Defining good and bad

Bad science is easy to spot: poorly-controlled experiments, bias or mistakes in interpretation, selective use of data to support a pre-determined viewpoint, and so on. We can look for bad science wherever there is very strong and specific self-interest.

Bad science is a big problem but it is usually exposed – eventually.

Good science is harder to define. Think about mathematical research rather than experimental science. We can agree what bad mathematics is – at least at an elementary level. It is incorrect mathematics.

But what is good mathematics? Or rather, what mathematics is really good? What is high quality maths?