Singularity: a point at which an otherwise continuous state performs a sudden "jump" or takes on an infinite value or a value beyond description.
In ►astronomy, a singularity is a spatial or temporal region of the universe in which the hitherto-known ►laws of nature do not apply. Such regions do exist. For example, near the center of a ►black hole, gravity strives toward an infinite value. At the center itself gravity in general is no longer susceptible to being described in terms of ►general relativity theory; hence, the center constitutes a singularity. For the same reason, the very moment at which the ►big bang occurred, as well as the first 10-43 seconds of the universe's existence, are singularities for the ►standard model of physics, though they may be subject to description, and hence explanation, by a more comprehensive theory.
In mathematics, a singularity is a point at which the behavior of a ►function or another mathematical object is not defined. For example, the function f(x) = 1/x has a singularity at x = 0, around which the value of the function goes to infinity. At the singularity itself the value of the function is not even defined.
In futurology, the concept of technological singularity denotes the point in time at which technological progress takes place with such speed that human beings are no longer able to follow it. More precisely, futurologists such as Ray Kurzweil imagine that the development of computer-generated artificial intelligence will trigger a technological singularity as soon as it manages to produce a ►soul and becomes superior to human intelligence. The ►Singularity Institute for Artificial Intelligence was founded with the express objective of constructing such a continuously self-improving artificial intelligence (Seed AI). However, despite the exponentially-increasing capabilities of computers, research in ►artificial intelligence has not greatly advanced in the past decades. This is why most AI scholars think that it may take many more decades or even centuries until the singularity occurs.