I am an engineering student and I can say that a helmet is a smart choice.
In a crash your head flying through the air has a certain momentum, and according to classical mechanics the only way to change that momentum is by an "impulse". Without using calculus
Impulse is defined as force X time. Your total impulse will always be the same (going from moving with a high momentum, to not moving or a low momentum [because you crashed]). What you can do to help yourself is make the time side of the impulse bigger, and accordingly the force your head takes will be smaller. Big time X little force equals little time X big force in terms of impulse, but not in terms of the integrity of your scull. Its the same idea as a seatbelt of air bag, as the foam on your helmet compresses, time is eaten up (big time) and the force your scull feels is dampened (little force)!
On a personal note I was riding back to my house from a fast food restaurant with some friends many years ago ( I was in 7th grade!) and plowed in to the side of a car that had rolled through a stop sign. I flew off the bike and smashed the guys windshield, with my forehead. I can say that my helmet probably saved my life or some severe head trauma in that instance just from the sharp glass!