iment became almost irresistible, at least
for the fortunate few who enjoyed the lux-
ury of a hands-on policy. When shared-
time operations became realistic, exper-
imental mathematics came of age. At
long last, mathematics achieved a certain
parity-the twofold aspect of experiment
and theory-that all other sciences enjoy.
It is, in fact, the coupling of the sub-
tleties of the human brain with rapid
and reliable calculations, both arithmeti-
cal and logical, by the modern computer
that has stimulated the development of
experimental mathematics. This develop-
ment will enable us to achieve Olympian
So far I have summarized the rebirth
of statistical sampling under the rubric
of Monte Carlo. What of the future—
perhaps even a not too distant future?
The miracle of the chip, like most mir-
acles, is almost unbelievable. Yet the fan-
tastic performances achieved to date have
not quieted all users. At the same time we
are reaching upper limits on the comput-
ing power of a single processor.
One bright facet of the miracle is the
lack of macroscopic moving parts, which
makes the chip a very reliable bit of
hardware. Such reliability suggests par-
The thought here is
not a simple extension to two, or even
four or eight, processing systems. Such
extensions are adiabatic transitions that,
to be sure, should be part of the im-
mediate, short-term game plan. Rather,
the thought is massively parallel opera-
tions with thousands of interacting pro-
Already commercially available is one
computer, the Connection Machine, with
65,536 simple processors working in par-
allel. The processors are linked in such
a way that no processor in the array is
more than twelve wires away from an-
other and the processors are pairwise con-
nected by a number of equally efficient
routes, making communication
ible and efficient. The computer has been
used on such problems as turbulent fluid
flow, imaging processing (with features
analogous to the human visual system),
document retrieval, and “common-sense”
reasoning in artificial intelligence.
One natural application of massive par-
allelism would be to the more ambitious
Monte Carlo problems already upon us.
To achieve good statistics in Monte Carlo
calculations, a large number of “histories”
need to be followed. Although each his-
tory has its own unique path, the under-
lying calculations for all paths are highly
parallel in nature.
Still, the magnitude of the endeavor
to compute on massively parallel devices
must not be underestimated. Some of the
tools and techniques needed are:
A high-level language and new archi-
tecture able to deal with the demands
of such a sophisticated language (to the
relief of the user);
Highly efficient operating systems and
Use of modern combinatorial theory,
perhaps even new principles of logic,
in the development of elegant, compre-
A fresh look at numerical analysis and
the preparation of new algorithms (we
have been mesmerized by serial com-
putation and purblind to the sophistica-
tion and artistry of parallelism).
Where will all this lead? If one were
to wax enthusiastic, perhaps—just per-
haps—a simplified model of the brain
might be studied. These studies, in turn,
might provide feedback to computer ar-
chitects designing the new parallel struc-
Such matters fascinated Stan Ulam. He
often mused about the nature of memory
and how it was implemented in the brain.
Most important, though, his own brain
possessed the fertile imagination needed
to make substantive contributions to the
very important pursuit of understanding
S. Ulam, R. D. Richtmyer, and J. von Neumann.
1947. Statistical methods in neutron diffusion. Los
Alamos Scientific Laboratory report LAMS–551.
This reference contains the von Neumann letter dis-
cussed in the present article.
N. Metropolis and S. Ulam. 1949. The Monte
Carlo method. Journal of the American Statistical
S. Ulam. 1950. Random processes and transforma-
tions. Proceedings of the International Congress of
Los Alamos Scientific Laboratory. 1966. Fermi in-
vention rediscovered at LASL. The Atom, October,
C. C. Hurd. 1985. A note on early Monte Carlo
computations and scientific meetings. Annals of the
History of Computing 7:141–155.
W. Daniel Hillis. 1987. The connection machine.
June, pp. 108–1 15.
N. Metropolis received his B.S. (1937) and his
Ph.D. ( 1941) in physics at the University of Chi-
cago. He arrived in Los Alamos, April 1943, as
a member of the original staff of fifty scientists.
After the war he returned to the faculty of the
University of Chicago as Assistant Professor. He
came back to Los Alamos in 1948 to form the
group that designed and built MANIAC I and II. (He
chose the name MANIAC in the hope of stopping
the rash of such acronyms for machine names, but
may have, instead, only further stimulated such use.)
From 1957 to 1965 he was Professor of Physics
at the University of Chicago and was the founding
Director of its Institute for Computer Research. In
1965 he returned to Los Alamos where he was made
a Laboratory Senior Fellow in 1980. Although he
retired recently, he remains active as a Laboratory
Senior Fellow Emeritus.