The 'characteristic age' of a pulsar is usually considered to approximate its true age, but this assumption has led to some puzzling results, including the fact that many pulsars with small characteristic ages have no associated supernova remnants. The pulsar B1757-24 is located just outside the edge of a supernova remnant; the properties of the system indicate that the pulsar was born at the centre of the remnant with a substantial velocity, and that it has subsequently overtaken the expanding blast wave. With a characteristic age of 16,000 yr, the pulsar is expected to have a proper motion of 63-80 milliarcseconds (mas) per year. Here we report observations of the nebula surrounding the pulsar, which limit its proper motion to less than 25 mas yr(-1), implying a minimum age of 39,000 yr. A more detailed analysis argues that the true age may be as great as 170,000 yr, which is significantly larger than the characteristic age. We conclude from this result and other discrepancies associated with pulsars that characteristic ages greatly underestimate the true ages of pulsars.