You can argue Newton fit the bill even though Liebniz was a peer of his. Einstein and Oppenheimer, etc.

Those are ones you can argue, though. Nobody would ever seriously argue that Kaczynski was anywhere near the top of his generation. There is no informed list of the greatest mathematicians that has Kaczynski on it.

Let's imagine that, instead of being caught, Kaczynski simply stopped bombing things and was never caught, and lived out the remainder of his life in that shack. In that case, he'd be an obscure genius mathematician who wrote a few exceptional papers. There are a lot of people like that.

I suspect that while right now, you think it's "a common phrase for an exceptional mind," if you really looked into its usage, you'd find that it's generally used for somebody who actually is uniquely exceptional for their time.

Its a common phrase for

No, that's you learning it from context without thinking about what the actual words mean. It's meant to be taken literally.