# Thoughts

4 later thoughts

0

It's interesting how many notational shortcuts mathematicians take would never be tolerated by a programmer.

For example the confusion as to whether $$f(x)$$ is referring to the function $$f$$ over the independent variable $$x$$ versus the value of $$f$$ given a value $$x$$.

It can get even worse in discussing something like coordinate transformations where you might have

$$x(r(x, y), \theta(x, y)) \equiv x$$
where sometimes $$x$$ is a function and sometimes it's an independent variable.

I'm just watching a wonderful lecture series by Pavel Grinfeld and he's (understandably) going to great lengths to clarify in each expression (including the equivalence above) whether something is a function or an independent variable. I suspect programmers get it much more quickly.

28 earlier thoughts