The London Mathematical Society and the Institute of Mathematics and its Applications are delighted to announce the 2025 LMS/IMA Joint Meeting on ‘Securing the Twenty-First Century Internet’. Cybersecurity is the challenge of making sure that our communications and operations on the Internet take place as intended. It is an ever-growing problem in both scale and complexity, and cybersecurity failures can have devastating real-world effects. Mathematics can be a significant enabler for good cybersecurity and new mathematical ideas for securing the twenty-first century Internet are constantly arising. The aim of this meeting is to bring together experts from mathematics and cybersecurity to highlight current research developments within this important area, including post-quantum algorithms, situational awareness from analysis of network data, and homomorphic encryption. We welcome all who are interested to attend this event, with registration open to both LMS and IMA members and to non-members.