TheoryA theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.
MathematicianA mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. One of the earliest known mathematicians was Thales of Miletus (624-546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem.
Philosophical methodologyIn its most common sense, philosophical methodology is the field of inquiry studying the methods used to do philosophy. But the term can also refer to the methods themselves. It may be understood in a wide sense as the general study of principles used for theory selection, or in a more narrow sense as the study of ways of conducting one's research and theorizing with the goal of acquiring philosophical knowledge.
Nonstandard analysisThe history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta procedures rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis originated in the early 1960s by the mathematician Abraham Robinson.
Algebraic geometryAlgebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
MetaphysicsMetaphysics is the branch of philosophy that studies the fundamental nature of reality. This includes the first principles of: being or existence, identity, change, space and time, cause and effect, necessity, actuality, and possibility. Metaphysics is considered one of the four main branches of philosophy, along with epistemology, logic, and ethics. It includes questions about the nature of consciousness and the relationship between mind and matter, between substance and attribute, and between potentiality and actuality.
EngineerEngineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the limitations imposed by practicality, regulation, safety and cost. The word engineer (Latin ingeniator) is derived from the Latin words ingeniare ("to contrive, devise") and ingenium ("cleverness").
ArchitectAn architect is a person who plans, designs and oversees the construction of buildings. To practice architecture means to provide services in connection with the design of buildings and the space within the site surrounding the buildings that have human occupancy or use as their principal purpose. Etymologically, the term architect derives from the Latin architectus, which derives from the Greek (arkhi-, chief + tekton, builder), i.e., chief builder. The professional requirements for architects vary from location to location.
Critical theoryA critical theory is any approach to social philosophy that focuses on society and culture to attempt to reveal, critique, and challenge power structures. With roots in sociology and literary criticism, it argues that social problems stem more from social structures and cultural assumptions than from individuals. It argues that ideology is the principal obstacle to human liberation. Critical theory finds applications in various fields of study, including psychoanalysis, sociology, history, communication theory, philosophy and feminist theory.
