List of interesting math podcasts? mathfactor is one I listen to.  Does anyone else have a recommendation?
 A: Strongly Connected components
 is a great podcast about interviews to several american mathematicians. 
A: I think Math for Primates is kind of good.
A: My favorite theorem is pretty good.
A: The Science of Better is a good applied math podcast.  Features applications of operations research to practical problems.
A: I listen to Math Mutation Podcast. The topics are interesting and understandable by a layman.
A: MAA podcast has an archive. http://www.maa.org/audio%20clips/podcast/podcast.html
I think it has stopped producing new ones.  
A: The Numberphile Podcast is relatively new.
Brady Haran, the maker of the Numberphile YouTube channel, interviews famous mathematicians about their life and their favorite math bits.
https://www.numberphile.com/podcast
A: Somewhat self promotion but Dave Gale and Colin Beveridge record the Wrong, But Useful Podcast on an approximately monthly basis.
http://www.flyingcoloursmaths.co.uk/category/podcasts/
Also can be found on iTunes.
A: I think http://lineardigressions.com/ is enticing. Especially if you're interests involve machine learning. 
A: Breakingmathpodcast.com
A new podcast series with a lot of diverse topics based out of the University of New Mexico. I think I've listened to all of the full episodes in a week (There are about 20). They discuss everything from the Navier Stokes equations, to Hacking culture.
Good depth for those who are looking for overviews. I am an applied math undergraduate with a background in the social sciences, and I follow most things just fine.
Their primary objective is to make math accessible to everyone. They attempt to break down higher-level math concepts in a way that an 8th-grade student will understand.
Plus...... It's rather funny.
-Cody
A: I would like to draw attention to the beautifully produced podcast Relatively Prime hosted by Samuel Hansen, which was funded through a successful kickstarter campaign. All eight episodes are well worth a listen and include interviews with some very high profile and influential mathematicians.
A: Peter Rowlett has a couple mathematical podcasts.  Travels in a Mathematical World produced 64 episodes, but recently stopped.  He has a new podcast Math / Maths that he co-hosts with Samuel Hansen.  
Samuel Hansen also has a couple other podcasts: Strongly Connected Components and Permutations and Combinations. Strongly Connected Components is more mathematical and often features interviews.  I've only listened to Permutations and Combinations once or twice.  I believe it's more of a comedy show.
A: More or Less is a BBC Radio 4 programme about maths and statistics in the news, and there is a free podcast. It's presented by Tim Harford, the Undercover Economist from the Financial Times.
A: The BBC has a History of Mathematics series. Worth listening to. http://www.bbc.co.uk/podcasts/series/maths
A: Recently I created a curated list about all Math resources I am subscribed to ( blogs, Youtube Channels and podcasts). Here are some podcasts:


*

*Relatively Prime

*Ben Ben Blue (This is from the creator of the youtube channel 3 Brown 1 Blue.)


And Interesting Channels:


*

*3Blue1Brown

*Mathologer

*NumberPhile

*PBS Infinite Series

*StandUpMaths
A: I think that Modellansatz from the KIT (Karlsruhe, Germany) is a good one. It is a podcast in German but it has many episodes in English since some interview partner do not speak German obviously.
The themes are as divers as Cerebral Flow, Crime Prevention, Nonlinear Electrodynamics, ...
A: Actually, I was looking for a good math podcast a while back and I didn't find one that fit my fancy, so I actually started one at my university interviewing mathematicians about what it is like to do research and work in academia. I've linked to it below if you want to check it out!
Group Theory Podcast
A: The YouTube channel Sense Makes Math has a a video-podcast called {Q,E,D}. Sometimes they do proofs so they use a whiteboard.
A: You can also check out the Lxt's Tylk Mzth podcast on Spotify here:
It's pretty much a chill and casual podcast about abstract algebra and math jokes in a someone rigorous way. Edit: I think it's also on Soundcloud.
A: I enjoy My Favorite Theorem. This podcast helped broaden my mathematical knowledge and diversified my interests by showcasing a broad range of mathematicians and their theorems. It's pretty neat!
A: There's a new maths podcast that you may be interested in that reviews "Maths at the Movies: Interstellar plus SPECIAL GUEST" in its first series. It's a slightly anarchic look at movies, mathematics, and life: www.mathsat.co.uk (direct link to podcast MP3 audio). There are some additional podcasts included as other blog entries.
A: I have a math podcast called the Life and Math Podcast (LaMP). I interview mathematicians from a wide variety of backgrounds to learn about

*

*Their path in life from high school to where they are now, and

*The math they do.

Each interview is released as 2 episodes, a "Life" and a "Math". It's up as audio or video format.
So far I've had a former WWE-style pro wrestler, a guy who dropped out of undergrad to join the Army, and a prof who didn't get into a single college or university who all became mathematicians.
The audio is available on most podcast hosts (apple, spotify, etc). Here's a link to the podcast on soundcloud.
The video version is on Youtube (link to Youtube channel). I also make instructional videos on topics that come up in the interview which can be found on the Youtube channel. Things like "What are categories, functors, & natural transformations?". Enough to help students follow along with the interviews.
Everything can also all be found at https://lifeandmath.com. Roughly one interview every 1-2 weeks.
