Mathematics has been the most successful and is the most mature of the sciences. Its first great master work – Euclid's ‘Elements’ – which helped to establish the field and demonstrate the power of its methods, was written about 2400 years ago; and it served as a standard text in the mathematics curriculum well into the twentieth century. By contrast, the first comparable master work of physics – Newton's Principia – was written 300 odd years ago. And the juvenile science of biology only got its first master work – Darwin's ‘On the Origin of Species’ – a mere 150 years ago. The development of the subject has also been extraordinarily fertile, particularly in the last three centuries, and it is perhaps only in the last century that the other sciences have begun to approach mathematics in the steady accumulation of knowledge that it has been able to offer. There has, moreover, been almost universal agreement on its methods and how they are to be applied. What we require is proof; and, in practice, there is very little disagreement over whether or not we have it. The other sciences, by contrast, tend to get mired in controversy over the significance of this or that experimental finding or over whether one theory is to be preferred to another.

According to relativists, people who speak simply of what's ‘true’ are naïve. ‘Whose truth?’ asks the relativist. ‘No claim is ever true, period. What's true is always true for someone. It's true relative to a particular person or culture. There's no such thing as the absolute truth on any issue.’

This sort of relativism is certainly popular. For example, many claim that we are wrong to condemn cultures with moral codes different from our own: their moralities are no less valid. Similarly, some claim that while astrology and Feng Shui might be ‘false’ from a Western, scientific viewpoint, they are ‘true’ when viewed from alternative, New Age points of view. What's ‘true’ and what's ‘false’ ultimately depend on where one is standing.

Is this sort of relativism about truth tenable?

In this article, John Hyman argues that beauty does not consist in mathematical perfection; that Hume was mistaken in claiming that beauty exists only in the mind; that we can discover what is really beautiful by learning to give reasons for our preferences; and that some things in the world are beautiful—probably many more than we imagine.