A mathematician involves the young Carl Friedrich Gauss. When Gauss was a child, his teacher asked the class to sum all the integers from 1 to 100, expecting to keep the students busy for a while. Gauss quickly realized a clever shortcut: pairing numbers from opposite ends of the sequence (1 + 100, 2 + 99, 3 + 98, etc.), each pair summing to 101, and there were 50 such pairs. Thus, he immediately found the sum to be 5,050, astonishing his teacher with his insight and speed.