I believe the blackboard is an essential tool for mathematics. Usually, to solve (or find) a problem, you have to make many incorrect guesses or other mistakes first. Writing on a blackboard is easily edited, which is useful in the process of shaping one’s own thoughts in the process of solving a problem. On paper, even pencil is more difficult to erase, so there is some underlying pressure not to waste space with ideas perceived to be bad — but these “bad” ideas might actually turn out to be very important, or at least inspire progress. Because writing on a blackboard is temporary, it is very easy to put an idea up and see what happens next.
from Do Not Erase: Mathematicians and Their Chalkboards by Wynne, Jessica.