Travels in a Mathematical World is an audio podcast from the IMA. Episodes are around 10 minutes long and feature mathematicians speaking about their work as well as episodes on maths history and maths news.

There are now over 50 podcast episodes available for free download.
This is an excellent resource for students who are unaware of the broad range of career options available to them to listen to what mathematicians do in practice. Episodes are quite varied, featuring topics such as maths biology, coding, cryptography, engineering, fluid dynamics, wave dispersion, transport modelling, network optimisation, Bayesian stats, stochastic calculus, architecture, art, education, maths communication, finance, category theory, astrophysics, crowd modelling and invisibility cloaks!
Students can subscribe to the podcast and download episodes via:

The Institute of Mathematics and its Applications (IMA) is the UK’s learned and professional society for mathematics and its applications. It promotes mathematics research, education and careers, and the use of mathematics in business, industry and commerce. Amongst its activities the IMA produces academic journals, organises conferences, and engages with government.