Carl Friedrich Gauss was a German mathematician in the 18th century, sometimes referred to as the “Prince of Mathematicians” and the “greatest mathematician since antiquity”. He has had a remarkable influence in many fields of mathematics and science and is ranked as one of history’s most influential mathematicians.
Gauss was a child prodigy. There are many anecdotes concerning his precocity as a child, and he made his first ground-breaking mathematical discoveries while still a teenager. At just three years old, he corrected an error in his father payroll calculations, and he was looking after his father’s accounts on a regular basis by the age of 5.
Legend has it that when Gauss was 7 years old, his school teacher gave his class, as an exercise , the assignment to calculate thinking that it would take the students several minutes to calculate. The teacher was quite surprised when young Gauss came up with the answer almost immediately! Gauss even at age 7 recognized that there was a quick way to add consecutive integers.
This is how he did it:
Then he wrote the sum in reverse which should also add to S.
He noted when you add the two sums you get 101, 100 times