Mathematics is the study of structure, quantity, space, and
change. Mathematicians seek out patterns, create new conjectures, and set up
truth by rigorous deduction from appropriately selected definitions and axioms.
There is debate over whether mathematical objects such as points
and numbers exist naturally or are human creations. The mathematician Benjamin
Peirce defines mathematics “the science that draws require conclusions”. Albert
Einstein, on the other hand, define that “as far as the laws of mathematics
refer to reality, they are not assured; and as far as they are definite, they
do not refer to reality.
Most of the mathematical basic concepts we encounter every
day – numbers, subtraction, addition – seem so basic, so hard to avoid in
discussing reality on even the most basic level, that it’s hard to imagine
someone having to invent and sit down them. Who was the first person to look at
two rocks and think, “Two more and I’ve got four?” The very idea almost seems absurd.
But mathematics is, in part, a language – not just a entailment
and set of logical relationships that seems deeper than words, but a set of
notations that allow us to show those relationships. You can’t see that twice
two build four, until you have a symbol for “two” that your brain will operate
with. And those symbols – that language – did have to prepare, strange as it will
seem. (Prehistoric artifacts seem to show that the earliest humans had only
four “numbers” at their disposal “none,” “one,” “two,” and “many” – showing
just how much our ability to talk about variables and numbers lies on having
the right words for them.
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