**Ivo Babuska** lived through difficult times in Czechoslovakia as he was growing up. The German invasion of the west of the country in September 1938 was followed six months later by the whole country being taken over by Germany at the start of World War II. Babuska was thirteen years old at this time and most of his secondary education, therefore, took place under German occupation. Only after the war ended in 1945 was he able to begin his university education.

Babuska studied civil engineering at the Czech Technical University in Prague and was awarded a Dipl. Ing in 1949. He undertook research in engineering, advised by F Faltus, and was awarded a Dr. Tech. by the Faculty of Civil Engineering of the Czech Technical University in 1951. However, simultaneously with this research in engineering, Babuska was a mathematics student at the Central Mathematical Institute in Prague studying under Vladimir Knichal. While Babuska was studying at the Institute, its name changed in 1953 to the Mathematical Institute of the Czechoslovak Academy of Sciences. At the Mathematical Institute, in addition to Knichal, he was strongly influenced by Eduard Čech who was appointed Director of the Central Mathematical Institute in 1950, and Director of the Czechoslovak Academy of Sciences in 1952. In 1955 Babuska was awarded his Candidate's degree (equivalent to a Ph.D.).

Given Babuska's training, coming first to engineering and, slightly later to mathematics, it is no surprise to see his publications being in the engineering area but become more slanted towards advanced mathematical techniques to solve engineering problems. His first papers, all written in Czech, were *Welding stresses and deformations* (1952), *Plane elasticity problem* (1952), *A contribution to the theoretical solution of welding stresses and some experimental results* (1953), *A contribution to one method of solution of the biharmonic problem* (1954), *Solution of the elastic problem of a half-plane loaded by a sequence of singular forces* (1954), (with L Mejzlik)** ***The stresses in a gravity dam on a soft bottom* (1954), *On plane biharmonic problems in regions with corners* (1955), (with L Mejzlik) *The method of finite differences for solving of problems of partial differential equations* (1955), and *Numerical solution of complete regular systems of linear algebraic equations and some applications in the theory of frameworks* (1955).

His 1954 paper investigating stresses in a gravity dam was a direct consequence of a project that he led between 1953 and 1956 on using computational techniques to examine the technology involved in building the Orlik Dam on the Vltava River about 80 km from Prague. This river, the longest in the Czech Republic, is a major source of hydroelectric power with several important dams creating artificial lakes. The Orlik Dam [6]:-

... is a gravitational concrete dam91m high. The group, consisting of civil engineers, material scientists, mathematicians, and desk calculator operators, concentrated on the technology without artificial cooling, which is usually used to remove the heat created during the hardening of concrete. All the computations were carried out on mechanical desk calculators.

Basically, the mathematical problem Babuska's group had to solve was to find a numerical solution to a nonlinear partial differential equation.

In 1955, after the award of his doctorate, Babuska was appointed as head of the Department of Constructive Methods of Mathematical Analysis of the Mathematical Institute of the Czechoslovak Academy of Sciences. In the same year, in collaboration with Karel Rektorys and Frantisek Vycichlo, he published his first book *The mathematical theory of plane elasticity* (Czech). A German translation was published in 1960. Frantisek Kroupa writes in a review of the original Czech edition:-

The book is devoted to the application of the theory of functions of a complex variable to solving plane problems of the classical mathematical theory of elasticity(for static problems without the effect of body forces). From the mathematical point of view it deals with the special method of solving a biharmonic equation for given boundary conditions. The book gives and further develops some of the results of N I Muskelishvili and collaborators. An original contribution is the axiomatic construction of the fundamentals of plane elasticity, the accuracy and generality of the mathematical procedures and some new numerical methods of solution.

In the following year, 1956, Babuska founded the journal *Applications of Mathematics* (Applikace Matematiky). In 1960 Babuska was awarded a Dr Sc. (the highest possible degree in Czechoslovakia, equivalent to a D.Sc.) by the Czechoslovak Academy of Sciences. His next important book, published in collaboration with Milan Práger and Emil Vitásek in 1964, was *Numerical Solution of Differential Equations* (Czech). It was translated into English and published under the title *Numerical processes in differential equations* two years later. Richard Hamming reviewed the English translation and writes:-

This book shows both how much mathematics has to contribute to computing when competent mathematicians actually look at what computing is(rather than treating it as if it were a branch of mathematics), and how much they can miss the current temper of computing. ... They make frequent experimental verifications of their theories, thus showing that they regard computing as a science whose results are to be accepted or rejected by the final authority of experience. ... The book is a significant contribution.

The political situation in Czechoslovakia has not been mentioned up to now in Babuska's biography since it has played a relatively small part. The Communists had seized control of the country in 1948 and it was under strong Soviet influence over the following years. Mathematics was allowed to develop without interference, however, and the applied and computational methods developed by Babuska found favour. Beginning in 1964 reformers had won many concessions which became more clear-cut in early 1968 when the country began to implement "socialism with a human face". The reforms came to a sudden end, however, in August 1968 when Soviet tanks rolled into Prague. Babuska had just been appointed as a professor at the Charles University of Prague but, given the political situation, he travelled with his family to the United States where he spent a year as a visiting professor at the Institute for Fluid Dynamics and Applied Mathematics at the University of Maryland at College Park. He was given a permanent appointment as a professor at the University of Maryland in the following year and he held this position until 1995. He was then appointed Professor of Aerospace Engineering and Engineering Mechanics, Professor of Mathematics, and appointed to the Robert Trull Chair in Engineering at the University of Texas at Austin. Although now over 85 years of age, he continues to hold these positions.

