Mathematician Hugo Duminil-Copin, who received the prestigious Fields Medal in 2022, and Emmanuel Sander, a professor of educational sciences at the University of Geneva, have published a book titled De l'autre côté du tableau noir (Seuil). The book explores the intersection of mathematics and cognitive psychology, discussing how mathematical thinking is a deeply human activity rooted in intuition, analogies, and trial and error. The authors argue that this perspective remains relevant even as artificial intelligence becomes capable of solving complex mathematical problems. Sander compares the role of AI in mathematics to that of robots reaching previously unreachable peaks—while impressive, such achievements do not add much to the expertise of human climbers. The authors emphasize the need to revalue the human science dimension of mathematics, focusing on the analysis of abstract concepts, their understanding, and transmission. They caution against the idea of "all logic," which would reduce mathematics to simple theoretical demonstrations. While AI may transform mathematical practices and replace humans in certain tasks, the authors stress that solving problems is not solely about demonstrating theorems. Instead, it involves a broader understanding of the concepts involved. The book originated from the authors' independent discussions, where Sander recognized in Duminil-Copin's work as a mathematician the same psychological mechanisms he studies in children. They explored the universality of learning skills by applying cognitive psychology tools to Duminil-Copin's mathematical experience. One of the dimensions of this parallel is the role of analogies, such as using the known to give meaning to the unknown. For example, the sign "=" may initially represent a result for children, making it difficult for them to understand equations where equality is an equivalence rather than a result. The book also emphasizes the role of intuition in mathematics, noting that it is closely tied to the feeling of understanding. However, when mathematical situations challenge intuition, it creates a cognitive dissonance that drives development. For instance, division challenges intuition when the result is larger than the original number, such as 2 divided by 0.25 yielding 8. Duminil-Copin rejects the myth of the "mathematical bump," acknowledging that while some people may be more at ease with mathematics, the field is multidimensional, and great mathematicians excel for various reasons. The book suggests that the idea of a single trait making someone good at mathematics is an illusion. Regarding mathematics education, the authors argue that students need to be trained to challenge their intuitions. Knowing how to perform calculations is insufficient without understanding when to apply them. School textbooks often reinforce initial intuitions, but they should also present situations that challenge them, allowing students to learn to reason differently. One of the book's highlights is the account of Duminil-Copin's discovery that earned him the Fields Medal. After years of working on "self-avoiding paths," he turned to the percolation problem, which studies how water passes through coffee. During a swim in Fréjus, the solution emerged in a flash, revealing that the tool developed for the percolation problem could solve the self-avoiding paths issue. Duminil-Copin confirms that this moment was real, emphasizing the importance of preparation and a period of disengagement from the problem for the solution to emerge. The authors give little space to the formalization of proofs, noting that while writing a proof can contain surprises, these are minor compared to the understanding of the problem itself. In the case of the Nienhuis conjecture, the formalization took about an hour, despite years of research.