Should I believe my computer?
Richard A. Earl · 2023
Abstract Scientists use mathematics in much of their work, but the theories of an ideal mathematical world cannot immediately be brought to bear on the real one. A sense of reality can only be achieved via experimentation, but how does a scientist move from a collection of experimental data to wholly defined functions? A likely further problem is that—once posed—a real-world problem won’t have an exact answer. How do scientists and mathematicians gain approximate answers? These are topics within ‘numerical analysis’, the theme of ‘Should I believe my computer?’ This question highlights that an algorithm may find an approximate answer by running for thousands of steps; given the problems of rounding errors, how much should we believe a computer’s answer?