, enigmatically resist structural uniformity..

Listen on Apple Podcasts, Spotify, TuneIn or your favorite podcasting app, or you can stream it from Quanta.

The universe seems like it should be unfathomably complex. How then is science able to crack fundamental questions about nature and life? Scientists and philosophers alike have often commented on the “unreasonable” success of mathematics at describing the universe. That success has helped science probe some profound mysteries — but as the physicist Nigel Goldenfeld points out, it also helps that the “hard” physical sciences, where this progress is most evident, are in major ways simpler than the “soft” biological sciences.

In this episode, Goldenfeld speaks with co-host Steven Strogatz about the scientific importance of asking the right questions at the right time. They also discuss the mysterious effects of “emergence,” the phenomenon that allows new properties to arise in systems at different scales, imposing unexpected order on cosmic complexity.

Listen on Apple Podcasts, Spotify, TuneIn or your favorite podcasting app, or you can stream it from Quanta.

During traumatic periods and their aftermath, our brains can fall into habitual ways of thinking that may be helpful in the short run but become maladaptive years later. For the brain to readjust to new situations later in life, it needs to be restored to the malleable state it was in when the habits first formed. That is exactly what Gül Dölen, a neuroscientist and psychiatric researcher at the University of California, Berkeley, is working toward in her lab. What is her surprising tool? Psychedelics.

In this episode, Dölen shares with co-host Janna Levin the surprising potential of psychedelics to change the lives of those grappling with addiction, depression and post-traumatic stress.

Listen on Apple Podcasts, Spotify, TuneIn or your favorite podcasting app, or you can stream it from Quanta.