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.
Ivo
Babuska Award
Acceptance Speech
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.
top
