Pure Mathematics Simple population modelling problems lead almost inevitably to the conclusion that the Earth will be impossibly overcrowded by the end of the 21st century. Compound interest is a good illustration of exponential growth, but can lead to a discussion of the economics and morality of interest in general. The Pythagoreans who first discovered that the square root of 2 is irrational were sworn to secrecy, because the discovery cast doubt on their fundamental religious beliefs. The introduction of calculus and the Newton-Leibniz controversy can be used as the basis of a discussion on scientific ethics in general. Those who apply for patents on human genes certainly seem to think so.
Similar calculations can lead to a discussion of acceptable levels of risk.
Many people are afraid of eating beef because of the risk of BSE, but the BSE death rate is much lower than the road accident death rate. The prosecution must adduce evidence against this hypothesis, sufficient to prove the defendant's guilt beyond reasonable doubt. A couple of our students over the past few years have considered as an exam project a survey of the extent of drug abuse among their fellow students. Ethical problems can arise in other areas. The mathematics of projectiles was developed almost entirely for its use in directing artillery, and various questions arise from this.