Information
Information is any entity or form that provides the answer to a question of some kind or resolves uncertainty. It is thus related to data and knowledge, as data represents values attributed to parameters, and knowledge signifies understanding of real things or abstract concepts. As it regards data, the information's existence is not necessarily coupled to an observer (it exists beyond an event horizon, for example), while in the case of knowledge, the information requires a cognitive observer.
Information Science
Information science is a field primarily concerned with the analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information. Practitioners within and outside the field study application and usage of knowledge in organizations along with the interaction between people, organizations, and any existing information systems with the aim of creating, replacing, improving, or understanding information systems. Historically, information science is associated with computer science, library science, and telecommunications. However, information science also incorporates aspects of diverse fields such as archival science, cognitive science, commerce, law, museology, management, mathematics, philosophy, public policy, and social sciences.
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change. It has no generally accepted definition.
Mathematics
A marveilous newtrality have these things mathematicall and also a strange participation between things supernaturall, imortall, intellectuall, simple and indivisible, and things naturall, mortall, sensible, compounded and divisible.
John Dee, The mathematicall praeface to the Elements of geometrie of Euclid of Megara (1570) as editor of Euclid's Elements, translated by Henry Billingsley.
Science
We say that the string is 'random' if there is no other representation of the string which is shorter than itself. But we will say that it is 'non-random' if there does exist such an abbreviated representation. ... In general, the shorter the possible representation... the less random... On this view we recognize science to be the search for algorithmic compressions. ... It is simplest to think of mathematics as the catalogue of all possible patterns. ... When viewed in this way, it is inevitable that the world is described by mathematics. ...In many ways the search for a Theory of Everything is a manifestation of a faith that this compression goes all the way down to the bedrock of reality...
John D. Barrow, New Theories of Everything (2007).