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Clocks, pianos, and the Rubik's cube are just a few of the items on display.

Let me ask you a question: do a clock, a piano, and a Rubik's cube have anything in common? I hope this has piqued your interest! If you're anything like me, you'd probably answer no when you first started your university math degree. The solution, however, is positive and comes from abstract algebra.

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Abstract algebra is a branch of mathematics that is commonly dreaded due to the idea that it is "hard," "difficult to grasp," or, unexpectedly, "too abstract." Other prominent arguments against algebra include the assertion that mathematics is not useful in "real" life and that we never see it. As a mathematician who has struggled with abstract algebra on numerous occasions, I am not going to sit here and tell you that it is always simple. Indeed, if you dive deep enough into it, algebra is an unlimited pool of surprises and head scratches. However, I would like to refute the assertion that it never presents itself in our environment.

A "group" is the most fundamental building component in abstract algebra. The connection between the clock, the piano, and the Rubik's cube is called group theory. The elements of each form a group, and mathematically examining this structure reveals the real-world features of the things in issue. Okay, so the clock isn't very exciting from this perspective (though it will be from the standpoint that 12+1 isn't always 13, but more on that later), but how about the fact that you can't solve the Rubik's cube without employing the necessary elements from the so-called Rubik's cube group?

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