It is common to say that math help us think but all academic subjects rely on thinking. Solving word puzzles, studying, reading, writing an essay, etc are thinking activities. However Math might involve much more thinking activities than other subjects because they concerned primarily with solving problems. The Math vocabulary represents some very powerful ideas.

Our understanding of quantity holds concepts refined over thousands of years (negatives, zero, decimals). Math ideas require extensive thinking to be grasped. Some languages only have words for one, two and many. In those languages the notion of many has never been subdivided and structured.

The notion of quantity has known several developments over the years:

Each quantity can be referred by number words (one, two, three, one hundred and five, one thousand two hundreds and fifty)

The number words can be written with symbols not with letters like lines in the sand. The tally system has a line for each quantity.

Shortcuts are used for large quantities. Romans numerals are then used in this case. Some examples are: V = five, X = ten, C = one hundred.

Emptiness is represented by zero.

The position of a number is a shortcut for another number. Example: 234 = 200+30+4.

Numbers can have very small differences. Examples: 1.1, 1.01, 1.001.

Numbers can be less than nothing. They are called negative numbers and reverse or opposite of another number. Example: negative height is underground. Negative saving is debt.

Numbers can be two dimensional (complex numbers).

Numbers can be very small and still doesn't represent zero.

The concept of numbers has shaped our world during millenia. Numbers were used to describe time in different calendar systems. One of the calendar system was modeled on the number system using the symbols BC and AD. Prices have been set by the stock market in increments of 1/8 until 2000 AD.

The notion of numbers has allowed us to conceptualize many physical ideas. For example the notion of zero allows us to understand the concept of vacuum or emptiness. The notion of negative numbers allows us to understand antigravity and antimatter.

The math vocabulary has shaped our different ways of thinking primarily thanks to the development of the numbers concept. Basic arithmetic is used in various fields of human activity. Multiplication and division which have been difficult concepts to be grasped by scholars for thousands of years are taught to small children in grade school. This is made possible because of better ways to describe quantity. The development of other branches in mathematics such as Geometry, Calculus and Statistics allow us to model and understand better the notions of shape, change and chance.

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