{ "id": "ep1z0vehgy", "slug": "john-toland", "title": "John Toland", "updated": "2026-10-15", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.scientists", "label": "Physical and mathematical scientists", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.scientists" }, { "id": "physical.scientists.mathematics-statistics", "label": "Mathematicians and statisticians", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.scientists.mathematics-statistics" }, { "id": "physical.scientists.mathematics-statistics.analysts-and-pde-researchers", "label": "Analysts and PDE researchers", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.scientists.mathematics-statistics.analysts-and-pde-researchers" }, { "id": "physical.scientists.mathematics-statistics.analysts-and-pde-researchers.partial-differential-equation-researchers", "label": "Partial differential equation researchers", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.scientists.mathematics-statistics.analysts-and-pde-researchers.partial-differential-equation-researchers" } ], "geo": [ { "id": "geo.weu.t1946.physical.scientists.mathematics-statistics.analysts-and-pde-researchers", "label": "Western Europe · 1946 to 2000: Analysts and PDE researchers", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.weu.t1946.physical.scientists.mathematics-statistics.analysts-and-pde-researchers", "path": [ { "id": "geo.weu", "label": "Western Europe", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.weu" }, { "id": "geo.weu.t1946", "label": "Western Europe · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.weu.t1946" }, { "id": "geo.weu.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.weu.t1946.physical" }, { "id": "geo.weu.t1946.physical.scientists", "label": "Physical and mathematical scientists", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.weu.t1946.physical.scientists" }, { "id": "geo.weu.t1946.physical.scientists.mathematics-statistics", "label": "Mathematicians and statisticians", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.weu.t1946.physical.scientists.mathematics-statistics" }, { "id": "geo.weu.t1946.physical.scientists.mathematics-statistics.analysts-and-pde-researchers", "label": "Analysts and PDE researchers", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.weu.t1946.physical.scientists.mathematics-statistics.analysts-and-pde-researchers" } ] } ], "excerpt": "John Francis Toland is a Northern Irish mathematician in nonlinear analysis who proved Stokes' conjecture on waves of greatest height in 1978 and led the Isaac Newton Institute.", "snippet": "John Francis Toland is a Northern Irish mathematician in nonlinear analysis who proved Stokes' conjecture on waves of greatest height in 1978 and led the Isaac Newton Institute.", "node": "physical.scientists.mathematics-statistics.analysts-and-pde-researchers.partial-differential-equation-researchers", "markdown": "# John Toland\n\n**John Francis Toland** is a Northern Irish-born mathematician working in nonlinear analysis, whose best-known result is a 1978 proof of Stokes' conjecture on waves of greatest height and whose career spans professorships at Bath and Cambridge, the directorship of the [Isaac Newton Institute](https://www.edgepedia.org/isaac-newton-institute), and the presidency of the London Mathematical Society.[1](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed) • [2](https://mathgenealogy.org/id.php?id=58235) The Royal Society, which elected him a Fellow in 1999,[1](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed) cites him \"for his original theorems and remarkable discoveries in nonlinear partial differential equations, including applications to water waves.