I is for Inverse Problems - the Oxford Mathematics Alphabet

All mathematical models require information to make their predictions; to get something out, you have to put something  in. To predict how an earthquake propagates through the ground, you have to know the material properties of the subsurface rocks. To predict the weather at noon, you have to give the initial conditions at dawn. To predict the drag coefficient of an aircraft, you have to specify its shape.

In many cases, however, we are faced with the opposite problem: given information about the outcome of a physical process, how did it come about? Such a problem is called an inverse problem, in contrast to the forward problems given above, for it inverts the relationship between cause and effect encoded in the underlying equations. Find out more in the latest in our Oxford Mathematics Alphabet.