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.
Research
Research comprises "creative and systematic work undertaken to increase the stock of knowledge, including knowledge of humans, culture and society, and the use of this stock of knowledge to devise new applications." It is used to establish or confirm facts, reaffirm the results of previous work, solve new or existing problems, support theorems, or develop new theories. A research project may also be an expansion on past work in the field. Research projects can be used to develop further knowledge on a topic, or in the example of a school research project, they can be used to further a student's research prowess to prepare them for future jobs or reports. To test the validity of instruments, procedures, or experiments, research may replicate elements of prior projects or the project as a whole. The primary purposes of basic research (as opposed to applied research) are documentation, discovery, interpretation, or the research and development (R&D) of methods and systems for the advancement of human knowledge. Approaches to research depend on epistemologies, which vary considerably both within and between humanities and sciences. There are several forms of research: scientific, humanities, artistic, economic, social, business, marketing, practitioner research, life, technological, etc.
Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. See glossary of probability and statistics.
Research
Research is something that everyone can do, and everyone ought to do. It is simply collecting information and thinking systematically about it. The word ‘research’ carries overtones of abstruse statistics and complex methods, white coats and computers. Some social research is highly specialised but most is not; much of the best research is logically very straightforward. Useful research on many problems can be done with small resources, and should be a regular part of the life of any thoughtful person involved in social action.
Raewyn Connell et al. (1975). How to do small surveys – a guide for students in sociology, kindred industries and allied trades. School of Social Sciences. Flinders University. p. 1.
Economics
The field of economics is not exempt from the consequences of chaos and complexity. Marketplaces are indeterminate; value is subjective; and outcomes are subject to interpretation. Economic forecasting is just as nebulous, being based on the probability of statistical information that may or may not be accurate.
L.K. Samuels, In Defense of Chaos: The Chaology of Politics, Economics and Human Action, Cobden Press (2013) p. 16.
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