Proof is sufficient evidence or argument to establishes a claim as a fact, and has limited application. For example, if we were face to face in Riverside, I could prove that I wasn't in Boston, and didn't commit a murder that might have occurred there half an hour earlier.But proof is evidence or argument helping to establish a fact or truth...
But that is an isolated incident.
If I want to prove an induction - a generalization about how reality works both now and in the future based on the observations of events in the past, I can't do it, and needn't do it. However many times I drop an apple in a gravitational field and it falls, I cannot prove that it will fall the next time. Laws and theories can be confirmed, but never proven. That is, they can be shown to be accurate in describing the past, and useful at predicting outcomes in the future, but not guaranteed to always be true.
Not for its greatest pronouncements, and only in the limited sense I already mentioned. I can only prove trivial facts, such as that the apple is on the floor by showing it to you there. And I can prove to you that an apple can fall by dropping one in front of you. But that's about where proof ends.Science needs proof.
Incidentally, proof is a relative term limited by the possibility that none of this is real - so called matrix reality or vat in a brain arguments - or that it we were all created last Thursday with our present memories of a longer history.
Such radical possibilities are merely logically possible and not realistic hypotheses, but they cannot be ruled out, and at the most fundamental level, overturn all proofs. That is, a dead body is normally considered proof that there was a birth followed by growth and then a death - unless the whole world were created moments ago exactly as we see it, including with memories of a reality that never actually occurred.
Bottom line: the word proof should be avoided when discussing science.