R2 Thoughts for You What Is Mathematics?
Note regarding this posting: This is a collection of different perspectives about what mathematics is from my point of view. I used these at various times while teaching both full time and part time from 1969 to 2004. I realize this is not in the same “spirit” of most of my other posts. Please reflect on your learning of mathematics and see if any of the points of view expressed in this posting help clarify this all important, but often elusive way of thinking – mathematics.
A visual organizer for the different perspectives discussed below
The Mandelbrot Set – created on a computer using mathematics
Consider the following three points of view:
1) Mathematics is a disciplined way of thinking. Often, mathematics is called a discipline. This implies that it is a way of thinking that involves certain rules and regulations. Though this is true it is not complete. When you think mathematically you are often doing a logical study of shape, arrangement, and quantity. The word logical implies that a system of principles, concepts, and assumptions is in the basis of the study. In other words, mathematics is not random thinking with no purpose or structure, but instead, it is a mental process that is based on logic and used to study the relationship between shape, arrangement, and quantity.
2) Q2 – When we think of mathematics, the concept of quantity is often assumed to be involved. Not always is quantity the only thing being considered. Quality (the characteristic element; that which makes something what it is) is generally involved. That leads us to another way of viewing mathematics: mathematics is the mental exercise of quantifying quality and qualifying quantity, therefore Q2.
3) BLAST – Math is a Beautiful Language, Art, Science, and Tool!
Mathematics has at least four roles that it plays in human thought.
A Julia Set – created on a computer using mathematics
Mathematics is a universal LANGUAGE. Language is a symbolic representation of human perceptions. Mathematics has its vocabulary, its symbols, its definitions, and expressions which help us internalize and clarify our thinking and communicate our ideas. Mathematics is a universal language for communicating the ideas of shape, arrangement, and quantity to be understood by all people of different cultures all over the world. It has also become the language of manufacturing, finance, social policy, science, and the technical work force.
Mathematics is an ART. Art is the practice of creating perceptible forms expressive of human feelings. Creative thinking and mathematics have a long, fascinating, and continuing history. The potential for mathematical discovery-the “aha” experience-is in all of us. The creative artists are using more mathematical applications in their workplace than ever before. To view mathematics as not creative is contrary to what has taken place throughout history. Over 200,000 new mathematical theorems, each requiring creative and artistic thought, are proven each year. In the 1990s alone, more theorems were proven than in all of the years prior to that. Each new theorem required the mathematician(s) to create thinking that expressed the affective as well as the cognitive thinking. All mathematics is artistic in human thought.
Not created on a computer using mathematics. This is A Spectacular Image to Celebrate the International Year of Astro – This image of M101 is a composite of data from NASA’s Chandra X-ray Observatory, Spitzer Space Telescope, and Hubble Space
Mathematics is a SCIENCE. Science is an activity which has as its goal the formulation and understanding of a complete model of the universe. Mathematicians observe, experiment, and make conjectures. They investigate, measure, calculate, and classify to explore their questions. Mathematics is not a passive pursuit nor a spectator sport, but rather an active attempt to identify, describe, and explain patterns (arrangements) wherever they exist and in whatever form. In this sense, mathematics can be described as the science of patterns.
Mathematics is a TOOL. A tool is a device designed to extend human powers. Mathematics is a tool to solve problems. Artists, musicians, scientists, athletes, and mechanics all use their tools to paint, compose, experiment, compete, and repair. Mathematicians use mathematics as a tool to solve problems. If a person can correctly interpret a mathematical formula, and identify the proper data to be used in the formula, it is possible to solve problems using mathematics as a tool without resorting to its more aesthetic roles such as science and art.
Therefore, math is a Beautiful Language Art Science Tool! Math is a B.L.A.S.T. :-)
Math is like a bath – it’s most useful when you are in it. Don’t just look at it, get in it! :-)
R2 Thoughts for You 