Answers on Frequently Asked Questions on the Nature of Mathematics

Instead, maths deals with rime or with other concepts that enkindle be defined precisely.

In this sense, maven could offer the following as a explanation of math: whenever integrity is dealing with a question to which the answer is a affaire of logic, not opinion, then hotshot is dealing with mathematics. tied(p) deep down fields that are not mathematical, there set up be subfields that are mathematical: acoustics within music, the mathematics of heredity within biology, statistics within the various social sciences, and logic within philosophy. Most of these involve numbers, but some do not. In any event, it is the precision of the reasoning that constitutes mathematics, not the use of numbers.

2. The exposition of mathematics given in Webster's Ninth New collegial Dictionary is as follows: "the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations." understandably it does cover arithmetic, algebra, geometry, and other numerical forms of mathematics. However, it does not cover non-numerical mathematics as discussed in the preceding question.

Of course, some people expertness want to insist on the adequacy of the above dictionary definition. If so, they would probably want to define non-numerical mathematics as existence a spe

3. The term " valued thinking" does not encompass all of mathematics unless one defines mathematics as being only numerical. Even in plane geometry, one is for the most part dealing with concepts and relationships, not numbers. If something can be quantified, then its relationships to other quantities can be defined precisely. However, precise definitions do not always overlook quantification, and some things that can be defined precisely can nevertheless not be quantified.

Bullock, James O. "Literacy in the voice communication of Mathematics." American Mathematical Monthly (Oct. 1994): n.p.

For example, if the Earth were a euclidian sphere of influence, then every point on its surface (say, at sea level) would be at the same distance from its center.

This tax write-off thus provides an hypothesis that can be tested by observation, measurement, and calculation. If the Earth turns out to differ significantly from a sphere in its shape (as it does), then these differences want to be accounted for, as they are by Newtonian concepts.

Furthermore, defining mathematics as "quantitative thinking" has two shortcomings. First, it would include any uses of numbers as part of mathematics; but such things as accounting, numerology, or economics are fields in which the " powerful" answer to a question is still a matter of opinion, not of logic, and which therefore would not be mathematical by the definition proposed in the answer to question 1 above.

cies of logic and therefore as being a subfield of philosophy. This would not count to be a very useful distinction. Set possibility and Venn diagrams are now taught at the high school level, and they do not involve any numbers or calculations.

Bullock's definition of mathematics as a metaphorical language need not conflict with the viewpoint that mathematics is characterized by difficulty solving. However, that is possible only so long as one does not define problem solving as being necessarily numerical. Similarly to what was propo
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