\"[3](https://royalsociety.org/people/john-toland-12423/)\n\n| Key fact | Detail |\n|---|---|\n| Signature result | In 1978 he proved Stokes' conjecture on the existence of gravity waves of maximum height on deep water, a problem dating to the 19th century[1](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed) |\n| Duality papers | \"Duality in nonconvex optimization\" (J. Math. Anal. Appl. 66(2), 399–415, 1978) and \"A duality principle for non-convex optimisation and the calculus of variations\" (Arch. Rational Mech. Anal. 71(1), 41–61, 1979)[4](https://scholar.google.com/citations?hl=en&user=q0EcMPoAAAAJ) |\n| Doctoral training | DPhil, University of Sussex, 1973, dissertation \"Topological Methods for Nonlinear Eigenvalue Problems\", advisor Charles A. Stuart[2](https://mathgenealogy.org/id.php?id=58235) |\n| Main posts | Professor of Mathematics at Bath from 1982; Scientific Director of ICMS 2002–2010; Director of the Isaac Newton Institute and N M Rothschild & Sons Professor at Cambridge 2011–2016[3](https://royalsociety.org/people/john-toland-12423/) • [1](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed) |\n| Honors | FRS 1999, FRSE 2003, LMS Senior Berwick Prize 2000, Royal Society Sylvester Medal 2012[3](https://royalsociety.org/people/john-toland-12423/) • [1](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed) |\n| Output | 111 publications listed by zbMATH since 1973; over a hundred research articles and two books per his Bath oration[5](https://zbmath.org/authors/?q=ai:toland.john-francis) • [6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/) |\n| Academic family | 8 doctoral students (all at Bath, 1986–2005) and 15 descendants[2](https://mathgenealogy.org/id.php?id=58235) |\n\n## Life and career\n\nToland was born in Londonderry and took his first degree at [Queen's University Belfast](https://www.edgepedia.org/queens-university-belfast), where he gained a first-class degree in pure mathematics.[6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/) • [7](https://www.sussex.ac.uk/news/features/archive/winter-graduation-2017/john-toland) Graduate study at the [University of Sussex](https://www.edgepedia.org/university-of-sussex) led to an MSc and then a 1973 DPhil on topological methods for nonlinear eigenvalue problems, supervised by Charles A. Stuart.[2](https://mathgenealogy.org/id.php?id=58235) • [6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/) A fellowship at the [University of Essex](https://www.edgepedia.org/university-of-essex)'s Fluid Mechanics Research Institute followed, and it was there that he began the research on the Stokes conjectures that shaped much of his career.[6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/)\n\nAfter two years at [University College London](https://www.edgepedia.org/university-college-london) he accepted a professorship at the [University of Bath](https://www.edgepedia.org/university-of-bath) at age 32.[6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/) The Royal Society record gives his Bath chair as 1982–2011,[3](https://royalsociety.org/people/john-toland-12423/) while the Isaac Newton Institute biography states he was professor at Bath between 1982 and 2010.[8](https://www.newton.ac.uk/about/history/professor-john-toland-frs-frse/) From 2002 to 2010 he was also Scientific Director of the International Centre for Mathematical Sciences in Edinburgh.[3](https://royalsociety.org/people/john-toland-12423/) In 2011 he left Bath, after 29 years, to become Director of the Isaac Newton Institute for Mathematical Sciences in Cambridge and N M Rothschild & Sons Professor of Mathematical Sciences, succeeding Sir David Wallace; he served until 2016 and was a Fellow of St John's College.[6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/) • [1](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed) • [9](https://www.newton.ac.uk/wp-content/uploads/2021/03/Jan-2017.pdf) He is now an Emeritus Professor in the Department of Mathematical Sciences at Bath.[10](https://researchportal.bath.ac.uk/en/persons/john-toland/)\n\n## Mathematical work\n\n**Water waves.** Toland's most celebrated contribution is the rigorous theory of steady waves on water, in particular the elucidation of the extreme wave originally conjectured by Stokes in 1880.[3](https://royalsociety.org/people/john-toland-12423/) In 1978 he proved Stokes' conjecture on the existence of gravity waves of maximum height on deep water, resolving a problem that had stood since the 19th century.[1](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed) His papers on this theme include \"On the Stokes conjecture for the wave of extreme form\" and \"On the existence of a wave of greatest height and Stokes's conjecture\".[4](https://scholar.google.com/citations?hl=en&user=q0EcMPoAAAAJ) From 2007 he collaborated with Pavel Plotnikov of the [Russian Academy of Sciences](https://www.edgepedia.org/russian-academy-of-sciences)' Hydrodynamic Institute in [Novosibirsk](https://www.edgepedia.org/novosibirsk), who made a nine-month visit to Bath in 2007/8, on the Stokes conjectures including the shape of a wave of greatest height.