By: Nathan Geng
For thousands of years, mathematicians have embraced advancements in human technology. But are they prepared for the introduction of artificial intelligence (AI)?
In a Los Angeles Museum, a portrait of Euclid from the 17th century serves as a reminder of his enduring influence. Euclid's writings have been the foundation of mathematical argumentation and reasoning for over 2000 years. Jeremy Avigad, a logician at Carnegie Mellon University, explains that Euclid's approach involved starting with poetic definitions and building upon them with successive steps, clearly following from prior notions, definitions, and theorems.
However, by the 20th century, mathematicians moved away from solving equations in a formal, geometric manner. Instead, they turned to computers for assistance. In 1976, the computer became the first tool to prove the 4-color theorem, which states that four colors are sufficient to fill a map without adjacent regions sharing the same color.
Today, mathematicians are embracing yet another tool: artificial intelligence. In 2019, Christian Szegedy, a computer scientist who previously worked at Google and now runs a startup in the Bay Area, predicted that AI would surpass the intellectual capabilities of the smartest human mathematicians within a decade. He later revised his prediction to 2026.
While Akshay Venkatesh, a mathematician at Princeton and a recipient of the Fields Medal, may not be personally interested in AI, he recognizes its potential impact. He wants his students to understand that the field of mathematics will undergo significant changes. Venkatesh emphasizes the importance of mindful and deliberate use of technology to support human understanding.
There are various risks associated with AI for humanity. For instance, many jobs may become redundant as AI bots can perform tasks that were previously done by humans. However, on the positive side, AI can tackle complex problems that surpass human capabilities. It is predicted that bots will eventually surpass humans and become the most intelligent entities on Earth.
The intersection of mathematics and artificial intelligence presents both exciting possibilities and potential challenges, shaping the future of mathematical exploration and discovery.