Following are the texts of the presentation remarks by Professor J. Tinsley Oden and acceptance speech by Professor Ivo Babuska during the presentation of the John von Neumann Medal at the Banquet of the Third U.S. National Congress on Computational Mechanics, Dallas, TX on June 13, 1995.

**Award Introduction**

J. Tinsley Oden

On behalf of the USACM and the Nomination and Awards Committee, I am pleased to announce that Professor Ivo Babuska is the second 1995 recipient of the USACM John von Neumann Medal.

Professor Babuska's work and its impact on the field of computational mechanics is well-known to the USACM. He holds three doctorates, a Doctor of Technical Sciences, from Prague University which he obtained in 1951; the Candidate of Sciences Degree, which he earned in 1955, and a third degree in 1960, which was a Dr. Sc. Given to scientists of international reputation. He was the head of the Department of Partial Differential Equations at the Mathematical Institute of the Czechoslovak Academy of Sciences. While in Prague, he completed a large volume of mathematical work including a text on the mathematical theory of elasticity.

He came to the United States with his family in 1968 and assumed the position of Professor at the Institute of Physical Sciences and Technology at the University of Maryland. In the late 1960s and early 1970s he began to develop a large volume of published works on the mathematical foundations of the finite element method and its application to problems in engineering. Over the last quarter century, Babuska and his colleagues and students have produced a number of seminal contributions to the subjects. In 1972, he, along with Aziz, published the monumental paper on the mathematical foundations of the finite element method for partial differential equations. This 345-page exposition contained many essential components of the mathematical basis for these numerical techniques and represents a cornerstone in the theory and application of modern computational methods. During this period, he developed the well-known inf-sup condition now labeled the Brezzi-Babuska condition (or LBB condition) which provides a means for establishing the stability of discrete Galerkin type approximations.

He was the first to provide a number of theoretical studies on a diverse collection of topics including numerical methods for domains with corners, singularities, infinite domains.

Babuska is credited with having developed the first detailed studies of a posteriori error estimation for finite element methods, adaptive techniques, p-version finite elements, and methods of hierarchical modeling.

Last year, Babuska was awarded the Birkhoff Prize by the Society of Industrial and Applied Mathematics for his fundamental contributions to applied mathematics and numerical analysis. I am pleased to report that Professor Babuska will soon become my professional colleague at the Texas Institute for Computational and Applied Methematics. In September he will move to the University of Texas where he will hold the Trull Chair in Engineering, The Professorship in the Department of Aerospace Engineering and Engineering Mechanics, and an appointment in the Department of Mathematics, and he will be a Senior Research Scientist at TICAM.

For these extraordinary contributions and the breadth and depth of his work, and their importance to the broad fields of computational mechanics, Professor Ivo Babuska is an especially deserving recipient of the 1995 von Neumann Medal.

**Award Acceptance Speech**

Ivo Babuska

Mr. President, Professor Oden, ladies and gentlemen. I would like to thank the Association for Computational Mechanics for the great honor of awarding me the von Neumann Medal. I am very proud to receive it.

On this occasion, please allow me to ponder on the legacy of von Neumann, a towering scientific mind of the 20th Century. Books have been written about von Neumann and a conference on his legacy was organized in 1988.

Who was this man who was tutored during his high school education by the famous mathematicians Szego, Haar, Riesz, Fekete, Fejer, and who published his first mathematical paper when he was only 17 years old? What kind of personality was von Neumann, a man who contributed so much to mathematics, who was the father of modern digital computers, who influenced profoundly U.S. policy in the Truman and Eisenhower Administrations? Who was the man who, near his death, had a meeting at Walter Reed Hospital, where gathered around his bedside and attentive to his last words of advice and wisdom were the Secretary of the Army, Navy and Air Force, and all the military Chiefs of Staff?

When Nobel Laureate Eugen Wigner visited his native Budapest a decade after von Neumann's death, he was asked whether it was true that in the early and middle 1950s the scientific and nuclear policies of the United States were largely decided by von Neumann. Wigner replied in his precise manner, "That is not quite so. But after von Neumann had analyzed a problem, it was clear what had to be done."

Von Neumann was born in 1903 and died in 1957. He studied simultaneously chemistry (which was the wish of his parents) and mathematics. He graduated from ETH Zurich in chemistry and soon afterward received his Ph.D. (1926) in mathematics in Budapest.

Von Neumann had legendary clear, precise and rigorous thinking of a mathematical nature which he used in all situations; one of them characterized by Wigner, as stated above. Von Neumann was able to envision outstanding problems to be solved and he solved them. What were his largest scientific achievements? When he was asked shortly before his death, what were his three greatest achievements, he, who was regarded as the main brain behind the modern digital computer, numerical meteorology, mechanics and many other important topics, replied: The theory of self-adjoint operators in Hilbert spaces, the mathematical foundation of quantum theory, and the ergodic theorem.

Von Neumann's understanding and philosophy of mathematics are described in his paper The Mathematician. Here he, on one hand, said: I think that it is correct to say that a mathematician's criteria of selection and also thoseof success are mainly aesthetical. On the other hand, he wrote: As mathematical discipline travels far from its empirical source, it becomes more and more purely aesthetizing. This need not be bad, but it may lead to the danger of degeneration, and the only remedy seems to be the reinjection of more or less directly empirical ideas.

So what are the legacies of John von Neumann almost 40 years after his death? There are many. Here are some which I see as the most important:

The demonstration that clear, rigorous, and precise formulation of problems and thinking with mathematical rigor is, in general, the most effective way to tackle any problem, and, in particular, in mathematics, numerical mathematics, physics, mechancs, modelling, engineering, etc.

That a vision of the problems which have to be solved is the best path for successful and extremely useful research, which, in addition, is a beautiful one.

That one has to be aware of the danger of degeneracy of the research.

John von Neumann was a very special kind of mathematician. Of course, there were and are other great mathematicians. So what makes von Neumann so special? It is that he used general mathematical tools for solving many important and useful problems. In this connection, I would like to mention an article of another great mathematician, G.H. Hardy, as a contrast to von Neumann's. Hardy formulated an idea in the article A Mathematician's Apology by stating that a mathematician, like a painter or poet, is the maker of patterns of ideas which must be beautiful. So, we see the similarity to von Neumann. But Hardy also stated that very little mathematics is useful practically and that little is comparatively dull. One aspect of Neumann's greatness was that he totally and convincingly disproved this thesis of Hardy. He has shown that useful mathematics is not dull, but it is beautiful.

Mr. President, I would like to thank you again for the great honor that has been bestowed upon me and to express my opinion that nearly 40 years afterthe death of von Neumann, a towering scientific figure of the 20th Century, we, who work in omputational mechanics, can still learn tremendously from the legacy, ideas and philosophy of John von Neumann.

Thank you and let me assure you that I will cherish this honor and try hard to be worthy of the John von Neumann Medal awarded me by the Association.