• What is "proof?"
    As I take the logical ladders down this well, I end up at the deeper question: "Is capital truth(or Truth) something that the human mind can realise".
    I think it is not, that is to say, we will never be able to prove anything is 100% True whilst we are using 'relatively blunt' tools like 'eyes', 'mathematics' and 'reason'.
    The logical conclusion of the empirical scientific method to me, is that if no experiment or observation can be conducted or recorded which disproves the leading theory, then the leading theory is generally considered to be “knowledge” or “proven” within that scientific field. This may not apply to new and emerging fields of study, as there is new ground being covered there. I am referring here to the classical sciences – biology, physics, astronomy etc.

    I think of Newton's conception of physics and gravity; and how - for hundreds of years, the brightest minds and sharpest thinkers the world could produce were not able to refute or disprove his theories. It was taught in schools, it was considered knowledge. Even when it seemed the theories were beginning to not accurately predict more technologically complex experiments as time moved forward, none other could conceive a theory so complete as Newton’s - until Einstein. With Einstein, we saw a “change of knowledge” in essence, it was also “change of something which was once considered proven”.
    And now, scientists seem to be demonstrably reaching the limits to Einstein’s equations and are seeing the breakdown of Einstein’s theories at the quantum scale and in black holes. Here is a quote from Andrea Ghez, an astrophysicist at UCLA working on black hole research:
    “Newton had a great time for a long time with his description [of gravity], and then at some point it was clear that that description was fraying at the edges, and then Einstein offered a more complete version. And so today, we're at that point again where we understand there has to be something that is more comprehensive that allows us to describe gravity in the context of black holes.”
    The more advanced we become technologically: the finer observations we can take, the further into the cosmos we can look, the more data we can map and model, the smaller the objects and forces we can detect. We will always be changing our theories. We will always be changing our knowledge, and I don’t believe we are equipped to ever arrive at the underlying Truth of anything, really.

    However, it does favor us in many circumstances to perceive these un-true theories as irrefutable facts of the universe. eg: to get to the moon, we don't need a perfect True theory of gravity, we just need one that is good enough to get us to the moon. So, it helps those with the goal of trying to get to the moon by accepting that Einstein's theory of gravity is proven fact, and using it to calculate their trajectories.

    To answer your question: I reckon the value of scientific fields having threshold criterion for a "proven fact" is so progress can be made. If we were never able to pin something down as a "fact" and teach it in schools because in 200 years it might be proven wrong by a smarter primate, we dont have any progress. I see it as a "near enough is good enough" approach to our collective human knowledge. How near and how good is up to the scientists, I suppose.