Dear Editor,

In October 2024, John Hopfield and Geoffrey Hinton joined the esteemed Nobel laureates by winning the Nobel Prize in Physics.

Their ground-breaking contributions to the development of artificial intelligence (AI) are not only a testament to their brilliance, but also a celebration of the deep connection between mathematics, physics and AI.

This win highlights the urgent need for countries like Jamaica to strengthen their foundations in mathematics and physics if they aim to contribute significantly to the ever-expanding world of AI.

Hopfield and Hinton are titans of AI. Hopfield, an American physicist at Princeton University, laid the foundation for the neural networks that underlie artificial intelligence with his model of associative memory, which could store and reconstruct patterns in data. His 1982 work became the cornerstone on which future AI developments would be built.

Geoffrey Hinton, often called the godfather of AI, advanced this field by introducing backpropagation, an essential technique for training deep learning models to learn from errors and improve over time. Together, they revolutionized the way machines learn, opening the door to applications like facial recognition and language translation.

What is remarkable about these men is that their work, now celebrated globally, was not always so highly regarded. In fact, for decades both Hopfield and Hinton were seen as eccentric visionaries, working in an obscure field that few thought had any practical value.

In the early 1980s, when neural networks were still in their infancy, they were met with skepticism. Hinton, who won the Turing Award, recounted how many in the scientific community thought their efforts were “nonsense” and a waste of time. However, their persistence paid off, and today AI is at the forefront of technological advancement.

But what lies beneath these AI breakthroughs is a sophisticated interplay between mathematics and physics. Neural networks, the backbone of AI, are modeled after neurons in the human brain. This concept has its roots in physics, where the idea of ​​interconnected nodes – similar to neurons – comes from dynamical systems theories and energy minimization.

Hopfield’s early work on associative memory, for example, was based on the physical principles of energy minimization, where patterns could be stored and remembered by moving the system to its lowest energy state. The math behind these ideas is just as essential, as complex algorithms govern the behavior of neural networks, helping them recognize patterns, learn from data, and make predictions.

At the heart of Hinton’s backpropagation algorithm is calculus—a mathematical tool that allows the AI ​​system to adjust its internal parameters by calculating gradients and minimizing errors. This iterative process is similar to how students learn from their mistakes, constantly refining their answers until they arrive at the correct solution. Without this mathematical foundation, it would be impossible to teach machines how to “think” or “learn.”

Thus, the development of AI is intrinsically linked to both mathematics and physics. The neural networks, algorithms and systems that power AI applications – ChatGPT from OpenAI or ClaudeAI from Anthropic—are not built by simple trial and error. Instead, they are the product of years of research in mathematics, physics and computer science. Tools like Python, TensorFlowand PyTorchwhile necessary for coding these applications, it would be insufficient without a deep understanding of the underlying mathematics and physics.

Horatio the Stag

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