"All the best moments in life are simple. Sitting in the grass on a sunny day. A dinner with old friends. Listening to a cassette tape. Recently, a friend I hadn't seen in many years stopped by for dinner. He lamented where we were as a country, and said he wasn't sure that he would bring kids into this modern world. I told him what I tell everyone: that those thoughts are a mental illness, and should be purged. He was brainwashed by the brainwashed people who write for the news. He cared too much about politics that was more ambiguous than he would like to admit. I gave him some advice. I told him he already didn't use social media, all that was left was for him to stop reading the news. He was so close to having perfect days. He just couldn't see it. But neither can so many of us. It's right there."

"Most explicit information on the eigenfunctions of a Laplace operator on a compact manifold comes from computations where a high degree of symmetry is present. In these cases, eigenspaces may be of large dimension, the zeros of the eigenfunctions are often critical points, and the eigenfunctions usually have degenerate critical points. However, these properties are all unstable under small perturbations of the metric, and are therefore rather misleading to one's intuition."

"In the last several years, the study of gauge theories in quantum field theory has led to some interesting problems in nonlinear elliptic differential equations. One such problem is the local behavior of Yang-Mills fields ... over Euclidean 4-space. Our main result is a local regularity theorem: A Yang-Mills field with finite energy over a 4-manifold cannot have isolated singularities. Apparent point singularities (including singularities in the bundle) can be removed by a gauge transformation. In particular, a Yang-Mills field for a bundle over R4 which has finite energy may be extended to a smooth field over R4 \cup {∞} = S4."

"How did gauge theory appear and become successful in mathematics in the space of a few years? The fundamental mathematical ingredients were in place. The basics of fibre and vector bundles and their connections were in daily use by geometers. Chern-Weil theory (and even Chern-Simons invariants) were studied in most graduate courses in differential geometry. De Rham cohomology and its realization via the Hodge theory of harmonic forms were standard items in differential topology. In hindsight, the Yang-Mills equations were waiting to be discovered. Yet mathematicians were in themselves unable to create them. Gauge field theory is an adopted child."

"While a small domain (consisting of fifty or fewer objects) can generally be analyzed as a unit, large domains must be partitioned to make the analysis a manageable task. To make such a partitioning, we take advantage of the fact that objects on an information model tend to fall into clusters: groups of objects that are interconnected with one another by many relationships. By contrast, relatively few relationships connect objects in different clusters. When partitioning a domain, we divide the information model so that the clusters remain intact... Each section of the information model then becomes a separate subsystem. Note that when the information model is partitioned into subsystems, each object is assigned to exactly one subsystem."

"The key books about object-oriented graphical modeling languages appeared between 1988 and 1992. Leading figures included Grady Booch [Booch,OOAD]; Peter Coad [Coad, OOA], [Coad, OOD]; Ivar Jacobson (Objectory) [Jacobson, OOSE]; Jim Odell [Odell]; Jim Rumbaugh (OMT) [Rumbaugh, insights], [Rumbaugh, OMT]; Sally Shlaer and Steve Mellor [Shlaer and Mellor, data], [Shlaer and Mellor, states] ; and Rebecca Wirfs-Brock (Responsibility Driven Design) [Wirfs-Brock]."

"An object in OOA represents a single typical but unspecified instance of something in the real world - any airplane, I don't care which one, as long as it is typical. The object-oriented analyst distinguishes this concept from that of a specified instance: Airplane number N2713A, Air Force One, or The Spirit of St. Louis, for example."