Why do paper cuts hurt so much?

Fingertips are packed with nociceptors, the nerve endings that sense pain, far more per square centimetre than most of our skin, because fingertips are our main tool for touch. A paper cut usually falls exactly there. The cut also tends to be shallow and wide, so it does not bleed much, and bleeding is what would normally form a protective clot over a wound. With the cut left open and exposed to the air, all those nerve endings keep firing. On top of that, paper only looks smooth: under magnification its edge is jagged like a tiny saw, so it tears the skin rather than cutting cleanly, which causes more irritation. Because we keep using our hands, everyday movement reopens the cut again and again, which is why it keeps stinging for so long.