How to put our scientific ideas into a mathematical model?
It is important to realise that mathematics doesn’t prove anything about a scientific theory. This is because the mathematical model will have been developed using assumptions about the real situation. Mathematics can then make predictions, and if these are verified it suggests that it is a good model and that the assumptions may be correct. If the predictions do not turn out to be true it doesn’t prove that the mathematics is wrong (although it could be) but that the assumptions were at least partly invalid. I was once told off by a lecturer in Physics. I had said that in the 19th century they thought something was X but we now know that it is Y. He said that in science you must never say ‘we know that . . .’, but must say ‘current understanding is that . . .’ Future scientists may discover something that changes our opinion. Pure mathematics is the only subject where you can be right or wrong with absolute certainty. That’s what I like about it.
