Corns are a common disorder on the foot. They are a natural reaction to pressure as the skin thickens up to protect itself from that pressure. At some stage the process breaks down and gets so thick that it's painful. You will find a consistent myth that corns have roots which they carry on growing back from when you try to remove them. This is like the analogy of plants which grow back from their roots if you cut the top of the plants off. This analogy continues to be given to corns since they carry on growing back, however they do not possess roots to grow back from.
Corns develop from pressure and a skilled podiatrist can readily get rid of a corn. However, after the corn is taken off if the pressure that caused it is still there then, obviously, it will come back. It grows back since the cause is still there rather than because the podiatrist left a root there for this to grow back from. That pressure could be from poor fitting footwear or from something like a hammer toe or bunion that leads to increased pressure on an area. When the corn is under the foot, then the cause is increased pressure on the spot where the corn is, probably because of the way you walk.
The myth continues simply because they do return, so its crucial that you eliminate the cause at the same time the corn is taken off. There is absolutely no root to be taken out. This means that the pressure over the foot the location where the corn was really needs to be reduced or removed. This may involve issues like using better fitting footwear or the use of padding to get pressure off the location where the corn is. Occasionally surgery will be necessary to the bone beneath the corn to remove the pressure. If that cause is not taken away or reduced then the corn will come back, so it is easy to understand where the myth regarding corn roots derives from.