What was the "science" behind catching the Unabomber? They invented some english writing science or something. How did or does that hold up to scrutiny in the scientific community?

I don't even know if I'd call it a science, just a series of inferential techniques. David Kaczynski believed that the author of the manifesto sounded a lot like his brother, and told the authorities, who analyzed it and debated whether Ted Kaczynski's letters were similar enough to the Unabomber manifesto to be the same person. It doesn't even need to be a robust scientific model to have the conversation. Really no different from sifting through witness descriptions of a suspect's appearance and seeing who those descriptions match. Investigators can compare their experiences/beliefs about which traits are rare or unique and which threads are worth investigating further. In the end, they had enough for a warrant, and the search itself revealed a lot more hard evidence that Ted Kaczynski was the Unabomber.