What does it mean to prove a scientific theory? What’s the role of mathematics in science? How do you define the scientific method? Take a look at the fundamental way people look at science, what proof means, and whether a hypothesis can be proven or unprovable. The story starts with an e-mail which seemed to criticize my support of the big bang theory which is, after all, unprovable. The author of the e-mail indicated that he thought this was tied into the fact that in my Introduction to the Scientific Method article, I have the following line: Analyze the data – use proper mathematical analysis to see if the results of the experiment support or refute the hypothesis. He implied that placing an emphasis on “mathematical analysis” was misleading. He claimed that mathematics was tacked on later, by theoreticians believed that science could be better explained using equations and arbitrarily assigned constants. According to the writer, mathematics can be manipulated to get the results desired, based on the scientist’s preconceptions, such as what Einstein did with the cosmological constant. There are a lot of great points in this explanation, and several which I feel are far wide of the mark. Let’s consider them point by point over the next few days. The big bang theory is absolutely unprovable. In fact, all scientific theories are unprovable, but the big bang does suffer from this a bit more than most. When I say that all scientific theories are unprovable, I’m referencing the ideas of famed philosopher of science Karl Popper, who is well known for discussing the idea that a scientific idea must be falsifiable. In other words, there has to be some way (in principle, if not in actual practice) that you could have an outcome which contradicts a scientific idea. Any idea which can be constantly shifted around so that any sort of evidence would fit it is, by Popper’s definition, not a scientific idea. (This is why the concept of God, for example, is not scientific. Those who believe in God use pretty much everything to support their claim and cannot come up with evidence — at least short of dying and finding that nothing’s happened, which unfortunately yields little in the way of empirical data in this world — which could, even in theory, refute their claim.) One consequence of Popper’s work with falsifiability is the understanding that you never really prove a theory. What scientists do is instead come up with implications of the theory, make hypotheses based on those implications, and then try to prove that specific hypothesis true or false through either experiment or careful observation. If the experiment or observation matches the prediction of the hypothesis, the scientist has gained support for the hypothesis (and therefore the underlying theory), but has not proven it. It’s always possible that there’s another explanation for the result.