After coming to the United States, Babuska became the world-leading expert in finite element analysis. The authors of [2] summarise his important contributions to this area:-

During his27year career at the University of Maryland, Professor Babuska established himself as the unquestionable leader of the international finite element community. In his landmark paper in1971, Ivo introduced the discrete inf-sup condition, generalizing the results of J Cea and R Varga, and setting the theoretical framework for stability and convergence analysis of arbitrary linear problems. Three years later, F Brezzi reinforced the formalism for problems with constraints, and the name of the famous discrete BB condition was coined. ... Ivo has had a unique ability to foresee the development of the field of finite elements. He has been the force behind many developments in this field. His work with W Rheinboldt on a-posteriori error estimation has essentially started the field on adaptive finite element methods. In a landmark paper in1979with B Kellogg and J Pitkäranta, the effect of h-adaptivity on the convergence rates for problems with singularities was explained. In the late seventies, Barna Szabo convinced Ivo to reexamine the then established concept of higher order methods, and the p-version of the Finite Element Method was born. The p-method turned out to be much less sensitive to incompressibility constraints(work with M Vogelius)and locking effects in the analysis of thin-walled structures. The monograph on the p-method with B Szabo(1991)reaches far outside of the constraints of the mathematical community and has become a standard reference for engineers practicing higher order methods.

The monograph referred to in this quote, written in collaboration with Barna Szabo, is *Finite Element Analysis* (1991). The authors write in the Preface:-

Our purpose in writing this book is to introduce the finite element method to engineers and engineering students in the context of the engineering decision-making process. Basic engineering and mathematical concepts are the starting points. Key theoretical results are summarized and illustrated by examples. Focus is on the developments in finite element analysis technology during the1980s and their impact on reliability, quality assurance procedures in finite element computations, and performance. The principles that guide the construction of mathematical models are described and illustrated by examples.

The reviewer [5] writes:-

Numerous books on the finite element method with a variety of objectives have appeared recently, so many that it would be quite lengthy to compare even a representative number of them. The present book has extensive detail with regard to examples, and its coverage of topics in linear elasticity is exhaustive. Both of these are essential for the book to be successful with an engineering audience.

Richard Scott writes in a review:-

I like this book. It is a very nice, and somewhat unique, blend of theory and engineering practice. ... I think the authors have succeeded admirably in their goals and I recommend the text for serious consideration for a first graduate course on finite elements.

In 2001, in collaboration with Theofanis Strouboulis, Babuska published *The finite element method and its reliability*. Carsten Carstensen writes:-

The reliability of a given numerical approximation is one essential task in applied science and engineering. Here, two leading scientists devote six chapters on eight hundred pages to it and fix the state of the art of rigorous 'a posteriori' finite element error analysis.

Babuska, with Ivan Hlavácek and Jan Chleboun, published *Uncertain input data problems and the worst scenario method* in 2004.

Among the many other services to mathematics which Babuska has given, we mention the many journals which have benefited by his accepting a position on their editorial board: Communications in Applied Analysis; Communications in Numerical Methods in Engineering; Computer & Mathematics; Computer Methods in Applied Mechanics and Engineering; Computers and Structures; Communications in Applied Analysis; International Journal for Numerical Methods in Engineering; Modelling and Scientific Computing; Numerical Mathematics - A Journal of Chinese Universities; Numerical Methods for Partial Differential Equations; and Siberian Journal of Computer Mathematics.

Babuska has received many awards for his contributions: the Czechoslovak State Prize for Mathematics (1968); the Humbolt Senior US Scientist Award of Federal Republic of Germany (1976); the Medal for Merit in the Development of Mechanics of the Czech Society for Mechanics (1993); and the George David Birkhoff Prize in Applied Mathematics awarded jointly by the American Mathematical Society and the Society for Industrial and Applied Mathematics (1994):-

... for important contributions to the reliability of finite element methods, the development of a general framework for finite element error estimation, and the development of p and h-p finite element methods...

In 1995 Babuska was awarded the John von Neumann Award by the Association for Computational Mechanics for:-

... extraordinary contributions and the breadth and depth of his work, and their importance to the broad fields of computational mechanics

Babuska ended his Acceptance Speech, which examined the legacy of von Neumann, with these words:-

Mr President, I would like to thank you again for the great honour that has been bestowed upon me and to express my opinion that nearly40years after the death of von Neumann, a towering scientific figure of the20th Century, we, who work in computational mechanics, can still learn tremendously from the legacy, ideas and philosophy of John von Neumann.

The Union of Czech Mathematicians and Physicists made him an honorary member in 1996 and, in the same year, presented him with their Commemorative Medal. He received the Bolzano Medal from the Czech Academy of Sciences in 1997 and the Honorary Medal "De Scientia et Humanitate Optime Meritis" from the same Academy in 2006. He has received honorary degrees from the University of Westminster, London (1996), Brunel University, London (1996), Charles University, Prague (1997), and the Helsinki University of Technology (2000). He was elected a fellow of the International Association of Computational Mechanics in 2002 and of the World Innovation Foundation in 2004. He was elected a member of the European Academy of Sciences in 2003 and of the National Academy of Engineering in 2005. The International Astronomical Union named asteroid No. 36030 "Babuska" in his honour in 2002.

Ivo Babuska is married to Renots.

**Article by:** *J J O'Connor* and *E F Robertson*