Professor Sir John Ball

Senior Fellow of Hong Kong Institute for Advanced Study, City University of Hong Kong

Professor at Heriot-Watt University, Edinburgh, UK

Director of the Oxford Centre for Nonlinear PDE, UK

Fellow of the Royal Society, UK

Member of the Academia Europaea

Professor Sir John Ball

Contact Information

Web: Personal Homepage
John Ball is Professor of Mathematics at Heriot-Watt University in Edinburgh. From 1996-2018 he was Sedleian Professor of Natural Philosophy at the Mathematical Institute, University of Oxford, He is an Emeritus Professor in Oxford and an Emeritus Fellow of The Queen's College. Before this he was Professor of Applied Analysis at Heriot-Watt University from 1982-1996. He took an undergraduate degree in Mathematics at Cambridge, and obtained a D.Phil. in 1972 at the University of Sussex under the direction of David Edmunds.

He moved to Heriot-Watt in 1972 on an SRC postdoctoral fellowship which enabled him to spend an extended period at Brown University, where he began work on the existence of solutions to the equilibrium equations of nonlinear elasticity, as well as furthering his interest in infinite-dimensional dynamical systems. The recipient from 1980-85 of an SERC Senior Fellowship, he has held Visiting Professorships at the University of California at Berkeley, at the Université Pierre et Marie Curie, Paris, at the Tata Institute of Fundamental Research, Bangalore, at the Institute for Advanced Study, Princeton, and at the University of Montpellier II.

He was elected a Fellow of the Royal Society of Edinburgh in 1980, a Fellow of the Royal Society in 1989, an Associé Etranger of the Académie des Sciences in 2000, a Fellow of the Institute for Mathematics and its Applications in 2003, a Foreign Member of the Istituto Lombardo in 2005, a Foreign Member of the Norwegian Academy of Science and Letters in 2007, a Member of the Academia Europaea in 2008, and a Fellow of the American Mathematical Society in 2012. Other awards include the 1981 Whittaker Prize of the Edinburgh Mathematical Society, the 1990 Keith Prize of the Royal Society of Edinburgh, the 1995 Naylor Prize in Applied Mathematics of the London Mathematical Society, the 1999 Theodore Von Karman Prize of the Society of Industrial and Applied Mathematics, the 2003 David Crighton Medal of the Institute of Mathematics and its Applications and the London Mathematical Society, the 2006 Royal Medal of the Royal Society of Edinburgh, the 2009 Sylvester Medal of the Royal Society, the 2012 John von Neumann Lecture and Prize of SIAM, the 2018 King Faisal Prize for Science, the 2018 Leonardo da Vinci award of the European Academy of Sciences, Honorary Fellowship of St John’s College, Cambridge in 2005, Honorary Membership of the Edinburgh Mathematical Society in 2008, and Honorary Doctorates from the Ecole Polytechnique Fédérale de Lausanne, Heriot-Watt University, the University of Montpellier II, the University of Sussex, the University of Edinburgh, the Université Pierre et Marie Curie and the University of Bucharest. He was a Council Member of the Engineering and Physical Sciences Research Council from 1994-1999, President of the Edinburgh Mathematical Society from 1989-90, and of the London Mathematical Society from 1996-1998 and in 2009, and President of the International Mathematical Union from 2003-06. From 2011-2018 he was a member of the Executive Board of the International Council for Science.

Research Interests

John Ball's main research areas lie in  the calculus of variations, nonlinear partial differential equations, infinite-dimensional dynamical systems and their applications to nonlinear mechanics. In solid mechanics, he is especially interested in the mathematics of microstructure arising from phase transformations in solids, using models based on nonlinear elasticity, where the problem of predicting microstructure morphology is related to deep unsolved questions of the multi-dimensional calculus of variations such as understanding quasiconvexity. A more recent research interest is in the mathematics of liquid crystals.

Academic Qualifications

  • Open Exhibition in Mathematics to St John’s College, Cambridge.
  • Honours Degree in Mathematics, Cambridge University.
  • D.Phil. in Mechanical Engineering (supervised by Professor D E Edmunds, Mathematics Division), University of Sussex.

