I was sitting in a coffee shop today, staring at data and figures and trying to make sense of them all, when I overheard a bit of a conversation taking place at another table concerning the relationship between science and mathematics. As the one guy explained to his friend, “Science deduces, and math is deductive. Science uses math as a language.” Said in another way, science is about drawing conclusions from observations, and math is about following a basic set of premises (axioms) to their logical conclusion.
The distinction between science and mathematics isn’t one that I normally stop to consider all that often. As a method for systematically explaining the way the universe works, science is firmly embedded in reality. The question of how ‘real’ a scientific idea is can be established in a straight forward way – by making careful observations of the phenomena in question. Mathematics is a different beast. Mathematics is a system in itself, and when a mathematician makes some sort of discovery, the question arises whether they have found some fundamental truth of the universe, or merely some piece of a system created by humans. This is because the ‘truth’ of mathematics is in its relationship to itself, rather than to some physical phenomena. The strange thing is that so much of what has been established as consistent within the logical formalism of mathematics can be used to describe some piece of reality out in nature. There are deep connections between mathematics and science, and what they are is not always so clear (to me anyway).
There’s a book sitting on my shelf titled ‘What is mathematics, really?’ by Reuben Hersh. One of these days I’ll hopefully get around to reading it.