A large part of mathematical expertise is being able to see the problem at hand from different perspectives. Gauss, one of the three greatest mathematicians of the modern era, provided an excellent example of that skill.

The story is a tale from when Gauss was still at primary school. One day Gauss' teacher asked his class to add all the numbers from 1 to 100, assuming that this task would occupy them for quite a while. He was shocked when young Gauss, after a few seconds thought, wrote down the answer 5050. The teacher couldn't understand how his pupil had calculated the sum so quickly in his head, but the eight year old Gauss pointed out that the problem was actually quite simple.

He had added the numbers in pairs - the first and the last, the second and the second to last and so on, observing that 1+100=101, 2+99=101, 3+98=101, ...so the total would be 50 lots of 101, which is 5050.

Later, Gauss generalized this approach with the formula we still use today for the sum of the numbers from 1 to N, N*(N + 1) / 2.