For science there needs to be experimental proof, not just inference. I like this definition from Feynman from almost 60 years ago.
No.
Hypothesis is a vital part of science.
correct, but it must be proven by observation and experiment.
Feynman describes the hypothetical deductive method popularised by Popper as conjectures and refutations. It does not attempt proof but, as Feynman makes clear (0:39), (lack of) disproof.
Richard Feynman said:
If it [the theory] disagrees with experiment, it's wrong.
Further, it is very difficult to prove as true a hypothesis that derives from a universal theory or more generally prove a theory to be true. Any attempt of such proof must include observations of any and all instances of that which the theory attempts to explain. Thus proof is impossible if there are any potential future instances of that which the theory attempts to explain - as is the case with most (if not all) theories of nature and also evolution and in particular. This relates closely to the problem of induction popularised by Hume.
For example, in order to prove the universal theory that all swans are white requires observation of any and all swans at any relevant moment. As there may be swans yet to be discovered or yet to become, proving the theory is impossible. (It's wrong by the way. There are black swans in Australia.)
Demanding proof is thus to set the bar so high as to guarantee failure.
However, while universal theories cannot be proven true, they may be proven wrong by observing only one instance of that which the theory attempts to explain that disagrees with the theory's prediction(s). While this may seem straightforward and the explicit mentioning of principal validity seems superfluous, practically, observations are often made using means or equipment based on other theories that themselves may still not be proven but have also not yet suffered disproof. Thus, any disagreement between the prediction of the main theory and an observation only implies that at least one of the theories is wrong but not which. In other words, the tested hypothesis is not just the prediction of the main theory but also any relevant predictions of the other theories. If the hypothesis is disproven, i.e. in disagreement with observation, it only follows that at least one prediction was wrong.
A common example given as disproof of evolution is finding a the fossil rabbit in the pre-cambrian. However, if such an observation seems to have been made, determining whether the fossil is indeed that of a rabbit and whether the it is indeed pre-cambrian requires additional theories such as that of the decay of unstable isotopes.
Disproof of a particular theory can thus also be very difficult.
Further, for this approach there are conditions that theories need to satisfy. Allowing theories that even in principle cannot be disproven by observation to be considered viable explanations of reality is silly on the face of it. Therefore, theories that attempt to explain reality must be falsifiable, i.e. it must make predictions that - in principle - can disagree with observations. Further, ad hocs are not allowed or constitute a new theory. In this sense, modification of a theory is the creation of a new one.
Since proof is not possible and disproof rather complicated, one might feel compelled to frustratedly throw one's hands in the air as objective evaluation of the truth or falseness of any theory seems out of reach. However, there still remains the subjective evaluation of the probability of the theory being true given the observations of the instances of that which the theory attempts to explain. Of course, this only makes sense if the same conditions of the previous paragraph apply as the probability of a theory that cannot be disproven being true is always 1. This is known as Bayesian epistemology named after Bayes to whom the idea of conditional probability is attributed.
For example, of two theories of which the predictions of both are in accordance with the observations,
if one has been tested thousands of times to great precision while the other has been tested only a couple times and not to even remotely as great precision, the first theory has greater probability of being true than the other theory.
Further, even if the predictions of a theory disagree with observation a couple of times, the probability of it being true may still be greater than zero if it is more likely that the failure stems from another theory. For example, if it is more likely that the dating of the rabbit was mistaken, evolution being true would still have non-zero probability or if it were more likely that a seemingly black swan was actually a white swan covered in coal dust, there would still be a non-zero probability that all swans are white.
Still, as the evaluation is subjective, there can be and is disagreement among scientist which theory is most probably true given the relevant observations. The limited time the scientists have further complicates this as they may not be familiar with all the relevant observations only those most relevant to their own work which - to further complicate things - may be motivated by things other than the available observations.
Given this, the astounding progress made is still testament to the robustness of the scientific method. However, one should not treat individual scientists or groups as unquestionable authorities. For example, contrary to some of his contemporaries (e.g. Bohr, Heisenberg), Einstein's views of quantum physics are rather questionable and are far from what is generally agreed on today.
TLDR: Proving universal theories is very difficult and proving theories of nature is impossible. Disproving universal theories is difficult and disproving theories of nature even more so. Thus, objective evaluation of the truth of theories of nature is very difficult if not entirely out of reach. However, theories of nature can be evaluated subjectively as the probability of the theory being true given the observations of the instances of that which the theory attempts to explain. However, scientists are only human as well, so disagreements are possible and existent and thus no individual scientist should be treated as an unquestionable authority.
