AI is already our best ally to solve the mathematical problems that seem impossible

The applications of the artificial intelligence (AI) are presumably unlimited. Beyond the daily uses with which many of us are already familiar with the design of drugs, Disease diagnosisthe OPTIMIZATION OF INDUSTRIAL PROCESSES or the Analysis of physical or chemical mechanisms complexes, among other options. It is even being used to solve mathematical problems of enormous difficulty.

In addition, algorithms that use deep neuronal networks and Automatic learning They are designed to identify complex patterns in large volumes of information, which allows them to recognize images, voice or process natural language greatly. AI has reached our lives, and it is clear that it will stay, but the most surprising thing is that it is consolidating as an extremely valuable tool in relatively exotic fields.

It is possible that AI helps us solve the mathematical problems of the millennium

In October 2024 Goal AIMeta’s artificial intelligence, managed to generalize Lyapunov’s function. The Russian mathematician Aleksander Lyapunov proposed the concept of the function that bears his name in 1892. His work is a very important tool in the study of dynamic systems, but mathematicians have since struggled to find a general method that allows identifying the functions of Lyapunov. And they have not been successful. However, goal has had it.

The strategy used by the company led by Mark Zuckerberg to solve the challenge of Lyapunov’s functions has consisted of training an AI model to recognize patterns and relationships between certain dynamic systems and its corresponding functions of Lyapunov. This is precisely what is good for AI. And it is a huge success because our mathematical knowledge will no longer be limited for intuition and human capacity. The AI ​​puts in our hands a new way of addressing complex mathematical problems, identifying patterns that a priori remain hidden for the human being.

However, in the field of mathematics AI still has to improve to help us solve the great challenges that the human being has ahead. Sergei Gukov, professor of theoretical physics and mathematics at the California Institute of Technology (Caltech), leads a team of researchers who is looking for ways to use AI to solve advanced mathematical problems that require thousands, millions, or even billions of steps. These scientists are currently working on The conjecture of Andrews-Curtisa group combinatorial theory proposed 60 years ago.

They have not yet managed to solve the main conjecture, but with the help of AI they have achieved something important: they have refuted several families of problems related to the conjecture of Andrews-Curtis and known as counterexamples that have remained open for more than 25 years. Gukov acknowledges that Current AI models have important limitations When facing very complex mathematical problems, but you hope that in the future this technology allows the human being to solve Mathematical Millennium Problems. According to this mathematician, the best asset that researchers have to face this challenge is to instruct AI by resorting to Reinforcement learning.

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More information | IEEE Spectrum

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