  Almost since the time it was formulated, the overwhelming consensus has been
that random matrix theory (RMT) is in excellent agreement with neutron
resonance data. However, over the past few years, we have obtained new
neutron-width data at Oak Ridge and Los Alamos National Laboratories that are
in stark disagreement with this theory. We also have reanalyzed neutron widths
in the most famous data set, the nuclear data ensemble (NDE), and found that it
is seriously flawed, and, when analyzed carefully, excludes RMT with high
confidence. More recently, we carefully examined energy spacings for these same
resonances in the NDE using the $\Delta_{3}$ statistic. We conclude that the
data can be found to either confirm or refute the theory depending on which
nuclides and whether known or suspected p-wave resonances are included in the
analysis, in essence confirming results of our neutron-width analysis of the
NDE. We also have examined radiation widths resulting from our Oak Ridge and
Los Alamos measurements, and find that in some cases they do not agree with
RMT. Although these disagreements presently are not understood, they could have
broad impact on basic and applied nuclear physics, from nuclear astrophysics to
nuclear criticality safety.