Awards and Fellowships

  • Fellow of Royal Society of Edinburgh (elected 1980).
  • Whittaker Prize of Edinburgh Mathematical Society 1981.
  • Junior Whitehead Prize of London Mathematical Society 1982.
  • Fellow of Royal Society of London (elected 1989).
  • Keith Prize, Royal Society of Edinburgh, 1990.
  • Honorary Degree, Ecole Polytechnique F´ed´erale de Lausanne, 1992.
  • Naylor Prize of London Mathematical Society, 1995.
  • Honorary D.Sc., Heriot-Watt University, 1998.
  • Theodore von Karman Prize of the Society for Industrial and Applied Mathematics, 1999.
  • Associ´e Etranger, Acad´emie des Sciences, Paris, (elected 2000).
  • Honorary D.Sc. University of Sussex, 2000.
  • David Crighton Medal, jointly awarded by the Institute of Mathematics and its Applications and the London
  • Mathematical Society, 2003.
  • Honorary D.Sc. Universit´e Montpellier II, 2003.
  • Fellow, Institute of Mathematics and its Applications, 2003.
  • Honorary D.Sc. University of Edinburgh, 2005.
  • Foreign Member, Istituto Lombardo, 2005.
  • Honorary Fellow, St John’s College, Cambridge, 2005.
  • Knighthood, 2006.
  • Royal Medal, Royal Society of Edinburgh, 2006.
  • Foreign Member, Norwegian Academy of Science and Letters, 2007.
  • Honorary Member, Edinburgh Mathematical Society, 2008.
  • Member. Academia Europaea, 2008.
  • Sylvester Medal, Royal Society, 2009.
  • Honorary Degree, Universit´e Pierre et Maris Curie, Paris, 2010.
  • John von Neumann Lecture and Prize, SIAM, 2012.

Current Professional Activities

National and International

  • Member Executive Board, International Council for Science, 2011-2018.
  • Member, Scientific Advisory Board, Heilbronn Institute, 2010 -.
  • Member, Mathematics Subgroup to the GCHQ Science Advisory Committee, 2013 -.
  • Member, EPSRC Mathematical Sciences Strategic Advisory Team, 2012 -.
  • Board Member of MARM (Mentoring African Research in Mathematics project of IMU, LMS, AMMSI).
  • Programme Committee, International Centre for Mathematical Sciences, Edinburgh, 1991-.
  • Member, Board of Governors and Scientific and Academic Advisory Committee, Weizmann Institute, Rehovot,
  • Israel, 1998-.
  • Council, Weizmann Institute Foundation, 2000-.
  • Member, EPSRC College, 2003-.
  • Member, Scientific Steering Committee, Basque Centre for Applied Mathematics, 2009-.
  • Trustee, Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University, 2010-.
  • Member, Project Euclid Advisory Board, 2011-.
  • Chair, Steering Committee for the CDT Cambridge Centre for Analysis, 2010-.
  • President, International Scientific Committee, Centre for Mathematical Modelling, Santiago, Chile, 2012-.
  • Member, Strategic Committee, Sorbonne Universities, 2012-.
  • Member, Advisory Board, Centre d’Excellence Africain en Sciences Mathematiques, Benin, 2014-.
  • Member, Adams Prize Committee, Cambridge, 2016-.
  • Member, Shaw Prize Committee, 2016-.
  • Member, Fudan Prize Committee, 2016-.
  • Member, Jose Luis Rubio de Francia’s Prize Committee, Royal Spanish Mathematical Society, 2017.


  • Director, Oxford Centre for Nonlinear PDE.
  • Co-Director, Oxford CDT in Analysis of Nonlinear PDE.

Most Significant Scholarly Outputs

  • J.M. Ball: Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977) 337-403.
  • J.M. Ball: Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. Royal Soc. London A 306 (1982), 557-611.
  • J.M. Ball and R.D. James: Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal. 100 (1987), 13-52.
  • J.M. Ball and A. Zarnescu: Orientability and energy minimization in liquid crystal models, Arch. Rational Mech. Anal. 202 (2011), 493-535.
  • J. M. Ball and R.D. James: Incompatible sets of gradients and metastability: Arch. Rational Mech. Anal. 219 (2015), 1363-1416.