What is Mathematics?

A couple of weeks ago I was asked to help out with the upcoming induction week for our mathematics undergraduate students. I am given one hour to give 70 students some idea of what they have come to study. After thinking about the question, “What is mathematics?”, I have found the following four-fold answer.

Mathematics helps us to…

  • … find precise answers to precise questions.
  • … find approximate answers to vague questions.
  • … interpret answers that seem precise but are not.
  • … figure out the right questions to ask.

Below I have tried to develop these points and to supplement them with examples. The text below is addressed at first year students of mathematics at Brunel University.

Continue reading “What is Mathematics?”