I often tell my students that mathematicians are motivated to do the things they do out of laziness. To avoid writing long and complicated expressions, we invent all sorts of notational devices as a sort of shorthand – a shorthand that must then be taught to others who may want to learn a little about the mathematics we develop. It is a type of code or language and if others want to communicate with us as mathematicians, I explain, then they must first learn and be comfortable with our symbols.

But mathematics encompasses more than just manipulation of symbols (apologies to all you abstract algebraists and number theorists out there – I have utmost respect for your symbolic machinations!). To me it is about establishing a world view that is concise and precise – and so the laziness comes from not so much a lack of energy or a desire to avoid hard work as from a perspective that says “Let’s try to get this done with as little effort as possible.”

So, a goal in this blog is to show you a little about how we do that – the secrets and apparent tricks we employ to make our work easier. Unlike the magician who wants to keep his tricks to himself, I want to show you the tricks and help you to avoid the traps. I will be sharing the things I find that give my students trouble with the hope that you can learn how to avoid those troubles – minimizing the effort you must expend by showing you how to avoid those blind alleys and false directions you may have traveled down before. But always remember, an occasional trip down the wrong path often leads to a surprising discovery – we’ll take that trip together and it won’t be so scary!