Do The Math

Keith Devlin -- who used to have a regular column in the Guardian that was avidly read in at least one household -- has a comment piece in the Graun in defense of maths.

Clinton's bypass operation is just one example among thousands of how our lives are dependent on science and technology. Behind that science and technology is mathematics - the often overlooked backroom boy on which everything depends.

Galileo, the father of modern science, said it best. In his book Il Saggiatore (The Assayer), published in 1623, he wrote: "[The universe] cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics ... without which it is humanly impossible to understand a single word of it ..."

The Guardian did see fit to publish a letter from a disgruntled dissenter than manages to be muddled and incoherent and without, it seems to me, a point.

If there is one, I think it's this. Maths contains paradoxes and is therefore to be taken with a pinch of salt. Especially as it's not real. Devlin and Galileo, of course weren't claiming that maths is reality. They were simply stating that in order to describe the reality (eg. do science or technology) you need maths. As for the paradox thing, maths inherently can't solve certain propositions. Mathematicians know this. They even have a name for it: Gödel's Incompleteness Theorem. Douglas Hofstadter summarised it as:

All consistent axiomatic formulations of number theory include undecidable propositions...

Essentially, in any consistent representation of maths it will always be possible to say something like "This statement is false", which is unprovable. It's slightly more complex than that as the above link explains. One consequence of this, however, is that some people think that this is what distinguishes us from machines, that "this (alleged) difference between "what can be mechanically proven" and "what can be seen to be true by humans" shows that human intelligence is not mechanical in nature."

Also, it is worth pondering the excellent question: If a barber shaves only those who don't shave themselves, who shaves the barber?