The Creativity Code: Art and Innovation in the Age of AI

by Marcus du Sautoy

In the 1970s, for example, a computer played a major role in settling the proof of the Four-Color Theorem, which had gone unsolved for over a century. This problem theorized that, if you wanted to illustrate a map—perhaps of Europe but really of any region actual or fictional—so that no two countries that shared a border were shown in the same color, you would need no more than four colors in total. Some maps could be executed in just three colors, but in no case would a fifth color be required. Already, the proof had been constructed for the claim that five colors would suffice, but before 1976 no one had yet been able to reduce this to four. That year, two mathematicians, Kenneth Appel and Wolfgang Haken, succeeded in doing so, after adding an interesting twist to their approach. They first established that, although there are infinitely many possible maps you can draw, there is a way to show that they can all be reduced to an analysis of 1,936 maps. But analyzing even this many maps by hand was going to be impossible—or, to be more accurate, impossible for a human. Appel and Haken managed to program a computer to go through the list of maps and check whether each one passed the four-color test. It took over a thousand hours for their lumbering computer of the 1970s to run through all the maps.