In a whole host of advanced disciplines, we find the old root-of-the-sum-of-the-squares formula pops up with astonishing regularity. In fact, if someone were able to demonstrate that one single right-angled triangle could exist which did not conform to this theorem, then it would be the mathematical equivalent of removing the foundation from a great classical building and thereby reducing it to a heap of rubble. Virtually every field of science would be affected and great minds would then set to work on the problem to find an explanation.

That is effectively what happened when Einstein74 showed our understanding of the laws of physics to be incomplete: the equivalent of the classical building, which consequently collapsed, was the Newtonian view of the universe. Einstein’s celebrated General Theory of Relativity caused reference books to become outdated, literally overnight. With magnificent insight, he completely overhauled previous notions of the relationship between time and space. It is rather encouraging to learn that Einstein himself actually struggled with the mathematics which were necessary to prove his theory; but nevertheless, prove it mathematically, he did.

The scientific method which utilises the experiment in order to verify the hypothesis, has produced a good deal of support for the theories of Einstein; and it doesn’t take a genius to digest the mathematical evidence which supports the Pythagoras theorem. In other areas of research, things are not so straightforward: as De Bono points out, ‘with a mathematical proof we move step by step according to the rules of mathematics, until we have completed the proof. Scientific proof is much less satisfactory because we have not actually constructed the universe75’.

When faced with issues like evolution, life on other planets, the Big Bang and so on, although we must listen carefully to what the experts tell us, we must also learn to be discerning; it is important to distinguish between truth, theory and hypothesis. Naturally, we laymen must increasingly depend upon the advice of the expert for guidance on matters in which we have no specialist knowledge. However, we should bear in mind that science can live with the replacement of previously acceptable and fashionable ideas with new ones, which may provide a better explanation of the observable facts for the present time. Theory revision is an integral part of scientific methodology.

As an example of how the process of scientific theory revision operates, let us consider the history of the theory of evolution (we will consider the theory itself later), or Darwinism; the only respectable alternative to the proposition of special creation by divine action. It is certainly ‘the consensus of science today … that the theory of evolution is … extremely well supported by evidence76’. But it was actually the scientists who eventually decided that Darwinism was an inadequate explanation and so the original theory was changed.

An amended theory known as neo-Darwinism replaced the original, but this theory also became subject to attack over the years, so new ideas were also incorporated into the revised theorem: ‘in 1972 the American palaeontologists Niles Eldredge and Stephen Jay Gould argued that natural selection - as expressed in neo-Darwinism - was inadequate to explain the evolutionary pattern seen in the fossil record77’. The most recent revision of evolutionary theory, known as ‘punctuated equilibrium78’, attempts to further adapt the theory to explain why it is that the fossils have not recorded the steady change which the evolutionists had predicted.