You probably will need to be able to program. You probably should know a little about how the web works, and a little about some sort of framework, and something about storing and accessing details in a database.

But all of that is minor to actually getting something running. Anything. Even if you have an idea and validate it by running a service by hand via email. If it starts getting popular (for which read - too much work to do by hand) then you need to automate. At that point you need to be able to code something, anything that works.

Then you need to improve like crazy. Get advice, get help, get a mentor, get a co-founder, or do it yourself.

But you still won't need detailed knowledge of algorithms, calculus, discrete math, etc.

Well, yeah, or your co-founder does.

Or outsource it albeit its much more cost saving if you can do it yourself or find yourself a cofounder. (You used as general case in this sentence).