Have you ever received an email and had a sneaking suspicion it was written by AI, rather than lovingly handcrafted? Mathematicians have been wrestling with similar feelings for half a century, and have some lessons for the rest of us.
It all began in 1976, when Kenneth Appel and Wolfgang Haken announced a proof of the four colour theorem, which states it takes a maximum of four shades to colour any map so that no two adjacent regions match. The theorem’s simplicity meant mathematicians were expecting an elegant proof revealing a greater mathematical truth. Instead, they got 60,000 lines of impenetrable computer code. Appel and Haken had solved the problem by programming a machine to systematically go through nearly 2000 kinds of map, representing every possible configuration.
At the time, it felt unsatisfactory. But over the decades, mathematicians came to terms with using code in this way and resolved many of the philosophical objections. This meant when the current AI wave arrived, mathematics was ready.
As we report here, AI is improving at such a rapid lick, it is taking many mathematicians by surprise. While Appel and Haken hand-wrote their code, we now have large language models doing the job, while other software can check it (and therefore the proof) is correct. This means there are no problems with hallucinations – where AIs simply make stuff up – because there are already systems in place to sift the good from the bad.
“ AI is improving at such a rapid lick, it is taking many mathematicians by surprise “
Outside of mathematics, things aren’t so straightforward. The tech press is awash with examples of AI-coding gone wrong, with varying levels of disaster. Meanwhile, US research firm Gartner recently predicted that half of firms that replaced jobs with AI will rehire people to do the same roles within the year.
The world isn’t mathematics, of course, but mathematicians have demonstrated that AI has its place if we can be both practically confident and philosophically comfortable with its output. It may take a while for everyone else to catch up.