A concern with physical quantities – energy, temperature, and the like – has inspired the development of modern mathematics. Scientific and engineering questions have provided a source of vitality to, among other fields, algebra, geometry and analysis.
A concern with logical and statistical quantities – information – is central to present-day science and engineering. The pertinent mathematics is being actively developed, as disciplines such as algorithms, complexity, communications and control motivate questions in adjoining fields such as probability, combinatorics, algebra and harmonic analysis. A common framework supporting the study of information and computation across disciplines is as yet a distant goal. The Caltech CMI is a home in which unfettered development of the mathematical foundations of information and computation can be influenced by, and influence in turn, progress in engineering and science.
The Mathematics are either pure or mixed... And as for the mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them as nature grows further disclosed.
— Francis Bacon, The Advancement of Learning, Book II, 1605.