This is a mathematics podcast created by Samuel Hansen in 2012. It is composed of 8 episodes and tells stories behind mathematics on topics including game-playing computers, music and architecture.
Travels in a Mathematical World
This is a podcast by Peter Rowlett, featuring episodes about mathematicians talking about their work, the history of maths and maths news.
Plus magazine is one of my favourite websites on mathematics, which has a section called Plus Podcasts. They have interviews on a various mathematical topics to support their written articles. However, they release episodes infrequently.
A Brief History of Mathematics
This is a BBC Radio 4 documentary in podcast form created by Professor of mathematics Marcus du Sautoy in 2010. It is composed of 10 episodes, each themed around a mathematician or group of mathematicians.
In this podcast, “Marcus du Sautoy reveals the personalities behind the calculations and argues that mathematics is the driving force behind modern science.“
Although new episodes are not published very frequently, Math Mutation is a podcast series by Erik Seligman, aiming to highlight “fun, interesting, or just plain weird corners of mathematics that you probably didn’t hear in school”.