Mathematical symbols make up a LANGUAGE for describing ABSTRACT IDEAS. Mathematical theorems start off with reasonable assumptions which are TRUE within the context set out. Such reasonable assumptions are often called AXIOMS when they describe abstract facts. The statement that "3 > 2" is a reasonable mathematical assumption, since it is true for the natural numbers which most of us are familiar with. More generally, the claim that "parallel lines never intersect" is a more abstract truth in Euclidean geometry. In metric spaces, an axiom about distances between 2 points, called X and Y, can be that the distance from X to Y is equal to the distance from Y to X and this may be written as: d(X,Y) = d(Y,X).
Theorems are proved by LOGICAL DEDUCTIONS from axioms. This is not magic and is concerned with the search for TRUTHs. However, this can be challenging and often requires concentration and discipline to understand. Unfortunately, symbols can be abused to deceive people who are ignorant. In this sense, mathematical knowledge becomes power not to be deceived. Mathematics becomes demystified when the MEANING of the mathematical symbols become clear.
The article below discusses a case study in social science on the UNREASONABLE respect which people may give for information when mathematical symbols are abused to impress, but are not actually meaningful:
http://journal.sjdm.org/12/12810/jdm12810.pdf
article by Kimmo Eriksson
Abstract (summary): Mathematics is a fundamental tool of research. Although potentially applicable in every discipline, the amount of training in mathematics that students typically receive varies greatly between different disciplines. In those disciplines where most researchers do not master mathematics, the use of mathematics may be held in too much awe. To demonstrate this I conducted an online experiment with 200 participants, all of which had experience of reading research reports and a postgraduate degree (in any subject). Participants were presented with the abstracts from two published papers (one in evolutionary anthropology and one in sociology). Based on these abstracts, participants were asked to judge the quality of the research. Either one or the other of the two abstracts was manipulated through the inclusion of an extra sentence taken from a completely unrelated paper and presenting an equation that made no sense in the context. The abstract that included the meaningless mathematics tended to be judged of higher quality. However, this "nonsense math effect" was not found among participants with degrees in mathematics, science, technology or medicine.
Theorems are proved by LOGICAL DEDUCTIONS from axioms. This is not magic and is concerned with the search for TRUTHs. However, this can be challenging and often requires concentration and discipline to understand. Unfortunately, symbols can be abused to deceive people who are ignorant. In this sense, mathematical knowledge becomes power not to be deceived. Mathematics becomes demystified when the MEANING of the mathematical symbols become clear.
The article below discusses a case study in social science on the UNREASONABLE respect which people may give for information when mathematical symbols are abused to impress, but are not actually meaningful:
http://journal.sjdm.org/12/12810/jdm12810.pdf
article by Kimmo Eriksson
Abstract (summary): Mathematics is a fundamental tool of research. Although potentially applicable in every discipline, the amount of training in mathematics that students typically receive varies greatly between different disciplines. In those disciplines where most researchers do not master mathematics, the use of mathematics may be held in too much awe. To demonstrate this I conducted an online experiment with 200 participants, all of which had experience of reading research reports and a postgraduate degree (in any subject). Participants were presented with the abstracts from two published papers (one in evolutionary anthropology and one in sociology). Based on these abstracts, participants were asked to judge the quality of the research. Either one or the other of the two abstracts was manipulated through the inclusion of an extra sentence taken from a completely unrelated paper and presenting an equation that made no sense in the context. The abstract that included the meaningless mathematics tended to be judged of higher quality. However, this "nonsense math effect" was not found among participants with degrees in mathematics, science, technology or medicine.
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