The problem that Mercator was trying to solve and the solution he came up with is super interesting to me. Very neat.

It is still not known for sure how he came up with mathematical details of the stretching and spacing of the latitudes.

The actual closed form was discovered much later and that too by sheer accident - by looking at log trig tables and noticing they match the Mercator scaling numerically, upto four places of decimals, not by working out the integral from first principles. Once the connection has been made it was formally derived of course.

100 years to solve an integral The history of the Mercator map and the integral of the secant https://liorsinai.github.io/mathematics/2020/08/27/secant-me...

https://news.ycombinator.com/item?id=24304311

https://news.ycombinator.com/item?id=43741273

Also, many find it very unintuitive that even in the absence of waves, winds, currents or such disturbances, you will have to constantly steer to follow constant bearing paths (North-South and equatorial East-West excluded). You have to steer even if you want to follow a latitude East-West, barring the Equator.

Its not that you can set your heading South by Southwest and be done with it, even if there are no disturbances.