Podcast Challenges - "AI hasn't invented anything: behind the most spectacular models lies the comeback of mathematics and statistics"

"AI hasn't invented anything: behind the most spectacular models lies the comeback of mathematics and statistics" - Podcast

Behind AI’s spectacular feats lie decades of research in mathematics and statistics. Gérard Biau, a professor at Sorbonne University, deciphers the scientific mechanisms fueling this technological revolution in DeepTechs, the Challenges podcast produced in partnership with Mascaret.

Artificial intelligence often feels like a technology that emerged almost overnight. Yet, behind the most spectacular models lie ancient scientific foundations, rooted particularly in statistics. This is the reminder shared by mathematician Gérard Biau, a professor at Sorbonne University, member of the Academy of Sciences, and machine learning specialist. To him, the current AI revolution is built, above all, on one simple idea: learning from data.

"The general principle of machine learning is to build a function capable of linking input information to a result," he explains. For instance, associating an image with its content—a face, an animal, an object—or predicting the next word in a sentence. These functions often take the form of neural networks: mathematical models made up of additions, multiplications, and non-linear transformations. Their unique feature is having a massive number of parameters, sometimes in the billions, which the algorithm must adjust to best fit the observed data.

This adjustment occurs during a training phase. The machine is presented with vast amounts of examples: medical images, texts, or signals. With each new piece of data, the algorithm slightly corrects its parameters to reduce errors. After millions of iterations, the model becomes capable of producing reliable predictions or classifications. 'Once the parameters are adjusted, the system can be used for inference—meaning, applying what it has learned to new cases,' summarizes Gérard Biau.

Behind this mechanics lies a direct kinship with classical statistics. Historically, statisticians were already seeking to estimate unknown parameters from data. During an election night, for instance, polling institutes attempt to evaluate a limited number of parameters: the share of votes obtained by each candidate. The logic of AI models is ultimately just an extension of this principle. 'The difference is the scale: instead of one or two parameters, we are now manipulating millions or billions of them,' the researcher points out.

To support these transformations, Sorbonne University established a center dedicated to artificial intelligence in 2019: the Sorbonne Center for Artificial Intelligence (SCAI), headed by Gérard Biau. The goal is not to create yet another laboratory, but to foster collaboration across disciplines. 'AI is inherently interdisciplinary,' he insists. Doctors, physicists, chemists, and mathematicians work together there, notably to set up research projects and secure national or European funding. In 2024, the center was officially designated an 'IA cluster' (AI cluster), a French government initiative designed to structure the national AI ecosystem.

France is striving to carve out a place for itself in the global competition dominated primarily by the United States and China. According to Gérard Biau, the country's main asset remains its scientific education. 'France trains excellent mathematicians and computer scientists,' he reminds us. International rankings consistently place the country around fifth or sixth in the world for AI—a respectable standing, yet one that demands constant investment.

Beyond the technological race, the researcher believes Europe can also play a balancing role. Indeed, AI raises numerous questions: environmental impact, social uses, and ethical challenges. 'These technologies involve our future as a society,' he points out. In this industrial revolution built on data and computing power, mathematics continues to provide a compass: one of scientific rigor and an understanding of the models already transforming both the economy and research.