VUB-professor Ann Dooms in De Tijd

Numerous mathematical prize winners wrote a series of recommendations this week for AI companies that want to use mathematics as a benchmark. Naturally, there is significant commotion in the field, and some outsiders have already loudly asked whether we will still need mathematicians in the future. However, history offers perspective, as it is also a history of the increasing outsourcing of mathematical labor to technology. As early as the 15th century, Leonardo da Vinci dreamed of a device that would assist him with time-consuming calculations. A century later, that dream became a reality. Blaise Pascal commercialized the mechanical calculator, which mathematicians subsequently used to perform gigantic calculations with precision for land surveying, astronomy, and navigation. In the 19th century, Charles Babbage and Ada Lovelace made that work more efficient by expanding the machine with the ability to combine operations. A hundred years later, Alan Turing proved that one could even build a machine capable of performing any combination of calculations that a human could perform by hand with much time. Consequently, human computers—mostly women—became the first programmers of the electronic computer, allowing them to apply their mathematical knowledge to devise such algorithms for the machine. Due to the acceleration of calculations, the sky was literally the limit. This is how we got humans into space and back again. In that same period, Turing thought about how one could build a machine that could "devise" such an algorithm itself to solve a given problem. That marked the beginning of AI.

New professions

Each time, new technology led to a shift in tasks and thus changed the professions for mathematicians, but it also repeatedly created new ones. At the same time, technological progress also led to new fields in mathematics, such as numerical aspects, data science, and the actual development of AI. It is precisely this progress that now also allows the machine to search for proofs itself. To assess the impact of this, we must look at what "doing mathematics" actually means. And that is much more than proving theorems. It is developing the language with which we solve problems. Often, the right "words" and their "grammar"—that is, the rules and relationships—still need to be invented. When the Swiss mathematician Leonhard Euler studied the problem of the seven bridges of Königsberg, where notables wanted to take a walk that crossed each of the city's seven bridges exactly once, he saw that distances, angles, and the precise shape of the city were irrelevant. Only which pieces of land were connected by which bridges mattered. He therefore created a new mathematical structure that provided the necessary abstraction. Thus, graph theory was born, which we now use in all sorts of networks and also in AI. New appropriate concepts only become powerful and more widely applicable when we further develop their theory. Proving what is true is, however, often a time-consuming part, which can now also be accelerated with AI. The magic lies in making logical connections within the enormous corpus of knowledge. Analyzing the rapidly growing output will certainly become a new field in mathematics, but the machine is once again becoming the perfect companion for the trained mathematician. This time, it is also to explore his mathematical imagination much faster. In recent decades, we rightly encouraged interdisciplinary work, but the translation process can sometimes be difficult. Now that AI can also bring together knowledge from different fields, the mathematician of tomorrow will more than ever be the connector who can tirelessly question the AI agents to better understand and abstract the problem. In this way, they can decide which questions should be asked to the machine to seek connections and unleash their learned imagination to develop what might be missing, from theory to its application. This is the perfect moment to become a mathematician. The world needs you.