The point is that there has to be some commonly understood and shared meaning, otherwise communication cannot happen. If a person chooses new meanings that are different to the standard meanings, then it is up to that person to state what they mean.
No, I mean that us "users" must verify we agree what the rules/meanings/precedences are, and not just assume they are some standard ones, because they do vary.
Just because the
PEMDAS infix notation is the only one you have been taught, does not mean it is the only one used. It is the only one you've ever used, perhaps... but the rest of us have used RPN and others, especially when using practical tools to solve practical problems. (Conversion between infix and postfix notation, using the
shunting yard algoritm, is a very common exercise in computer science.)
For example, if you show
$$ y = c_i x^i $$
to a mathematician, they probably think it is an odd way to specify a monomial whose degree depends on some constant named \$ i \$; but physicists know this is just shorthand,
Einstein notation (as having the constant factor name depend on the degree of the monomial makes no sense!), equivalent to
$$ y = \sum_i c_i x^i $$
In quantum mechanics you have Dirac or
bra-ket notation, \$ \left\lt\varphi\right\rvert \$ and \$ \left\lvert\theta\right\gt \$, that follow the rules of linear algebra, and actually represent matrices; but because of their properties, they are rarely if ever expanded to their actual matrix representations. For example, the superposition of wave functions \$\varphi\$ and \$\theta\$ is \$ \left\lt\varphi\right\rvert\left.\theta\right\gt = \int \left\lt\varphi\right\rvert\left. x \right\gt \left\lt x \right \rvert \left . \theta \right \gt dx = \int \overline{\varphi(x)} \theta(x) dx\$, where \$ \overline{\varphi(x)} \$ is the complex conjugate of the wave function \$\varphi(x)\$, \$\left\lvert \varphi \right\gt\$ is the state (column) vector for the wave function \$\varphi\$, and \$\left\lt \theta \right\rvert\$ is the Hermitian conjugate of the state vector for the wave function \$\theta\$.
Here, you don't just need to know the notation, you need to know the domain-specific rules that apply to this notation, to save yourself a fuckton of extra work.
(Stuff like Gaussian error functions, elliptic integrals, and so on, being already implemented in many programming languages and math libraries is what typical programmers might not know, and instead open-code inferior/approximate versions of. And that some languages/applications use a different order of arithmetic and unary/binary/boolean operators than you might expect.)
Notation rules are not universal, they do vary. The more complex the application domain is, the more likely it is they use their own notation and rules to simplify it.
Hence, in the original question, it is reasonable to ask where the parentheses are, and reasonable to answer "no parentheses, normal laws of arithmetic", or "no parentheses, in Excel spreadsheets".
Fully agreed; and the core of what I am trying to say too.