Oh, but wait. You can't talk about science and proof. Proof is something we will never find in science. It would be a great boon if it were possible, but it isn't. In order to use proofs, you need axioms. From axioms, we can use deduction and come up with new ideas. These ideas can then be proven to be true, if we consider the given axioms and the rule of inference to be valid.
However, there can be no such thing in science, as the whole point of science is to figure out what would be a good set of axioms for such a deduction. If we fix the axioms now, we can no longer rely on experiment, as they might invalidate the basic foundations of science. This would of course be a very stupid thing to do, as science is intended to describe nature, and when nature does something else than science would predict, we should take it that nature is right, and current scientific theories are wrong. This, of course, should be regarded as the only axiom of science.
There is of course three other problems with science, so two new axioms are needed. The first problem is that we must believe there is such a thing as a real world, existing outside our minds, and that we can measure the properties it have with some reliability, and use this as a description of the real world. The second problem is that science relies on induction. There is no logical reason to believe that just because something happens again and again during experiment, it will continue to do so the next time we try, (or when nobody is looking). The third problems is that we must believe that the outside world is governed by some set of rules, that it is possible for us to find. If we are looking for proof, we won't find it.
Ok, so scientist remain pretty about their results, don't they? How can they then feel sure without proof? Well, the truth is, they shouldn't! And in fact, most of them aren't! There are some scientific theories that over the years have established themselves as a good description of either the world, or the laws that we assume must govern it. Most scientists believe these to be a good description of nature, but wouldn't take them as axioms. We might find other evidence later that shows inconsistensies in these theories with the actual behaviour of nature. So really, nothing in science is settled, and nothing can be proven.
So then, how does scientific discovery work? Shouldn't we try to use proofs of some kind? No we shouldn't! The scientific method deals with one construct only; the hypothesis. After observing a regularity in nature, a scientist might propose that there is some law of nature governing this behaviour. In an attempt to describe this law of nature, he forms a hypothesis. The hypothesis will try to explain why this happens, and ideally, it should also predict other behaviour of nature we haven't earlier observed, that it would (at least theoretically) be possible to conduct an experiment to test.
The ability of a hypothesis to predict other behaviour than it attempted to describe is important. If it doesn't, we have no way of increasing our confidence in it. Any variation of the original hypothesis (and there are infinitely many of them) would explain the original phenomenon just as well, and we would never know which one to choose. Even more important, we have know way of knowing that it is false. If we cannot (even in theory) conduct new experiments that show a hypothesis to be false, it should be considered worthless for the purposes of science.
To sum up. Scientists observe nature. They form a hypothesis trying to describe it's behaviour. The hypothesis will be of a general nature that can also be used to predict other behaviour of nature. We conduct a new experiment, testing if this behaviour occurs in nature as well. If it does, the hypothesis is strengthened, and more people will start believing in it. If it is not, the hypothesis is proven wrong, as it disagrees with nature.
Ok, so proof occurs in science, but only to prove an idea wrong, not to prove an idea right. Still, I feel pretty confident about those parts of scientific knowledge that has been tested, and retested for centuries.
Of course, you can never expect the popular media to understand this. Heck, most media people wouldn't even understand what an experiment is. If you read popular media reports on science, you will see that when they describe scientists doing an experiment, they really describe it as some sort of demonstration. An experiment will be a failure only if it fails to produce valuable data. On the other hand, a demonstration has failed when it fails to convince the viewers that the hypothesis of some authority must be right.
Science itself works ok, most of the time. Given the scientific progress of the last century, you would be an idiot to proclaim anything else. Popular media, however, is not interested in science, as most people aren't. Popular media is interested in creating sensations, so when scientists try something controversial, it is bound to find the press. Thus most everything that you read about science in the popular media will have to be from the most unreliable parts of science.