Why Can a Piece of Paper Hurt More Than a Deeper Cut?
A paper cut is usually shallow, but its location and shape make it unusually difficult for the nervous system to ignore.
Paper cuts commonly occur on fingertips, where the skin contains a dense network of sensory receptors. Fingers must detect texture, pressure, temperature, and the edges of objects, so the brain devotes considerable attention to signals arriving from them. A small injury there may feel more intense than a larger injury on a less sensitive part of the body.
The edge of paper also behaves differently from a sharp blade. Under magnification, it is rough and flexible rather than perfectly smooth. It can tear through skin irregularly, leaving a narrow wound with irritated tissue along both sides. Recent physical experiments suggest that paper is most likely to cut when it falls within a particular range of thickness. Paper that is too thin bends, while material that is too thick spreads the force instead of slicing.
Because the wound is shallow, it may bleed very little. It remains exposed whenever the finger bends, touches water, encounters soap, or presses against another object. Normal hand movements repeatedly pull at the damaged skin and renew the pain.
The size of an injury and the intensity of pain do not always match. Pain is partly a warning system, and fingertips are valuable enough to receive loud warnings. The paper cut hurts because it damages a highly monitored surface that cannot easily be left alone.
Source: Why Do Paper Cuts Hurt So Much, Ohio State Health and Discovery - Competition Between Cutting and Buckling in the Paper Cut, Physical Review E

Grandidier's Baobab, picture taken near Morondava, Madagascar
Source: By Bernard Gagnon