Ask HN: What is an algorithm design job like?

So I've had some rough times since dealing with some recent company events and was looking out toward a new type of job that deals with pure algorithm design (image processing in this case). I'm a bit worried that I won't be prepared mentally for the right mindset of this kind of job since right now I'm just used to mindlessly making reports and addressing tickets and the like.

What does a job like this entail? Of course I've been reviewing all my algorithm books and basic maths (concrete mathematics, linear algebra, diff Eq, etc.) so I'm not worried of that stuff, but I'm curious: can anyone that does this sort of work elaborate on what your typical day-to-day is like?

Thanks!