In the field of mathematics rigorous proofs abound. There are various formal proofs of 1+1 =2, ranging from a few lines, to several pages, which is perhaps surprizingly long for something seemlingly so obvious. Similarly, Fermat's Last Theorem was in the general news headlines in 1994 when Andrew Wiles completed the proof in 129 pages after mathematicians had been trying since 1637. Yes, mathematicians will go to enormous lengths. There is a common misconception that scientists work in the same way; however, no one can prove a scientific theory.
Science works on the basis that we come up with ideas, or hypotheses, and test them. While the tests all prove positive, we still have a working theory. When a test gives a result which contradicts the theory, then it has been disproved, or falsified, and we need to move on to find something better. Newton's theory of gravitation was very good, and still is used in most situations. It was written in a way that meant that it could be tested and falsified. In the end it was found to be lacking and Einstein replaced it with general relativity. This is also formulated in a way that can be falsified, but no test has yet given a contradictory result after over 100 years. There are reasons, though, why even general relativity cannot be the final theory of gravitation. No theory is ever proven in science - we are always testing and moving forwards.
Science has to be carried out rigorously if it is going to mean anything and we have to accept that proof is utterly illusive.
There is, however, quite a lot of hype about the theory of evolution. Many biologists, if you
were to put it to them that evolution has not been proven, react quite strongly. Various arguments include that it is inconceivable that evolution did not take place, or that the use of falsifiability in the definition of theories about the past is inappropriate. These responses mean that they understand the issue, but consider it unfair to call it into play in this case. We can understand the problems of dealing with historical data, where experiments cannot be repeated, but that doesn't make theories which can't be tested properly scientific.
We could only show that evolution actually is possible if one species were ever to transform into another, yet that would still not prove that it happened in the past. However, so far, although it is clear that there is evolution within species (micro-evolution) the sort of changes that produce radically different species of animals or plants (macro-evolution) have never been observed. Even the famous experiments on fruit flies, where it is possible to get through vast numbers of generations in a relatively short space of time, have never led to anything other than fruit flies.
As a final note of caution, although there is no direct evidence for macro-evolution and no way of proving that it occurred in the past, even if it were ever to be observed in the future, it is important that creationists don't fall into the same trap of discounting the proposals of other scientists without proper scientific presentation of their arguments. There is still a lot of valid work to be done in this field from both perspectives.
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