The major activities of the Society are:
- The provision of grants to support mathematics, especially conferences and joint research activities linking groups at different Universities. It is particularly concerned to provide help for young mathematicians (including research students). It also has schemes to support educational outreach activities and assistance to those with home commitments who wish to attend conferences, etc.
- Society Meetings are held at least five times during the year, including the Annual General Meeting of the Society which takes place each November. Meetings include formal business of the Society such as elections and admissions, as well as lectures intended for a broad mathematical audience.
- The Society is a major academic publisher, producing the Proceedings (est. 1865), the Journal (est. 1926), the Bulletin (est. 1969), the LMS Journal of Computation and Mathematics (est. 1998) and the Journal of Topology (est. 2008); four book series: LMS Lecture Notes, LMS Student Texts, LMS Monographs, and (jointly with the American Mathematical Society) History of Mathematics. The Society publishes Nonlinearity jointly with the Institute of Physics, Compositio Mathematica on behalf of a Dutch Foundation, and Mathematika on behalf of University College London. It has collaborative arrangements to produce translations of three leading Russian mathematical periodicals as well as the Transactions of the Moscow Mathematical Society.
- The Society contributes to public debate on matters affecting mathematics and mathematics education, including position statements outlining Society policy.
- The Society's Library consists of a substantial collection of periodicals obtained in exchange for the Society's publications, copies of books and journals published by the Society and items acquired by the Society as review copies or gifts. The LMS Library is housed in the Library of University College London.
- The award of medals and prizes for outstanding contributions to mathematics. These include the De Morgan Medal, the Pólya Prize and the Whitehead Prizes. The Society jointly with the Institute of Mathematics and its Applications awards the David Crighton Medal.
- The appointment of several lecturerships in the UK, including the Hardy and Mary Cartwright Lecturers, and overseas, including the Forder & Aitken Lecturership.
Submitted by Donald Eastwood on