In fact Gauss is who discovered this expression. There is a famous story about how Gauss discovered it:
In primary school his teacher, J.G. Büttner, tried to occupy pupils by making them add up the integers from 1 to 100. The young Gauss produced the correct answer within seconds by a flash of mathematical insight, to the astonishment of his teacher and his assistant Martin Bartels. Gauss had realized that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050
I think that’s only a story, nothing more. Like others stories that said that Einstein was terrible in math at school.
If you don’t understand the definition in the previous quotation, here is the mathematical proof:
I think the image is pretty clear, brilliant indeed!