Or so I've heard. But it isn't true. Put it with the myth that all codes can be broken if you use enough computer power. Not true.
But can you prove a negative? Some you can't prove. For example, you can't prove that unicorns don't exist. Maybe somewhere, in a galaxy far far away, there's a frolicking herd of unicorns - we don't know. Maybe even in an unexplored part of a dense jungle in Earth.
But some you can prove, and I'm going to give an example.
To prove: there is no largest prime. A prime is an integer that is divisible by one and by itself, and not any other integer, with no remainder. For example: 2, 3, 5, 7, 11, 13 ...
Suppose there is a largest prime, P. Then let's line up all the primes less than P, and let's multiply them all together, and add 1. That gives us a number larger than P. And if you try to divide it by any of the lower primes, you get a remainder of 1, so this new larger number is a prime, which is larger than the number we thought was the largest prime.
So, there cannot be a largest prime.
Quod erat demonstrandum
So, there's an example of a negative that can be proved. So not all negatives are unprovable, only some of them.