Visualize a global map segmented by national borders. How many distinct colors are required to shade each country without overlapping the same hues?

The solution is four. Regardless of the map’s structure, four colors are always adequate. However, demonstrating this required delving deep into mathematical theory. The four-color theorem was the inaugural major theorem proved with computer assistance, with validation efforts starting in 1976 that involved analyzing numerous map configurations via software.

At that time, many mathematicians were skeptical. They questioned whether a crucial proof, reliant on an unidentified machine, could be trusted. This skepticism has led to computer-assisted proofs remaining a niche practice.

However, a shift may be underway. The newest wave of artificial intelligence is challenging this stance, as proponents argue, “AI might revolutionize mathematical methodologies.” Why should we trust flawed human reasoning, which is often riddled with assumptions and shortcuts?

Not all share this perspective, however. The debate regarding AI’s application in mathematics mirrors broader challenges confronting society. When is it appropriate to let machines take the lead? Tech companies are increasingly focused on alleviating tedious tasks, from invoice processing to scheduling. Yet, our attempts to navigate daily life relying solely on AI agents (as detailed in “Flashes of Glow and Frustration: Running my day on an AI agent”) revealed that these systems are not entirely ready.

Entrusting sensitive information, such as credit card details or passwords, to an enigmatic AI provokes similar apprehensions as the doubts surrounding the four-color proofs. We may not be coloring maps anymore, but we’re striving to define boundaries in uncharted territories. Will we soon have reliable evidence we can trust from machines, or is it merely a digital version of “the Dragon Here”?