That’s a really interesting and philosophical question. Science works like this:
1. Somebody comes up with a theory based on a combination of maths, other theories and observations of the world.
2. That theory is compared to other observations of the world.
3. If the observations agree with the theory, then the theory becomes more trusted. If the observation does not agree with the theory, then the theory is wrong (or maybe there was a mistake in the observation, so you have to be very careful with measurements).
If there are many many many observations that support the theory, eventually it is considered to be ‘proved’. For example, we now have enough measurements and observations to know that the Earth goes around the Sun – we considered that to be proved.
I have to say, this is one of my favourite questions so far – it really gets to the essence of what science is about 🙂