The subtle feeling that an email might not be human-penned is a modern conundrum. Mathematicians, however, have been grappling with analogous sentiments for the past half-century, a journey offering valuable insights applicable to broader challenges.
This intellectual reckoning began in 1976. Kenneth Appel and Wolfgang Haken presented their proof of the four-colour theorem. This theorem posits that any map can be colored using no more than four distinct shades, ensuring no adjacent regions share the same color. The theorem’s conceptual elegance led mathematicians to anticipate a similarly sophisticated and insightful proof. Instead, they were presented with approximately 60,000 lines of computer code, largely incomprehensible to human readers. Appel and Haken had achieved their solution by employing a computer to systematically examine nearly 2,000 distinct map configurations, thereby covering all potential scenarios.
Initially, this approach felt unsatisfactory to many. Yet, over the subsequent decades, the mathematical community gradually adapted to the integration of code in this manner, addressing and resolving numerous philosophical objections. This prior acclimatization proved instrumental when the current surge of artificial intelligence emerged, finding mathematics already prepared for its implications.
As reported, the pace of AI advancement is rapid, genuinely surprising many practitioners in the field. While Appel and Haken manually developed their code, contemporary large language models can now perform similar tasks. Furthermore, other software is available to verify the code’s correctness, and by extension, the validity of the proof. This preemptive existence of verification systems mitigates the risk of AI “hallucinations”—scenarios where artificial intelligence fabricates information—because robust mechanisms are already in place to distinguish accurate outputs from erroneous ones.
The landscape outside of pure mathematics, however, is considerably less straightforward. The technology press frequently highlights instances of AI-generated code failure, with outcomes ranging in severity. Concurrently, a recent projection from the US research firm Gartner suggests that within a year, half of all companies that replaced human roles with AI will re-employ individuals for those same positions.
Undeniably, the world at large does not operate under the same principles as mathematics. Nevertheless, mathematicians have underscored AI’s potential utility, contingent on achieving both practical confidence and philosophical acceptance of its outputs. It is plausible that it may take some time for broader society to reach this same understanding.