Mathematicians don’t agree about the definition of mathematics. Mathematicians have pushed the limits of math for thousands of years. The word “mathematics” comes from ancient Greek and means, “that which is learnt.”
Various Math Definitions
Dictionary.com defines mathematics as “the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically.”
Merriam-Webster defines mathematics as “the science of numbers and their operations, interrelations, combinations, generalizations, and abstraction and of space configurations and their structures, measurement, transformations and generalizations”
Aristotle defined math as “the science of quantity.”
Bertrand Russel said, “All Mathematics is symbolic logic.”
Some say that mathematics is “the science that deals with the logic of shape, quantity and arrangement.” Many mathematicians say they don’t care about defining math and say simply, “mathematics is what mathematicians do.”
Applied and Pure Math
Pure mathematics is more like an art than a science and applied mathematics is more like a science than an art.
Applied mathematics helps solve problems in science, engineering, finance, physics, cryptology, technology, astronomy, forensics and other fields. Newton invented calculus to describe objects in motion.
Pure mathematics explores math patterns, puzzles, and abstract ideas. Pure mathematicians are not constrained by the limits of the real world. Just as composers do not expect that their music will solve a problem, neither does the pure mathematician expect their ideas to solve a problem. Albert Einstein said, “Pure mathematics is, in its way, the poetry of logical ideas.”
Abstract ideas from pure mathematics sometimes do lead to practical applications. Computer programming started because of the ideas from the “Turing Machine” in pure mathematics. Alan Turing imagined the Turing Machine with infinite tapes. A Turing Machine is impossible to build, but the logic in the Turing Machine paved the way for programmable machines, like your cell phone.
How does Mathnasium of Littleton define math?
We like Bertrand Russel’s definition that “All Mathematics is symbolic logic. “ We focus on the math studied in elementary, middle school, and high school. All math at that level is applied math. Schools classify math into several disciplines, including:
· Arithmetic (all of elementary school and some middle school)
· Pre-Algebra (typically taken in seventh or eighth grade)
· Algebra (typically taken in eighth, ninth and/or eleventh grade)
· Geometry (taken after passing algebra)
· Trigonometry (often combined with Geometry, the second year of Algebra or Pre-Calculus)
· Pre-Calculus (taken after passing two years of Algebra and Geometry)
· Calculus (taken after passing Pre-Calculus)
· Statistics, Computer Science, and Multi-Variable Calculus (These courses are less common at the high school level. Some high schools offer them instead of, or after calculus.)
We may not be able to help mathematicians define math, but we can help your child succeed in math. Click the button at the bottom of the page to learn more about our program.
For more information about defining math and pure math read:
https://www.etymonline.com/word/mathematic
https://theconversation.com/explainer-the-point-of-pure-mathematics-2385
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