The applications of artificial intelligence appear to be limitless. Beyond the everyday uses many are familiar with, AI is being utilized in various fields, including pharmaceutical design, disease diagnosis, optimization of industrial processes, and analysis of complex physical and chemical mechanisms. AI is also being employed to solve highly challenging math problems.
Moreover, algorithms powered by deep neural networks and machine learning are designed to identify intricate patterns within large volumes of data. This enables them to efficiently recognize images and speech and process natural language. AI has become a significant part of people’s lives and is here to stay. Notably, it’s also emerging as a highly valuable tool in relatively specialized fields.
AI Is Good at Math
For 132 years, the world’s leading mathematicians have struggled to find a generalized Lyapunov function. This mathematical tool is used to predict the behavior of dynamic systems and determine their stability. While this definition may seem complex, it’s actually pretty straightforward. A dynamical system consists of one or more objects that can interact and evolve over time according to a set of rules.
Examples of dynamical systems include the financial market, weather patterns, and even a neutron star orbiting a black hole. Under specific conditions, the Lyapunov function can identify whether the behavior of these systems will remain stable over time or become chaotic. If a dynamic system is stable, its behavior can be predicted. However, if it’s chaotic, it becomes completely unpredictable.
Russian mathematician Aleksander Lyapunov introduced the concept of Lyapunov functions in 1892. The concept is a crucial tool in the study of dynamical systems, yet mathematicians have struggled for over a century to find a universal method for identifying these functions. So far, they haven’t succeeded. However, Meta AI, the artificial intelligence team at Meta, has made significant progress where humans have struggled.
Meta’s strategy involved training an AI model to recognize patterns and relationships between specific dynamical systems and their corresponding Lyapunov functions. This aligns perfectly with what AI excels at. Additionally, the achievement is groundbreaking because it expands our mathematical capabilities beyond human intuition and limitations. AI provides a new approach to complex mathematical problems by uncovering patterns that often remain hidden from human analysis.
In the coming years, AI is expected to achieve similar feats. In fact, artificial intelligence could potentially help with numerous mathematical problems that have been unsolved for over a century. However, it’s important to remember that AI isn’t infallible and has limitations.
In this regard, human intuition is likely to be more valuable for problems that can’t be clearly articulated for AI. Additionally, using AI to tackle challenges that might be beyond human capacity also has ethical implications.
Image | Saad Ahmad
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