Most of you have probably heard the song New Math by singer-songwriter-mathematician Tom Lehrer. The song explains how to do “new math”, and uses subtraction in base-10 as its first example. This is how I learned to do subtraction in elementary school. Lehrer then moves on to a more abstracted way to do subtraction: base-8. Before singing the calculation, he humorously comments, “Base eight is just like base ten really – if you’re missing two fingers.”

This portion of his song reminds me of Abstract Algebra because it explains how to do a fairly simple calculation (342-173) with an unfamiliar binary operation. To understand this section, I had to read the lyrics and do the calculation myself. That is when I understood the irony of this song. The calculation described is incredibly simple, but the explanation itself is difficult to follow, making the techniques of “new math” hard to understand. Below is a the video and a copy of my work (LaTeX was not cooperating).