The Child Prodigy-Gauss
Carl Friedrich Gauss
Gauss, Carl Friedrich (1777-1855), was a great German mathematician. Gauss was born in Brunswick. He attended the University of Gottingen. His ideas had enormous influence in nearly all areas of mathematics. Gauss proved the fundamental theorem of algebra, which states that certain algebraic equations called polynomial equations have at least one root. He also helped bring about the acceptance of imaginary numbers (the square roots of negative numbers). He became a professor at the University of Gottingen and director of the Gottingen Observatory. Gauss contributed to the mathematical theory of electromagnetism. His contributions to astronomy included calculating the orbit of Ceres, the first asteroid discovered.
The Story Behind the Discovery
The year was 1787. Ten year old Carl Friedrich Gauss was enrolled at a primary school in Germany. At times, his attention in class wandered and his teacher, Master Buttner did not think he was very bright. Master Buttner was a good teacher for history and Latin but he did not like to teach mathematics. He spent little time on the subject and had students do tedious problems. On one occasion, the teacher asked the students to do the following problem " Add the whole numbers from 1 to 100".
Carl sat at his desk with his hands on his chin, thinking about the problem. Master Buttner saw him and thought Car was daydreaming. He shouted," Get busy, Carl Gauss." Carl looked up and said, " I already have the answer, Master." When young Carl told the master this, he went up to the chalkboard and showed the dumbfounded teacher how he arrived to the answer...
The Solution
He first wrote the the imagine shown below and said " Each pair totaled 101, and I figured there were 50 of these 101s. So I multiplied 101×50 and got 5050 for the sum of all real numbers from 1 to 100.
The professor was already a little lost, but Gauss went on to note that the same approach could be used to calculate the sum of the first n whole numbers. Here is the equation:
