How can anyone say something with certainty about infinity? What can we really know about the mysterious prime numbers without knowing all of them? Just as scientists need data to assess their hypotheses, mathematicians need evidence to prove or disprove conjectures. But what counts as evidence in the intangible realm of number theory? In this episode, Steven Strogatz speaks with Melanie Matchett Wood, a professor of mathematics at Harvard University, to learn how probability and randomness can help establish evidence for the airtight arguments demanded of mathematicians.“The Joy of Why” is a podcast from Quanta Magazine, an editorially independent publication supported by the Simons Foundation. Funding decisions by the Simons Foundation have no influence on the selection of topics, guests, or other editorial decisions in this podcast or in Quanta Magazine. “The Joy of Why” is produced by Susan Valot and Polly Stryker. Our editors are John Rennie and Thomas Lin, with support by Matt Carlstrom, Annie Melchor and Leila Sloman. Our theme music was composed by Richie Johnson. Our logo is by Jackie King, and artwork for the episodes is by Michael Driver and Samuel Velasco. Our host is Steven Strogatz. If you have any questions or comments for us, please email us at quanta@simonsfoundation.org.