The 2020 LMS Prize winners were announced at the Society Meeting on Friday 26 June 2020. The LMS extends its congratulations to this year’s prize winners and for their continued contributions to mathematics.

**Professor Martin Liebeck** of Imperial College London is awarded the Pólya Prize for his profound and prodigious contributions to group theory, particularly the subgroup structure of simple groups and probabilistic group theory. See the full citation here.

**Professor Peter Clarkson** of the University of Kent is awarded the Senior Anne Bennett Prize in recognition of his tireless work to support gender equality in UK mathematics, and particularly for his leadership in developing good practice among departments of mathematical sciences. See the full citation here.

**Professor Thomas Hales** of the University of Pittsburgh is awarded the Senior Berwick Prize in recognition of his book ‘Dense sphere packings. A blueprint for formal proofs’, published in the LMS Lecture Note Series in 2012. See the full citation here.

A Shephard Prize is awarded to **Regius Professor Kenneth Falconer, FRSE**, of the University of St Andrews, for his many original and profound results in fractal geometry, particularly the description, occurrence, geometrical properties and dimensional analysis of fractal sets and measures. See the full citation here.

A Shephard Prize is awarded to **Professor Des Higham, FRSE**, of the University of Edinburgh. Higham has sought to make the theory, application, and insights from network science accessible to wide audiences, with much effort invested in public events and transparent descriptions. He is a natural communicator and presents in an engaging way, highlighting some intriguing paradoxes. See the full citation here.

**Professor Françoise Tisseur,** of the University of Manchester, is awarded the Fröhlich Prize for her important and highly innovative contributions to the analysis, perturbation theory, and numerical solution of nonlinear eigenvalue problems. See the full citation here.

**Dr Maria Bruna,** of the University of Cambridge, is awarded a Whitehead Prize in recognition of her outstanding research in asymptotic homogenisation, most prominently in the systematic development of continuum models of interacting particles systems. See the full citation here.

**Dr Ben Davison,** of the University of Edinburgh, is awarded a Whitehead Prize in recognition of his outstanding contributions to the foundations, the structure and applications of Donaldson–Thomas invariants. See the full citation here.

**Dr Adam Harper,** of the University of Warwick, is awarded a Whitehead Prize for his deep and important contributions to analytic number theory, and in particular for his work on the value distribution of the Riemann zeta-function and random multiplicative functions using sophisticated ideas and techniques from probability theory. See the full citation here.

**Dr Holly Krieger,** of the University of Cambridge, is awarded a Whitehead Prize for her deep contributions to arithmetic dynamics, to equidistribution, to bifurcation loci in families of rational maps, and her recent proof (with DeMarco and Ye) of uniform boundedness results for numbers of torsion points on families of bielliptic genus two curves in their Jacobians. See the full citation here.

**Professor Andrea Mondino** of the University of Oxford is awarded a Whitehead Prize in recognition of his contributions to geometric analysis in differential and metric settings. In particular, he has played a central part in the development of the theory of metric measure spaces with Ricci curvature lower bounds. See the full citation here.

**Dr Henry Wilton** of the University of Cambridge is awarded a Whitehead Prize for his remarkable contributions to geometric and combinatorial group theory. See the full citation here.