Since few of us can see any indication we are nearing the end of search and discovery in cosmology we have to adopt a convention for the meaning of ``cosmology solved.'' I take it to be a positive outcome of accurate and well cross-checked tests of the relativistic Friedmann-Lemaître cosmological model. We are not there yet, but all signs are that now, some seven decades after the first of the tests were proposed, we may be approaching a major closure.
Many of my colleagues have concluded that the observational successes of the Friedmann-Lemaître model combined with its logical plausibility already make the case, and it is time to move on to the issue of how initial conditions for this model were set by the deeper physics of the very early universe, and how that led to the origin of the world as we know it. This positive attitude is healthy but maybe a little incomplete. I am taken by Willem de Sitter's (1931) remark: ``It should not be forgotten that all this talk about the universe involves a tremendous extrapolation, which is a very dangerous operation.'' Observational advances since then have greatly reduced the danger, but I think should leave us with a sense of wonder at the successes in probing the large-scale nature of the physical universe and caution in deciding just how well we understand the situation.
A satisfactory understanding is easily defined: there must be more pieces of evidence than parameters we are free to adjust to fit the evidence. In Section 2 I comment on the still uncomfortably similar lengths of the lists of hypotheses and observational constraints in cosmology. Many cosmological tests constrain the two dimensionless parameters m and that measure the relative contributions of matter and Einstein's cosmological constant to the expansion rate in the Friedmann-Lemaître model. If we can establish that concordant values of these parameters follow from many more than two observational constraints we will have an important positive test of the model. I argue in Section 3 that there still is an uncomfortably large number of open issues: the parameters are not strongly overconstrained. In short, many commonly discussed elements of cosmology still are on dangerous ground. Work in progress promises to improve the situation; the community will be following the results with great interest to learn whether this aspect of cosmology may at last be declared ``solved.''