Carl Friedrich Gauss :
Gauss was one of those remarkable infant prodigies whose natural aptitude for mathematics soon becomes apparent. As a child of three, according to a well-authenticated story, he corrected an error in his father's payroll calculations. His arithmetical powers so overwhelmed his schoolmasters that, by the time Gauss was 10 years old, they admitted that there was nothing more they could teach the boy. It is said that in his first arithmetic class Gauss astonished his teacher by instantly solving what was intended to be a "busy work" problem: Find the sum of all the numbers from 1 to 100. The young Gauss later confessed to having recognized the pattern
1+100=101, 2+99=101, 3+98=101, ..., 50+51=101.
Since there are 50 pairs of numbers, each of which adds up to 101, the sum of all the numbers must be 50 × 101 = 5050. This technique provides another way of deriving the formula
1 + 2 + 3 + ... + n = (n(n+1))/2
for the sum of the first n positive integers. One need only display the consecutive integers 1 through n in two rows as follows:
1 2 3 ... n-1 n n n-1 n-2 ... 2 1Addition of the vertical columns produces n terms, each of which is equal to n+1; when these terms are added, we get the value n(n+1). Because the same sum is obtained on adding the two rows horizontally, what occurs is the formula n(n+1) = 2(1 + 2 + 3 + ... + n).
Fascinating isn't it ? -_-
note: today in math class we were discussing Gauss and Mr. Parro explained to us that true geniuses don't need to be taught. They are revolutionaries, they see the World in their own way. For example, one of Mozart's pupils (age 17) begged Mozart to teach him how to write a fugue. Mozart refused. The student asked why he didn't want to teach him if Mozart wrote his first fugue at age 6. Mozart replied "Yes, but i didn't need to be taught"