Theory of relativity
The Theory of Relativity is a geometrical theory of gravitation, stating that the speed of light and laws of physics are constant for all observers, regardless of their velocities relative to eachother.
The theory of relativity was proposed based on mathematical theory (derived from a series of thought experiments by Einstein) rather than observation. The theory rests on two postulates that are themselves difficult to test, and then derives mathematically what the physical consequences should be (and hence experimentally testable predictions). Those two postulates are that the speed of light never changes, and that all laws of physics are the same in every (inertial) frame of reference no matter where it is or how fast it is traveling. This theory rejects Isaac Newton's theory of gravitation and replaces it with a concept that there is a continuum of space and time, and that large masses (like the sun) bend space in a manner similar to how a finger can depress an area of a balloon. From this proposed bending of space the expression arose that "space is curved." But experiments later proved that space is flat overall.
Relativity is important for massive or fast-moving bodies: at low mass or high speed, it can be accurately approximated by classical mechanics (such as Isaac Newton's laws of motion). At the two extremes, modelling the behaviour of electrons requires that relativistic effects be taken into account (the chemically significant phenomenon of electron spin arises from relativity), and light passing through a region containing many massive bodies such as galaxies will be distorted. These are both experimentally confirmed (electron spin was known before relativity arose, and telescopic observations confirm that galactic clusters distort the paths of the light passing through them). One of the mathematical consequences of the theory - the well known equivalance between energy and matter, E=mc^2 - predicted the release of energy in nuclear reactions, explaining the source of the sun's fusion energy and spurring the development of fissile weapons (the atomic bomb). Another was the effect of high-relative-speed ("relativistic") travel on the passage of time: from this relativity was able to explain, and accurately predict, the anomalous orbit of the planet Mercury (travelling at high speed very close to the sun).
British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir Arthur Eddington, an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse. Upon his return to England declared that his observations proven the theory of relativity. In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data was inconclusive about the theory of relativity. The experiment was later confirmed by more rigorous experiments, such as those performed by the Hubble Space Telescope.
Like most significant scientific discoveries, relativity has been widely adopted as a social analogy with little factual basis. For example the idea of moral relativity exists independent of (and substantially predates) the theory of relativity.
