if i remember correctly, you get 1 sketch for free every day from your tinker. you need to have all different sketches of a discovery before you can discover it.

mathematics requires 6 sketches, sketch 1 to 6, you need 1 of every 6 before you can discover it, you can trade duplicate sketches on the market. your tinker can give you the same sketch multiple times, i think i got dynamo sketch 12 ten days in a row.

if you have all the sketches plus enough resources and you still can't discover it, i'd suggest submitting a ticket to support.

i hope my answer is helpfull to you

*hugs*

 To do Banking the number of rum distlieries doesn't matter, if I remember correctly. But mathmatics and smugglings need to completed first. To be able to research a sketch the discover button needs to be Red, like in the screen below. Note the required resources are less than the screen. To show you what this looks like I had to take a screen of one of mine that isn't researched. But the same requirements apply to you.

Got it thx.    I got the wrong impression, that you could go directly to discovering Banking after upgrading a Rum Distillery to Level 10.

And isn't the objective to build a Windmill to get faster rum production?

How do I get to build the Windmill?