The article explores how concavity in utility functions relates to risk aversion. It finds that concavity doesn't always mean being risk averse, but rather implies a milder form of risk aversion called risk aversion for independent gambles. The researchers introduce two new concepts, uniform risk aversion and uniform risk aversion for independent gambles, to better understand concavity. They show that concavity is linked to uniform risk aversion for independent gambles, and that with certain conditions, concavity is equivalent to uniform risk aversion.