One Mathematical Cat, Please! An Interactive Slide Show

Languages evolve to make essential ideas easy to express.

The language of mathematics makes it easy to express
the kinds of thoughts that mathematicians need to express.

It is:

PRECISE (able to make very fine distinctions):
compare

$\,5x^2\,$ and $\,(5x)^2\,$

CONCISE (able to say things briefly):
the expression

$\,3x^2 - 5x + 7\,$ represents this sequence of operations:
take a number, square it, multiply it by $\,3\,,$ subtract five times the original number, then add $\,7\,$

POWERFUL (able to express complex thoughts with relative ease):
It takes a full week of classes to fully flesh out this statement, which is the central idea in Calculus:

$$ \begin{gather} \lim_{x\rightarrow c} f(x) = \ell\cr \text{ is equivalent to }\cr \forall\ \ \epsilon \gt 0\ \ \exists\ \ \delta \gt 0\ \ \text{s.t. if}\ \ x\in\text{dom}(f)\ \ \text{and}\ \ 0 \lt |x - c| < \delta\ \ \text{then}\ \ |f(x) - \ell| \lt \epsilon \end{gather} $$