Well, if it is undiscovered, then actually we cannot know whether it exists or not.
But i am wondering if theorems/equalities like $Pythagorean$ $Theorem$ or maybe $Fermat's$ $Last$ $Theorem$ have been discovered in the recent past.
So, can we know (or feel) that a very basic theorem exists, but hasn't been discovered yet?
This question came to my mind when I learned that as people thought that the boundary/end of geometry has almost been reached, Riemann founded the Riemann Geometry.
On
The abc-conjecture is pretty basic. It says that for every $\epsilon\gt0$ there exist only finitely many triples $(a, b, c)$ of positive coprime integers, with $a + b = c$, such that $c\gt{\rm rad}(abc)^{1+\epsilon}$, where the "radical" of $n$ is the product of the distinct primes dividing $n$. It's also pretty recent, as it was first proposed less than 30 years ago. And if it were proved, it would have huge consequences in Number Theory --- see the Wikipedia link.
Examples are the Euler line and Morley's miracle. Both are theorems that in principle could have been proved by the Greeks, but took more than a thousand years to notice. It is certainly possible that many such are lurking in the woodwork.