[6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/) The mathematics Toland said he was most proud of was a substantial joint paper with Plotnikov that finally showed the existence of proper periodic solutions to the standing wave problem on deep water.[11](https://www.essex.ac.uk/-/media/documents/alumni/honorary-graduates/2009/johntoland2009oration.pdf) With C. J. Amick he published \"Uniqueness and related analytic properties for the Benjamin-Ono equation — a nonlinear Neumann problem in the plane\", connecting the water-wave program to another nonlinear equation of mathematical physics.[4](https://scholar.google.com/citations?hl=en&user=q0EcMPoAAAAJ) • [5](https://zbmath.org/authors/?q=ai:toland.john-francis) Late in his career he co-authored the survey \"Traveling water waves — the ebb and flow of two centuries\" with Haziot, Hur, Strauss, Wahlén, Walsh, and Wheeler, published in the *Quarterly of Applied Mathematics* 80(2), 317–401.[10](https://researchportal.bath.ac.uk/en/persons/john-toland/)\n\n**Duality and variational methods.** In 1978 and 1979 Toland published two papers that established a duality principle for non-convex optimization and the calculus of variations: \"Duality in nonconvex optimization\" in the *Journal of Mathematical Analysis and Applications* 66(2), 399–415, and \"A duality principle for non-convex optimisation and the calculus of variations\" in the *Archive for Rational Mechanics and Analysis* 71(1), 41–61.[4](https://scholar.google.com/citations?hl=en&user=q0EcMPoAAAAJ) Convex and non-convex duality theory remains listed among his research interests, alongside nonlinear analysis and PDEs, analytic, variational, and topological methods, bifurcation theory, and nonlinear hydrodynamic waves.[10](https://researchportal.bath.ac.uk/en/persons/john-toland/)\n\n**Bifurcation and other work.** The Royal Society citation records fundamental contributions to abstract global bifurcation theory, non-convex optimization, dynamical systems, and the stability of rotating chains.[3](https://royalsociety.org/people/john-toland-12423/) The work that earned him the Senior Berwick Prize was carried out in part jointly with the Australian mathematician E. N. Dancer.[11](https://www.essex.ac.uk/-/media/documents/alumni/honorary-graduates/2009/johntoland2009oration.pdf) His Bath portal also lists joint work with Buffoni, including \"Connected Sets in Global Bifurcation Theory\", and a paper with Plotnikov in *Annali di Matematica Pura ed Applicata* 202(4), 1803–1833.[10](https://researchportal.bath.ac.uk/en/persons/john-toland/)\n\n## By the numbers\n\nzbMATH lists 111 publications since 1973, including works on the Benjamin–Ono equation and the Peierls–Nabarro equation.[5](https://zbmath.org/authors/?q=ai:toland.john-francis) His Bath oration counts over a hundred research articles, most of substantial length, and two co-authored books.[6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/) The Mathematics Genealogy Project records 8 doctoral students, all supervised at Bath between 1986 and 2005, including Mark Jones (1986), Elaine Crooks (1996), Owen Lyne (1996), and Eugen Varvaruca (2005), and 15 descendants in total.[2](https://mathgenealogy.org/id.php?id=58235) His Bath chair lasted 29 years by his oration's count.[6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/)\n\n## Leadership and service\n\nToland served as President of the London Mathematical Society from 2005 to 2007.[8](https://www.newton.ac.uk/about/history/professor-john-toland-frs-frse/) In 2010 he was appointed Chair of the Mathematical Sciences panel for the Research Excellence Framework by HEFCE, and between 2010 and 2018 he sat on the Executive Committee of the [International Mathematical Union](https://www.edgepedia.org/international-mathematical-union), including its Mentoring African Research in [Mathematics](https://www.edgepedia.org/mathematics) subcommittee.[8](https://www.newton.ac.uk/about/history/professor-john-toland-frs-frse/) • [6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/) As INI Director he welcomed the [Turner Prize](https://www.edgepedia.org/turner-prize) winner Grenville Davey as Artist in Residence in 2012 and the poet John Kinsella as Poet in Residence from 2014, and he chaired the 2014 Research Excellence Framework.