How a 1935 concept of a universal machine paved the way for modern AI

Science · Published 22 October 2026 Swipe more like this →

In short: Long before modern neural networks, the foundations of artificial intelligence were being laid through abstract logic and mathematical models. From the concept of a machine that can modify its own instructions to the complex linear algebra driving today's algorithms, discover the mathematical origins of intelligence.

Tracing its origins to the 1930s, the foundations of AI lie in the research of Alan Mathison Turing, a British logician. Turing's 1935 paper introduced a theoretical computer featuring infinite storage and a mechanism for scanning symbols. This 'universal Turing machine' featured a stored-program concept where instructions were stored as symbols, implying that a machine could potentially operate on and improve its own programming. This abstract model utilized a scanner that moved back and forth through the memory to read and write symbols.

While Turing served as a leading cryptanalyst at Bletchley Park during World War II, he spent considerable time contemplating machine intelligence. In a 1947 London lecture, he publicly proposed the need for machines that could learn from experience, suggesting that the ability to alter one's own instructions provided the necessary mechanism for such learning. By 1948, he had introduced several central AI concepts in his report, 'Intelligent Machinery,' which included the idea of training networks of artificial neurons. His colleague Donald Michie noted that Turing frequently explored how machines might use guiding principles for heuristic problem solving. This vision of machines learning from experience was a central theme of his early work.

Today, the technical execution of these early visions relies on a sophisticated mathematical framework. Modern machine learning and recommendation systems, such as those used by Netflix, utilize complex operations like matrix multiplication, eigenvalues, and eigenvectors. These elements of linear algebra, alongside calculus-based processes like derivatives and integration, allow digital computers to perform tasks like reasoning, generalizing, and learning from past experiences—the very hallmarks of intelligence Turing envisioned. Beyond these operations, the field also relies on Markov Chain models and the calculation of determinants and inverses. These mathematical tools are essential for the collaborative filtering used in modern recommendation systems.

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