I always struggled with math, so I just don’t get how an astrophysicist could look at some numbers and symbols and say, “Aha, it’s proof of black holes!”
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Math didn’t by itself prove the existence of black holes. What it did was show that black holes were *possible* in that the laws of physics allows them to exist, and gave us some idea of what we might see if we were looking at one. Then, armed with that knowledge, we could look at the sky and say “hey, that thing looks like how the math predicts a black hole would look.”
In other words, math didn’t prove the existence of black holes, but it told us what to look for.
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