To be brief, the reason I ask this question is that I was recently selected to become an Aviator in the U.S. Army. Aviators are required to have a more advanced knowledge of math (specifically algebra & trigonometry) compared to other branches of officers. It made me wonder how that could compare, given the similar navigational requirements of both air and sea.
Additionally, after reading books such as the Horatio Hornblower series, I recall situations in which Captain Hornblower would calculate the displacement of forces along a sail, among other calculations. Having a degree in Physics, I am confident that Hornblower would have needed some knowledge of Integral Calculus to solve that example. He would have been quite the math prodigy to have learned Calculus before becoming a Midshipman at the age of seventeen.
Were Royal Naval officers really required to have that high level of math, or was that just another example of historical fiction/inaccuracy?
I wrote about this before:
To summarize: officers would need to know at least trigonometry to be able to navigate and calculate their position on the globe, which usually implies a knowledge of algebra as well. That need for at least a few years of math led to midshipmen increasingly being required to spend time ashore learning maths, or be tutored onboard.
Also, Hornblower wouldn’t have become a mid at 17 — 11 or so is more likely, and 15 was considered quite too old.