Always Easy When You Can Do It

The response “it’s always easy when you can do it” is often said in jest, but is very applicable to Mathematics.

There is a very real case to be made for Mathematics being the biggest, oldest and most far-reaching academic study in existence. We begin to study Mathematics in the form of counting almost before we can speak, and even continuing to study it for a lifetime can barely begin to scratch the surface of all the branches of the subject.

When we start school, we have a very limited idea of what Mathematics is. I have a very clear memory of being 7 years old and being convinced that once I had fully mastered division, I would have ‘finished’ Mathematics. Little did I know that I would be learning and teaching the subject 44 years later! As we learn more, new avenues of Mathematics open up in front of us. The famous German Mathematician, David Hilbert wrote that (a branch of Mathematics) is “a paradise from which we shall never be expelled”.

In the following sections you will look at how the questions posed by Mathematics change as we learn more. The questions range from those suitable for Primary School students to the end of an undergraduate Mathematics course. Please not you are not expected to do the questions (though do feel free to have a go!) – just look at the way the subject changes and opens out into new areas…