[9](https://www.newton.ac.uk/wp-content/uploads/2021/03/Jan-2017.pdf)\n\n## Honors and recognition\n\nToland was elected [Fellow of the Royal Society](https://www.edgepedia.org/fellow-of-the-royal-society) in 1999 and of the Royal Society of Edinburgh in 2003.[1](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed) He received the London Mathematical Society's Senior Berwick Prize in 2000 and the Royal Society's Sylvester Medal in 2012.[3](https://royalsociety.org/people/john-toland-12423/) Honorary doctorates followed from Queen's University Belfast (2000), the [University of Edinburgh](https://www.edgepedia.org/university-of-edinburgh) (2007), [Heriot-Watt University](https://www.edgepedia.org/heriot-watt-university) (2007), and the University of Essex (2009), and he became an honorary fellow of UCL in 2008.[1](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed) He held an EPSRC Senior Research Fellowship from 1997 to 2002 and was the first recipient of the University of Bath Vice-Chancellor's Medal for Research.[8](https://www.newton.ac.uk/about/history/professor-john-toland-frs-frse/) • [6](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/) In 2013 he gave the Seventh Brooke Benjamin Lecture in Fluid Dynamics at Oxford, entitled \"the fascination of what's difficult: Mathematical aspects of classical water wave theory from the past 20 years\".[12](https://www.maths.ox.ac.uk/node/852)\n\n## References\n\n1. [Next Director of the Isaac Newton Institute appointed, University of Cambridge](https://www.cam.ac.uk/news/next-director-of-the-isaac-newton-institute-for-mathematical-sciences-appointed)\n2. [John Toland, The Mathematics Genealogy Project](https://mathgenealogy.org/id.php?id=58235)\n3. [Professor John Toland FRS, Royal Society Fellow record](https://royalsociety.org/people/john-toland-12423/)\n4. [Prof. J.F. Toland, Google Scholar profile](https://scholar.google.com/citations?hl=en&user=q0EcMPoAAAAJ)\n5. [Toland, John Francis, zbMATH](https://zbmath.org/authors/?q=ai:toland.john-francis)\n6. [Professor John Francis Toland: Oration, University of Bath](https://www.bath.ac.uk/corporate-information/professor-john-francis-toland-oration/)\n7. [Professor John Toland FRS FRSE, University of Sussex news](https://www.sussex.ac.uk/news/features/archive/winter-graduation-2017/john-toland)\n8. [Professor John Toland FRS FRSE, Isaac Newton Institute](https://www.newton.ac.uk/about/history/professor-john-toland-frs-frse/)\n9. [INI Director John Toland retires, INI Newsletter, January 2017](https://www.newton.ac.uk/wp-content/uploads/2021/03/Jan-2017.pdf)\n10. [John Toland, University of Bath research portal](https://researchportal.bath.ac.uk/en/persons/john-toland/)\n11. [John Toland honorary graduate oration, University of Essex, 2009](https://www.essex.ac.uk/-/media/documents/alumni/honorary-graduates/2009/johntoland2009oration.pdf)\n12. [Professor John Toland gives the Brooke Benjamin Lecture in Fluid Dynamics, University of Oxford](https://www.maths.ox.ac.uk/node/852)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Physical and mathematical scientists › Mathematicians and statisticians › Analysts and PDE researchers › Partial differential equation researchers*\n\n*Initially written Oct 10, 2026 · Edited: Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [ "https://scholar.google.com/citations?hl=en&user=q0EcMPoAAAAJ" ], "url": "https://www.edgepedia.org/john-toland", "markdown_url": "https://www.edgepedia.org/john-toland.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"John Toland\", Edgepedia (EdgeChat), https://www.edgepedia.org/john-toland. Edgepedia Community License 1.0.", "credit_md": "\"[John Toland](https://www.edgepedia.org/john-toland)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/john-toland](https://www.edgepedia.org/john-toland). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"John Toland\", Edgepedia (EdgeChat), https://www.edgepedia.org/john-toland. Edgepedia Community License 1.0.", "speakable": "John Francis Toland is a Northern Irish mathematician in nonlinear analysis who proved Stokes' conjecture on waves of greatest height in 1978 and led the Isaac Newton Institute." }