Mathematicians and physicists predicted the existence of black holes before we ever found them; perhaps unsurprising since they don’t give off any light. But eventually we figured out that they really could exist, and then we predicted that they should in fact emit radiation, and then we found that radiation and all sorts of other hints that tell us they’re actually there.
That makes it sound easy, but it was extremely hard. Filtering out all the radiation we get from space to identify just some bits of it as coming from matter as it falls into a black hole is very tricky. Scientists used a mathematical technique called Fourier analysis which can identify different frequencies of signal from one incoming mashed-up signal. And their analysis worked in identifying stuff that was radiating as a result of black holes.
Later on some clever scientists at CSIRO in Australia were trying to solve the problem of how lots of people in the same space, or that were moving around, could have their computers all networked. Running a wire to everyone is impractical. Using a radio signal would be possible but at the relatively low powers, short ranges, and confined spaces needed they got lots of signal reflections that made the incoming signal a bit mashed-up.
But these clever folks remembered what the black hole scientists had done and used Fourier techniques to disentangle the signals they needed from that mashed-up mess. And wifi communication was born.