Quadratic Reciprocity Joke I found a joke on a site made by user Zev Chonoles on quadratic reciprocity, the joke is as follows: $$\text{Quadratic reciprocity: } \left(\frac{p}{q}\right)=\left(\frac{q}{p}\right), \text{ up to sign.}$$ I assume it's a joke because the quadratic characters on opposite sides of the equality can only take on values $\pm 1$ (assuming $p \ne q$ are distinct primes) making the statement trivial. That is the joke right? If not can someone explain

That is the joke, but a related fact is that systematizing and simplifying the sign (such as eliminating it, or making it independent of $p$ and $q$) was part of the motivation for using other forms of the symbol instead of Legendre's. For example, $(p,q)=(q,p)$ for the Hilbert symbol.