Let me say it again a little more emphatically: Maths is NOT Science. The major difference I want to focus on here is the concept of truth. Things are true in Maths, but they are not in Science.

Let me explain. As far as I can tell, Science is about coming up with models that explain how things work which match closely to what we observe and allow us to make accurate predictions for what might happen next. No model is technically ever “true”, it simply does a super good job at making predictions and matching our observations. There is always the possibility that someone might come up with a better model in the future.

This is why a very accurate idea accepted by all scientists is only called a “theory”, rather than a “truth”. The word theory doesn’t diminish the decades or even centuries of work that has gone into it or diminish the great job it does of matching the universe we see. It just highlights the fact that the aim of science is to come up with ideas that work, not necessarily ideas that are “true”.

The “laws” you learn at school are in fact descriptions of observation, which is why they are true — the only things that are true in Science are the actual observations we make ourselves (and even then these are subject to some error).

(Any scientist reading this, feel free to slap me for simplifying it all too much!)

On the other hand, Maths is all about truth. A mathematician tries to find out what is true and what is not true, given a set of starting rules (and some of them try to work backwards to find a set of starting rules that will MAKE things true). And once something in Maths is proven true or false, then it always was true or false and it always will be true or false. The sum of the proper divisors of 6 will always be 6, the number pi will always be irrational with no repeating pattern to its digits, an angle of 30 degrees will always be impossible to trisect with only a ruler and compass, and two ovoids in a finite projective space of even order who share all of their tangents will always meet in an odd number of points. No-one is going to come up with a new idea in the future that changes the truth of these things.

Of course, people may come up with new types of numbers or new types of geometries, or new sets of starting rules. They may decide that there is a better way of writing the maths notation, or that something else is better for solving problems in the “real world”. But that still won’t change the truth of all the maths before it. If you start with the same set of rules you will always get the same results. That’s what maths is about.

So, don’t try to find a repeating pattern to the digits of pi or prove that it is in fact possible to trisect any angle! Because Maths is NOT Science — things in Maths are true forever.