Career and Education

Sir John Ball is Professor of Mathematics at Heriot-Watt University in Edinburgh. He studied Mathematics as an undergraduate at the University of Cambridge and completed his D.Phil. in 1972 at the University of Sussex under the supervision of Professor 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. There 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.

Following his early research, he was Professor of Applied Analysis at Heriot-Watt University from 1982–1996, during which (1980-1985) he was the recipient of an SERC Senior Fellowship. In 1996, he moved to the University of Oxford, where he held the Sedleian Professorship of Natural Philosophy until 2018. He is now an Emeritus Professor there and an Emeritus Fellow of The Queen’s College.

Throughout his academic journey, he has held prestigious Visiting Professorships at the University of California at Berkeley, the Université Pierre et Marie Curie, Paris, the Tata Institute of Fundamental Research, Bangalore, the Institute for Advanced Study, Princeton, and the University of Montpellier II. His international engagements have continued with a Yusuf Hamied Visiting Professorship to India in 2020, and he was recently awarded a research fellowship at the Institute for Advanced Study, Princeton from 2025–2026.

Honours, Awards and Leadership

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.

Complementing these prestigious fellowships, his career has been recognized with a vast array of global prizes and medals. His prizes and honours include the Whittaker Prize of the Edinburgh Mathematical Society (1981), the Keith Prize of the Royal Society of Edinburgh (1990), the Naylor Prize in Applied Mathematics of the London Mathematical Society (1995), the Theodore Von Karman Prize of the Society of Industrial and Applied Mathematics (1999), the David Crighton Medal of the Institute of Mathematics and its Applications and the London Mathematical Society (2003), the Royal Medal of the Royal Society of Edinburgh (2006), the Sylvester Medal of the Royal Society (2009), the John von Neumann Lecture and Prize of SIAM (2012), the King Faisal Prize for Science (2018), the Leonardo da Vinci award of the European Academy of Sciences (2018), the ISIMM Senior Prize (2018), and the De Morgan Medal of the London Mathematical Society (2022), as well as Honorary Fellowship of St John’s College, Cambridge (2005), and Honorary Membership of the Edinburgh Mathematical Society (2008). He has also received Honorary Doctorates from the École 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.

Beyond his research distinctions, he has also served extensively in international scientific leadership. He was a Council Member of the Engineering and Physical Sciences Research Council from 1994-1999, President of the Edinburgh Mathematical Society from 1989-1990, and of the London Mathematical Society from 1996-1998 and in 2009, and President of the International Mathematical Union from 2003-2006. Following his service on the Executive Board of the International Council for Science from 2011-2018, he most recently served as the President of the Royal Society of Edinburgh from 2021-2025.

 

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. He has also carried out extensive research on the mathematics of liquid crystals, for example concerning orientability of the director and 2D exterior problems in the Oseen-Frank theory, the form of the bulk energy in the Landau-de Gennes theory, and smectic thin films. A more recent interest is in elasticity-based models in computer vision.

 

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

1. Fellow of Royal Society of Edinburgh (elected 1980).
2. Whittaker Prize of Edinburgh Mathematical Society 1981.
3. Junior Whitehead Prize of London Mathematical Society 1982.
4. Fellow of Royal Society of London (elected 1989).
5. Keith Prize, Royal Society of Edinburgh, 1990.
6. Honorary Degree, Ecole Polytechnique F´ed´erale de Lausanne, 1992.
7. Naylor Prize of London Mathematical Society, 1995.
8. Honorary D.Sc., Heriot-Watt University, 1998.
9. Theodore von Karman Prize of the Society for Industrial and Applied Mathematics, 1999.
10. Associé Etranger, Académie des Sciences, Paris, (elected 2000).
11. Honorary D.Sc. University of Sussex, 2000.
12. David Crighton Medal, jointly awarded by the Institute of Mathematics and its Applications and the London Mathematical Society, 2003.
13. Honorary D.Sc. Université Montpellier II, 2003.
14. Fellow, Institute of Mathematics and its Applications, 2003.
15. Honorary D.Sc. University of Edinburgh, 2005.
16. Foreign Member, Istituto Lombardo, 2005.
17. Honorary Fellow, St John’s College, Cambridge, 2005.
18. Knighthood, 2006.
19. Royal Medal, Royal Society of Edinburgh, 2006.
20. Foreign Member, Norwegian Academy of Science and Letters, 2007.
21. Honorary Member, Edinburgh Mathematical Society, 2008.
22. Member. Academia Europaea, 2008.
23. Sylvester Medal, Royal Society, 2009.
24. Honorary Degree, Université Pierre et Maris Curie, Paris, 2010.
25. John von Neumann Lecture and Prize, SIAM, 2012.
26. King Faisal Prize for Science, 2018.
27. Honorary Degree, University of Bucharest, 2018.
28. ISIMM Prize, 2018.
29. Leonardo da Vinci award of the European Academy of Sciences, 2018.
30. Member. European Academy of Sciences, 2018.
31. Yusuf Hamied Visiting Professorship, 2020.
32. De Morgan Medal of London Mathematical Society, 2022.

 

Current Professional Activities

1. Programme Committee, International Centre for Mathematical Sciences, Edinburgh.
2. Member, Board of Governors and Scientific and Academic Advisory Committee, Weizmann Institute, Rehovot, Israel.
3. Council, Weizmann Institute Foundation.
4. Member, EPSRC College.
5. Member, Project Euclid Advisory Board.
6. President, International Scientific Committee, Centre for Mathematical Modelling, Santiago, Chile.
7. Member, Advisory Board, Centre d’Excellence Africain en Sciences Mathématiques, Benin.

 

Most Significant Scholarly Outputs

1. J.M. Ball: Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977) 337-403.
2. J.M. Ball: Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. Royal Soc. London A 306 (1982), 557-611.
3. J.M. Ball and V.J. Mizel, One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation, Arch. Rational Mech. Anal. 90 (1985), no. 4, 325–388.
4. J.M. Ball and R.D. James: Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal. 100 (1987), 13-52.
5. J.M. Ball and A. Zarnescu: Orientability and energy minimization in liquid crystal models, Arch. Rational Mech. Anal. 202 (2011), 493-535.
6. J. M. Ball and R.D. James: Incompatible sets of gradients and metastability: Arch. Rational Mech. Anal. 219 (2015), 1363-1416.
7. J.M. Ball, Slip and twinning in Bravais lattices, J. Elasticity (2023).
8. J.M. Ball and C.L. Horner: A Nonlinear Elasticity Model in Computer Vision, SIAM Journal on Imaging Sciences. 18 (2025) 2458-2488.