The sociology of mathematical knowledge

Studies of mathematical practice and quasi-empiricism in mathematics are also rightly part of the sociology of knowledge since they focus on the community of those who practice mathematics. Since Eugene Wigner raised the issue in 1960 and Hilary Putnam made it more rigorous in 1975, the question of why fields such as physics and mathematics should agree so well has been debated. Proposed solutions point out that the fundamental constituents of mathematical thought, space, form-structure, and number-proportion are also the fundamental constituents of physics. It is also worthwhile to note that physics is more than merely modeling of reality and the objective basis is upon observational demonstration. Another approach is to suggest that there is no deep problem, that the division of human scientific thinking through using words such as ‘mathematics’ and ‘physics’ is only useful in their practical everyday function to categorize and distinguish.

Fundamental contributions to the sociology of mathematical knowledge have been made by Sal Restivo and David Bloor. Restivo draws upon the work of scholars such as Oswald Spengler (The Decline of the West, 1918), Raymond Louis Wilder and Leslie Alvin White, as well as contemporary sociologists of knowledge and science studies scholars. David Bloor draws upon Ludwig Wittgenstein and other contemporary thinkers. They both claim that mathematical knowledge is socially constructed and has irreducible contingent and historical factors woven into it. More recently Paul Ernest has proposed a social constructivist account of mathematical knowledge, drawing on the works of both of these sociologists.

Criticism

SSK has received criticism from theorists of the actor-network theory (ANT) school of science and technology studies. These theorists criticise SSK for sociological reductionism and a human centered universe. SSK, they say, relies too heavily on human actors and social rules and conventions settling scientific controversies. The debate is discussed in an article titled Epistemological Chicken.

See also

• Academic careerism
• Cliodynamics – Mathematical modeling of historical processes
• Economics of scientific knowledge
• Historiography of science
• Paradigm shift – Fundamental change in concepts
• Philosophy of social science – Study of the logic, methods, and foundations of social sciences
• Public awareness of science – Aspect of education and communication
• Science studies – Research area analyzing scientific expertise
• Science and technology studies – Academic field
• Scientific community metaphor
• Social constructionism – Sociological theory regarding shared understandings
• Sociology of knowledge – Field of study
• Sociology of scientific ignorance – Study of ignorance in science
• Sociology of the history of science

Disputes:

• Bogdanov affair – French academic dispute
• Sokal affair – 1996 scholarly publishing sting accepted by an academic journal

The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups:

• Formal sciences: the study of formal systems, such as those under the branches of logic and mathematics, which use an a priori, as opposed to empirical, methodology.
• Natural sciences: the study of natural phenomena (including cosmological, geological, physical, chemical, and biological factors of the universe). Natural science can be divided into two main branches: physical science and life science (or biology). Social sciences: the study of human behavior in its social and cultural aspects.# ISO certification in India

Scientific knowledge must be based on observable phenomena and must be capable of being verified by other researchers working under the same conditions. This verifiability may well vary even within a scientific discipline.

Natural, social, and formal science make up the fundamental sciences, which form the basis of interdisciplinarity- and applied sciences such as engineering and medicine. Specialized scientific disciplines that exist in multiple categories may include parts of other scientific disciplines but often possess their own terminologies and expertises.

The formal sciences are the branches of science that are concerned with formal systems, such as logic, mathematics, theoretical computer science, information theory, systems theory, decision theory, statistics.

Unlike other branches, the formal sciences are not concerned with the validity of theories based on observations in the real world (empirical knowledge), but rather with the properties of formal systems based on definitions and rules. Hence there is disagreement on whether the formal sciences actually constitute a science. Methods of the formal sciences are, however, essential to the construction and testing of scientific models dealing with observable reality,and major advances in formal sciences have often enabled major advances in the empirical sciences # ISO certification in India

Logic (from Greek: λογική, logikḗ, ‘possessed of reason, intellectual, dialectical, argumentative’) is the systematic study of valid rules of inference, i.e. the relations that lead to the acceptance of one proposition (the conclusion) on the basis of a set of other propositions (premises). More broadly, logic is the analysis and appraisal of arguments.

It has traditionally included the classification of arguments; the systematic exposition of the logical forms; the validity and soundness of deductive reasoning; the strength of inductive reasoning; the study of formal proofs and inference (including paradoxes and fallacies); and the study of syntax and semantics.# ISO certification in India

Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century). More recently, logic has been studied in cognitive science, which draws on computer science, linguistics, philosophy and psychology, among other disciplines.

Data Science

Main article: Data science

See also: Data visualization and DIKW pyramid

Information Science

See also: Information visualization and DIKW pyramid

Mathematic

Mathematics, in the broadest sense, is just a synonym of formal science; but traditionally mathematics means more specifically the coalition of four areas: arithmetic, algebra, geometry, and analysis, which are, to some degree, the study of quantity, structure, space, and change respectively.

Statistics

For a topical guide, see Outline of statistics.

Statistics is the study of the collection, organization, and interpretation of data.It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.# ISO certification in India

A statistician is someone who is particularly well versed in the ways of thinking necessary for the successful application of statistical analysis. Such people have often gained this experience through working in any of a wide number of fields. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.

The word statistics, when referring to the scientific discipline, is singular, as in “Statistics is an art.”This should not be confused with the word statistic, referring to a quantity (such as mean or median) calculated from a set of data, whose plural is statistics (“this statistic seems wrong” or “these statistics are misleading”).# ISO certification in India

Systems theory

Systems theory is the transdisciplinary study of systems in general, to elucidate principles that can be applied to all types of systems in all fields of research. The term does not yet have a well-established, precise meaning, but systems theory can reasonably be considered a specialization of systems thinking and a generalization of systems science. The term originates from Bertalanffy’s General System Theory (GST) and is used in later efforts in other fields, such as the action theory of Talcott Parsons and the sociological autopoiesis of Niklas Luhmann.

In this context the word systems is used to refer specifically to self-regulating systems, i.e. that are self-correcting through feedback. Self-regulating systems are found in nature, including the physiological systems of our body, in local and global ecosystems, and climate.# ISO certification in India

Decision theory

Decision theory (or the theory of choice not to be confused with choice theory) is the study of an agent’s choices. Decision theory can be broken into two branches: normative decision theory, which analyzes the outcomes of decisions or determines the optimal decisions given constraints and assumptions, and descriptive decision theory, which analyzes how agents actually make the decisions they do.

Decision theory is closely related to the field of game theory and is an interdisciplinary topic, studied by economists, statisticians, psychologists, biologists, political and other social scientists, philosophers,and computer scientists.

Empirical applications of this rich theory are usually done with the help of statistical and econometric methods. # ISO certification in India

Theoretical computer science

Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on more mathematical topics of computing, and includes the theory of computation.

It is difficult to circumscribe the theoretical areas precisely. The ACM’s Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description:

TCS covers a wide variety of topics including algorithms, data structures, computational complexity, parallel and distributed computation, probabilistic computation, quantum computation, automata theory, information theory, cryptography, program semantics and verification, machine learning, computational biology, computational economics, computational geometry, and computational number theory and algebra. Work in this field is often distinguished by its emphasis on mathematical technique and rigor.# ISO certification in India