foundations

Foundations is a term used across different fields to denote the underlying base that provides support, stability, or justification for something. In a literal sense, it refers to the part of a structure that transmits loads from the building to the ground. More broadly, it can describe the essential base of an idea, organization, or system.

In architecture and civil engineering, foundations are designed to transfer structural loads to soil or rock while resisting settlement and environmental effects. They range from shallow foundations, such as spread footings, strip footings, isolated footings, and raft foundations, to deep foundations, such as piles and caissons. The choice depends on factors including soil bearing capacity, load magnitude, depth to stable strata, groundwater, and potential heave or frost action. Construction practices and local building codes govern execution, inspection, and safety.

In philanthropy, foundations are nonprofit organizations that provide funding for charitable purposes. They may be private foundations funded by individuals or families, corporate foundations, or community foundations. Foundations typically manage endowments and make grants to support education, health, scientific research, arts, social services, and other public-benefit activities. Governance is usually by a board of trustees or directors, with oversight for program strategy, grantmaking, and compliance with tax and reporting requirements.

In mathematics, foundations study the basic concepts and logical structure of the subject. This includes axiomatic systems, formal theories, and the justification of methodologies. The Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC) is a common foundational framework, though alternative foundations such as type theory and category theory have been proposed and developed to address foundational questions and philosophical perspectives. Foundations thus encompass both concrete structural bases and abstract underpinnings across disciplines.