Obviously scientists are not constant in how many problems they cause, or else the answer would be either 'science could never get off the ground' (if they caused more problems than they solved) or 'they're not a net negative (since science is making progress and obviously made it off the ground). So presumably there's some sort of changing marginal returns; usually, marginal returns diminish.

What does it look like if marginal returns are positive? Well, you toss in 1 scientist and get n more units of scientific output. What does it look like if marginal returns have fallen to 0? You toss in 1 more scientist and get 0 more units of scientific output. And if marginal returns have become negative, then you toss in 1 more scientist and see -n units, or scientific output in absolute terms falls.

Currently, all the datapoints I know of like the pharmaceutical industry point to diminishing returns (eg. fall in per-capita output, but not absolute output), and not negative ones. But it's very hard to quantify scientific output...