In my high school library, there was a copy of the classic book “Men of Mathematics” by E.T. Bell. Each chapter is a short biography of a notable mathematician of the past (and yes, they are all men). In the chapter on Carl Friedrich Gauss (1777-1855), I first encountered the famous story of how, as a 10 year old student, Gauss baffled his teacher by instantly solving a problem that the teacher assumed would occupy his student’s an hour or more.

In this post, I will describe Gauss’ insight, then show how a related problem can be solved by using some informed guesswork.

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Most people who have studied some physics or chemistry know that it is important to keep the units of our numbers straight when we do calculations. Failure to attend to units usually leads to wrong answers.
What is not well known is that the analysis of units can often help scientists to derive formulas, even when the underlying physics is not well understood. How it works seems a bit mysterious, and the technique was not understood or appreciated until about 1870, when the great physicist James Clerk Maxwell laid out the principles of the technique, which is formally known as Dimensional Analysis.

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