Ernst Hairer

Ernst Hairer
Hairer at Oberwolfach, 2006
Ernst Hairer
Born	6/19/1949
Birthplace	Nauders, Tyrol, Austria
Nationality	Austrian
Occupation	Mathematician, university professor
Employer	University of Geneva
Known for	Numerical analysis, geometric numerical integration, numerical methods for ordinary differential equations
Education	PhD in Mathematics, University of Innsbruck
Children	1
Awards	Peter Henrici Prize
Website	http://www.unige.ch/~hairer

Ernst Hairer (born 19 June 1949) is an Austrian mathematician and professor at the University of Geneva whose career has been defined by foundational contributions to numerical analysis, particularly in the fields of numerical methods for ordinary differential equations and geometric numerical integration. Over a career spanning more than four decades, he has authored several landmark textbooks that have become standard references in computational mathematics, including Solving Ordinary Differential Equations (co-authored with Syvert Paul Nørsett and Gerhard Wanner) and works on geometric numerical integration. Hairer completed his doctoral studies at the University of Innsbruck under the supervision of Gerhard Wanner and subsequently built his academic career at the University of Geneva, where he has served on the faculty for decades. He is a recipient of the Peter Henrici Prize, awarded by the Society for Industrial and Applied Mathematics (SIAM), recognizing his distinguished contributions to applied mathematics and numerical analysis. He has also served on the editorial boards of prominent journals, including Mathematics of Computation and the Journal of Scientific Computing. Hairer is the father of Martin Hairer, a mathematician who received the Fields Medal in 2014 and the Breakthrough Prize in Mathematics in 2021 for work in stochastic partial differential equations.

Early Life

Ernst Hairer was born on 19 June 1949 in Nauders, a municipality in the Landeck district of the Austrian state of Tyrol. Nauders is a small Alpine village located near the border with Switzerland and Italy, in the western reaches of Austria. Growing up in this region of Tyrol, Hairer pursued his early education in Austria before entering higher studies in mathematics. Details of his childhood and family background prior to his university studies remain limited in publicly available sources.

Hairer came of age during a period of significant expansion in computational mathematics, as digital computers were beginning to transform the landscape of applied mathematics and scientific computing. The postwar decades saw rapid growth in the development of numerical methods, and Austrian and Swiss universities were active centers of research in this domain. It was within this intellectual environment that Hairer developed his interest in the mathematical foundations underlying numerical computation, an interest that would shape the trajectory of his entire academic career.

Education

Hairer pursued his doctoral studies at the University of Innsbruck, one of Austria's leading research universities, located in the capital of the state of Tyrol. He completed his PhD in mathematics under the supervision of Gerhard Wanner, who would become his most significant and enduring collaborator. The doctoral research focused on topics in numerical analysis, laying the groundwork for the pair's subsequent decades of joint work on numerical methods for differential equations. Following the completion of his PhD, Hairer moved to the University of Geneva in Switzerland, where he joined the mathematics faculty and where Wanner was also based. This institutional connection proved instrumental in fostering one of the most productive collaborations in modern numerical analysis.

Career

University of Geneva

Ernst Hairer has spent the majority of his professional career at the University of Geneva, where he holds a professorship in the Section de mathématiques. The University of Geneva's mathematics department has been a notable center for numerical analysis research, in significant part due to the presence of Hairer and his collaborators. His work at Geneva has encompassed research, teaching, and the supervision of doctoral students. Among his doctoral students is Christian Lubich, who has himself become a prominent figure in the field of numerical analysis, particularly in the study of geometric integration methods and the numerical treatment of differential equations.

Throughout his tenure at Geneva, Hairer has maintained an active research program centered on the development and analysis of numerical methods for ordinary differential equations (ODEs), the study of structure-preserving algorithms, and the mathematical foundations of scientific computing. His contributions have influenced both the theoretical understanding of numerical algorithms and their practical application in computational science and engineering.

Numerical Methods for Ordinary Differential Equations

Hairer's most widely recognized contributions lie in the field of numerical methods for ordinary differential equations. His multi-volume work Solving Ordinary Differential Equations, co-authored with Syvert Paul Nørsett and Gerhard Wanner, is considered a standard reference in the field. The first volume, subtitled Nonstiff Problems, covers classical and modern methods for the numerical solution of ODEs that do not exhibit stiffness, including Runge-Kutta methods, extrapolation methods, and multistep methods. The second volume, Stiff and Differential-Algebraic Problems (co-authored with Wanner), addresses the more computationally challenging domain of stiff differential equations and differential-algebraic equations, covering implicit methods, BDF methods, and Radau methods, among others.

These volumes have been published by Springer and have gone through multiple editions, reflecting both the ongoing relevance of the material and the authors' continued refinement of the presentation. The books are notable for their combination of rigorous mathematical analysis with practical computational guidance, including discussions of implementation details and software considerations. They have been widely used as graduate-level textbooks and as reference works by researchers and practitioners in computational mathematics, physics, engineering, and other fields where the numerical solution of differential equations is essential.

Geometric Numerical Integration

A major theme of Hairer's later research has been geometric numerical integration, a field concerned with the design and analysis of numerical integrators that preserve geometric properties of the continuous dynamical systems they approximate. These properties may include symplecticity (for Hamiltonian systems), volume preservation, conservation of energy or other first integrals, and the preservation of symmetries and reversibility.

Hairer, together with Christian Lubich and Gerhard Wanner, authored the monograph Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, which has become the definitive reference on the subject. The book provides a comprehensive treatment of symplectic integrators, symmetric methods, the Störmer-Verlet method, splitting methods, and the backward error analysis that underpins much of the theoretical framework of geometric integration.

