The applications of artificial intelligence (AI) are presumably limitless. Beyond the everyday uses with which many of us are already familiar, it is being used in drug designthe diagnosis of diseases, the optimization of industrial processes or the analysis of complex physical or chemical mechanisms, among other options. It is even being used to solve extremely difficult mathematical problems.
Additionally, algorithms using deep neural networks and machine learning are designed to identify complex patterns in large volumes of information, allowing them to recognize images, speech, or process natural language very effectively. AI has come into our lives, and it is evident that it is going to stay, but the most surprising thing is that it is establishing itself as an extremely valuable tool in relatively exotic fields.
AI is good at math
For 132 years the best mathematicians in the world have resisted the generalization of the Lyapunov function. This mathematical tool is used to predict the behavior of a dynamic system and determine whether or not it is stable. This definition seems complicated, but it is actually simple. A dynamic system is nothing more than one or several objects (understanding the meaning of ‘object’ in its broadest sense) with the capacity to interact and evolve over time according to a set of rules.
The financial market, the climate or a neutron star orbiting a black hole are dynamic systems. And the Lyapunov function has the ability, under certain circumstances, to identify whether the behavior of these systems as time passes will be stableor if, on the contrary, they will behave in a chaotic manner. If a dynamic system is stable it is possible to predict its behavior, but if it is chaotic it will be completely unpredictable.
Mathematicians have struggled unsuccessfully to find a general method for identifying Lyapunov functions.
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 dynamical systems, but mathematicians have struggled since then to find a general method to identify the Lyapunov functions. And they have not been successful. However, Meta AI, Meta’s artificial intelligence, has triumphed where human beings have failed for more than a century.
The strategy used by the company led by Mark Zuckerberg to solve the Lyapunov functions challenge has consisted of training an AI model to recognize patterns and relationships between certain dynamic systems and their corresponding Lyapunov functions. This is precisely what, as we have seen, AI is good at. And it is a huge success because our mathematical knowledge will no longer be limited by intuition and human ability. AI puts in our hands a new way of approaching complex mathematical problems, identifying patterns that a priori remain hidden from humans.
In all likelihood, over the next few years we will witness more AI achievements similar to the one Meta just starred in. In fact, there are many other mathematical problems posed more than a century ago in which this tool presumably has a lot to say. However, AI is not infallible. It has limitations.
In those problems, regardless of their scope, that cannot be described in an intelligible way by an AI, human intuition will probably be more valuable. And furthermore, we must not overlook the ethical implications that involves the use of this tool to solve challenges that would otherwise be beyond the reach of human beings. But this is another matter and if you want we can address the ethical consequences of AI in another article.
Image | Jeswin Thomas
rmation | Medium
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