Stéphane Mallat: a pioneer in applied mathematics

The Real-World Mathematician: Stéphane Mallat and the Power of Applied Mathematics. Imagine mathematics not as a distant, abstract world, but as a living discipline intimately connected with the messiness and creativity of reality itself. This is the philosophy embodied by Stéphane Mallat, a celebrated mathematician and the 2025 recipient of France's most prestigious scientific distinction. Mallat's journey is a testament to the dynamic interplay between abstract thought and tangible application, showing how mathematics can not only describe the world but actively shape it. Mallat's career began with a fascination for the structures underlying images and signals. Early on, he found inspiration in the theory of wavelets—a mathematical tool that revolutionized how we process, compress, and interpret digital information. Whereas classical methods like Fourier analysis excelled at representing steady, repeating patterns, wavelets were designed to capture fleeting, transient phenomena—those tiny, important bursts of information that our senses instinctively notice, like a sudden silence in a noisy restaurant or the sharp attack of a piano key. This breakthrough led to transformative advances in fields as varied as image compression, where wavelet-based algorithms became the foundation for formats able to store vast quantities of visual information with remarkable efficiency, and medical signal analysis, where subtle changes in an ECG can be detected and interpreted. The beauty of the wavelet approach lies in its universality: once abstracted, these mathematical ideas find echoes in seemingly unrelated domains, from geophysical exploration to quantum mechanics. Mallat's work is also a story of bridges—between pure and applied mathematics, between academia and industry, and between the worlds of engineering and scientific research. He speaks candidly about the different rhythms of these domains: the researcher's long, patient pursuit of insight versus the engineer's race against time to solve immediate problems. Yet in both, creativity, teamwork, and the willingness to pursue a naive, world-changing idea are indispensable. In recent years, Mallat has turned his attention to the explosive growth of artificial intelligence. He has witnessed firsthand the shift from logic-based AI to machine learning and deep learning—the era of neural networks able to learn, generalize, and tackle problems once thought intractable. The underlying questions remain deeply mathematical: How do these vast networks manage to extract meaning from oceans of data? What hidden structures do they exploit to achieve results that often surprise even their creators? And, perhaps most tantalizingly, can we ever truly open the “black box” and understand the mathematical essence of their intelligence? Mallat is also passionate about education. He sees the current crisis in mathematics teaching as a call to reconnect the subject with reality, to help students see math not as an abstract hurdle, but as a toolkit for understanding and transforming the world. Through innovative programs, he advocates for problem-based learning rooted in real data and real decisions—whether it's distinguishing authorship of a classic text or making life-and-death calls based on medical signals. The aim is to spark intuition, engagement, and a sense of relevance, empowering students and teachers alike to rediscover the living heart of mathematics. Stéphane Mallat's story is a powerful reminder: the greatest mathematical breakthroughs often emerge from the fertile ground where theory and application meet, where curiosity about the world is matched by the rigor of abstraction, and where the quest to understand reality leads, again and again, to new realms of possibility.