A notable contribution in this area is Hairer's work on the Störmer-Verlet method, a classical numerical integrator with deep roots in celestial mechanics and molecular dynamics. In a 2003 paper published in Acta Numerica, Hairer, Lubich, and Wanner provided a detailed survey of geometric numerical integration as illustrated by the Störmer-Verlet method, covering the method's properties, its long-time behavior, and its connections to symplectic geometry and backward error analysis. This paper demonstrated how the Störmer-Verlet method, despite its simplicity, possesses remarkable structure-preserving properties that account for its effectiveness in long-time simulations of Hamiltonian systems.

The development of geometric numerical integration as a coherent field of study owes much to Hairer's contributions. The framework of backward error analysis, in which a numerical integrator is understood as exactly solving a modified differential equation, has proved to be a powerful tool for understanding the long-time behavior of numerical methods, particularly in the context of Hamiltonian systems and molecular dynamics simulations.

History of Analysis

Beyond his work in numerical analysis, Hairer has contributed to the history of mathematics. Together with Gerhard Wanner, he authored L'analyse au fil de l'histoire (published in English as Analysis by Its History), a book that presents the development of mathematical analysis from a historical perspective. The work traces the evolution of key concepts in analysis—including functions, series, integration, and differential equations—through the contributions of mathematicians from antiquity through the modern era. The book is notable for its integration of historical narrative with mathematical exposition, making it accessible both as a textbook for students and as a scholarly work on the history of mathematical ideas.

Editorial Service

Hairer has served on the editorial boards of several prominent academic journals in mathematics and scientific computing. He is a member of the editorial board of Mathematics of Computation, a journal published by the American Mathematical Society that is one of the leading venues for research in computational mathematics and numerical analysis. He has also served on the editorial board of the Journal of Scientific Computing, published by Springer, which covers computational methods and their applications across the sciences.

Conference and Community Activity

Hairer has been an active participant in the international numerical analysis community. He has delivered invited lectures at major international conferences and workshops. He was listed as a plenary speaker at the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM) in 2009. In 2009, on the occasion of his 60th birthday, a conference was organized at the University of Geneva in his honor, bringing together colleagues and former students to celebrate his contributions to the field. The event featured presentations on topics ranging from numerical methods for ODEs and PDEs to geometric integration, backward error analysis, and applications to molecular dynamics and celestial mechanics, reflecting the breadth of Hairer's influence on the discipline.

Personal Life

Ernst Hairer is the father of Martin Hairer, who was born in Geneva in 1975 and has become one of the most prominent mathematicians of his generation. Martin Hairer received the Fields Medal in 2014 for his development of the theory of regularity structures, a groundbreaking framework for the study of stochastic partial differential equations. In 2021, Martin Hairer was awarded the Breakthrough Prize in Mathematics, carrying a prize of three million US dollars, for his contributions to stochastic analysis.

Austrian media coverage of Martin Hairer's Breakthrough Prize noted the family's Austrian roots, with the Universität Innsbruck — the institution where Ernst completed his doctorate — issuing a press release celebrating the award. The father-son pair represents a notable instance of mathematical distinction spanning two generations, with both having made significant contributions to different branches of mathematics — Ernst in numerical analysis and deterministic differential equations, and Martin in stochastic analysis and probability theory.

Recognition

Peter Henrici Prize

Hairer is a recipient of the Peter Henrici Prize, awarded jointly by the Society for Industrial and Applied Mathematics (SIAM) and the ETH Zurich. The prize recognizes original contributions to applied analysis and numerical analysis and/or exposition appropriate for applied mathematics and scientific computing. The award is named after Peter Henrici, a Swiss-American mathematician who made fundamental contributions to numerical analysis and applied mathematics. The receipt of this prize places Hairer among a select group of mathematicians recognized for their combined contributions to research and mathematical exposition, an apt recognition given the lasting influence of his textbooks and monographs.

Honorary Recognition

The organization of a conference at the University of Geneva in 2009 to mark Hairer's 60th birthday served as a further testament to the esteem in which he is held by the international mathematical community. The conference, which attracted leading researchers from across the field of numerical analysis, highlighted the broad impact of his work across multiple subdisciplines.

Legacy

Ernst Hairer's contributions to numerical analysis have had a lasting impact on both the theory and practice of computational mathematics. His textbooks on the numerical solution of ordinary differential equations, written in collaboration with Gerhard Wanner and Syvert Paul Nørsett, have educated multiple generations of mathematicians, scientists, and engineers. These works are distinguished by their mathematical rigor, their attention to the historical development of ideas, and their practical orientation, combining theoretical analysis with discussions of algorithm implementation and software design.

The field of geometric numerical integration, which Hairer helped to establish and systematize through his research and his monograph with Christian Lubich and Wanner, has become a major area of research in computational mathematics. The insight that numerical methods should respect the geometric structure of the underlying continuous problem has influenced the design of algorithms for molecular dynamics, celestial mechanics, quantum mechanics, and many other domains of computational science. The concept of backward error analysis for numerical integrators, which Hairer and his collaborators developed into a comprehensive theoretical framework, has provided deep insights into why certain numerical methods perform well over long time intervals and has guided the design of new algorithms.

Hairer's doctoral students, including Christian Lubich, have gone on to make significant contributions of their own, extending the reach of his intellectual legacy. His editorial work for leading journals has contributed to maintaining the quality and rigor of published research in computational mathematics.

The mathematical achievements of his son, Martin Hairer, in stochastic analysis have added a further dimension to the family's impact on mathematics, with both father and son having made contributions that are recognized at the highest international level — Ernst through the Peter Henrici Prize and his landmark publications, and Martin through the Fields Medal and the Breakthrough Prize in Mathematics.