It is amazing how much information we can get from the electromagnetic spectrum emitted by an object even though it might be a billion light years away. It's the same sort of technology that is used to determine who should hang for drug smuggling.
Want to know another amazing feat of mathematics? It is simple maths that determines the Lagrange point that now contains the James Webb telescope. Without the math we wouldn't have a clue where to put the telescope in space. The James Webb telescope is at L2.
https://webbtelescope.org/contents/media/images/01F4STZH25YJH07WTN7XJYQP8P