The London Institute does research in theoretical physics and mathematics. Its work spans four themes: Mathematics that unifies; The elegant universe; Life, learning and emergence; and the Theory of human enterprise. Its researchers have published papers on statistical physics in
Nature Reviews Physics; algebraic geometry in the
Journal of High Energy Physics; graph theory in the
European Journal of Combinatorics; and network theory in
Physical Review Letters. In 2024, researcher Oleksandr Gamayun’s paper on topological solitons became LIMS's first to be published in
Nature. In 2021, the UK government announced the launch of
Advanced Research and Invention Agency (ARIA), a new science agency designed to support projects that may create "a paradigm shift in science". Following the agency's creation, LIMS compiled a list of the 23 Mathematical Challenges of our time, inspired by
David Hilbert's list of
23 challenges published in 1900, 17 of which have been solved or partially resolved; the LIMS list was published in full in
The Times. == Leadership and governance ==