AI poses a potential challenge to human intelligence. We train AI models by having computers mimic human behavior, much like a baby learning, and this training successfully demonstrates aspects of human intelligence. However, we as humans still hesitate to acknowledge that AI’s intelligence is comparable to human intelligence. Among the professions strongly opposed to the idea that AI will replace humans, mathematicians stand out as particularly skeptical. Are we just like dinosaurs, stubbornly refusing to accept our obsolescence?
Why is this unlikely? We need a reason. People’s beliefs are starting to waver, and more individuals are beginning to think that AI will eventually replace all of our work. Why is this improbable? Humans require explanations. To discuss the reasoning from mathematicians, we must introduce Hilbert and Gödel.
“We will know, and we must know,” Hilbert famously declared. As a mathematician, his dream was to create a world of axiomatic systems. He believed that all mathematical statements could be derived from a set of basic axioms. In this world, every statement would be either true or false, and there would exist a machine capable of determining the truth value of any statement. This was Hilbert’s program—an ambitious attempt to create a perfectly logical world. However, it’s important to note that this concept is not Gödel’s first incompleteness theorem; rather, Gödel’s work would later challenge Hilbert’s vision.
Those who believe that AI will replace humans are those who still cling to Hilbert’s ideal world—a world already dismantled by Gödel. Gödel’s first incompleteness theorem states that for any consistent formal system complex enough to encode arithmetic, there must exist statements that can neither be proved true nor false within that system. Even more striking, Gödel’s second incompleteness theorem demonstrates that such a system cannot prove its own consistency, implying that some statements within it could be either true or false.
This remarkable result once again rescues humanity from being merely a replacement for machines. In philosophical terms, a perfect world doesn’t exist because of self-reference. We cannot have a barber who only cuts the hair of those who don’t cut their own hair. It doesn’t make sense to say, “What I am saying is a lie.” Self-reference is a line that separates humans and machines. While self-reference may seem nonsensical, humans can always create meaning from apparent nonsense. This creative capacity allows our mental world to flourish. Maybe it is not political correct in science, we might say that self-reference give rise to beliefs and even creates religions. These beliefs can be understood by other people and can spread. This is because of we, as humans, can comprehend and constitute of common sense.
Therefore, why do we still need to learn math? It’s because we recognize our world’s imperfections and must continue seeking truth. We have a responsibility to share the truths we discover. Moreover, we need to teach the next generation how to distinguish between common sense and statements that require proof. This is why we still need math and mathematicians.