AI and Symbolic Memory
When discussing AI and its ability to solve complex mathematical problems, it's tempting to think that it has become smarter than humans. However, this notion often stems from a misunderstanding of what truly empowers AI: its ability to access a virtually limitless external symbolic memory.
Human Working Memory
Working memory is the mental system that allows us to hold and manipulate information over short periods. In mathematics, this means remembering what each variable represents, which operations have been performed, and what the end goal is. However, human working memory capacity is remarkably limited. According to Cowan (2001), human working memory can hold about 4 to 7 items at once.
AI and Its Advantages
Unlike humans, an AI system can keep hundreds of intermediate equations, abandoned approaches, definitions, constraints, and previous conclusions inside its context window. This doesn't necessarily reflect superior reasoning but rather the removal of one of the greatest limitations of human cognition: limited working memory capacity.
Use Cases and Recent Examples
Consider DeepMind's AI, AlphaFold, which has revolutionized the field of biology by predicting protein structures with unprecedented accuracy. Although not directly related to mathematics, it perfectly illustrates how AI uses vast memory capacity to process complex data and generate solutions that humans would struggle to conceive alone.
Implications for Mathematicians
Mathematicians aren't threatened by obsolescence due to AI, but are instead encouraged to collaborate with it. By using AI as a powerful tool to handle vast amounts of data and complex calculations, mathematicians can focus on innovation and creativity, areas where humans excel.
Conclusion
Ultimately, AI doesn't replace human intelligence but complements it by removing certain cognitive limitations. As mathematics continues to evolve, the collaboration between AI and mathematicians could pave the way for discoveries yet unimaginable.
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