A fresh approach

Reimagine democracy. Reimagine capitalism. Reimagine education. For all the reimagining thrown at big ideas, they don’t seem much perturbed. You can reimagine a problem too, but it probably won’t be fruitful. It won’t help you find the end of the Sellotape, or balance the books (unless you worked for Enron).
 
But some problems really are amenable to a fresh perspective. According to legend, the mathematician Carl Friedrich Gauss was tasked at primary school with adding up the numbers from 1 to 100. The obvious approach is (to quote the King of Hearts from Alice in Wonderland) ‘Begin at the beginning, and go on till you come to the end: then stop.’ Gauss saw the problem in a different light. He spotted that the numbers split into 50 neat pairs: 1 + 100, 2 + 99, 3 + 98, which each add up to 101. There are 50 such pairs, so the problem shrinks dramatically.