Although his teacher did not think so, Carl was a very bright student. At times his attention wandered, but he loved to learn and discover new ideas, especially in mathematics.
Carl's teacher, Master Büttner, was a good teacher of history and Latin, but he did not like to teach mathematics. He spent little time on the subject, and had the students do tedious problems or problems which they already understood.
He walked up to the chalk board to write the day's problem. "Students, for math work today, I want you to add the whole numbers from 1 to 100." And he wrote---"Add the whole numbers from 1 to 100."
Each student had a slate board and chalk to work on, and by tradition the first student who finished would put his slate face down on Master Büttner's table.
As each student completed the task, his slate would join the pile. All the students except Carl unenthusiastically pulled out their slates, and began adding.
Master Büttner saw him and thought Carl was daydreaming. He shouted, "Get busy, Carl Gauss." Startled, Carl looked up and said, "I already have the answer, Master Büttner."
"I did the problem in my head," replied Carl. Master Büttner got a nasty smile on his face and said, "Well then, come up to the board and show us all how you solved it, Carl."
Master Büttner thought he had trapped Carl in a lie. Carl stood up and walked slowly but confidently to the front of the room. He went to the chalk board and began to write and explain the following:
"Each pair totalled 101, and I figured there were 50 of these 101s. So I multiplied 101 × 50 and got 5050 for the sum of 1 + 2 + 3 + 4 + 5 + ... + 95 + 96 + 97 + 98 + 99 + 100."
Everyone was startled, especially Master Büttner. "The boy is right," he thought. All the students applauded, and Master Büttner had to compliment Carl on his work.