Yves Chevallard passed away on 16 March 2026. He was 79 years old. Born in Tunis, he trained at the École normale supérieure in Paris, where he earned an agrégation de mathématiques. He went on to become a professor at Aix-Marseille Université, and it was there, over several decades, that he built one of the most ambitious research programmes in the didactics of mathematics. A 1976 encounter with Guy Brousseau at the IREM in Bordeaux defined his path.

His first major contribution was the theory of didactic transposition, developed through the 1980s and crystallised in La Transposition didactique: du savoir savant au savoir enseigné (1985). The question at its core was deceptively simple: what happens to knowledge when it moves from the research context where it was created into the classroom where it is taught? The answer, Chevallard argued, was that it is transformed far more deeply than anyone usually admits. From that insight, he went on to develop the Anthropological Theory of the Didactic (ATD), a framework that pushed the study of teaching and learning into the territory of culture, institutions, and the social life of knowledge. The International Commission on Mathematical Instruction awarded him the Hans Freudenthal Medal for that work in 2009.

His connection with the CRM was long. He first came in January 1991 for a research stay, returned in December 1994 for a seminar alongside Miguel de Guzmán, Guy Brousseau, and Paolo Boero, and went on to participate in the 3rd International Congress on the ATD (January 2010), an Intensive Research Programme (June–July 2019), and the 7th and 8th CITAD (June 2022 and January 2026). The last of those was held here just two months ago.

He left behind a body of work that asks hard questions about what school mathematics is actually for. In a 2017 article for the Gaceta de la RSME, he argued that mathematics is taught as a treasure to be visited, not used, and that most students sense, correctly, that it was never really meant for them. He spent his life trying to fix that.

Our deepest condolences go to his family, his colleagues, and the community of researchers who carried his work forward alongside him.

Somewhere in the eastern Pyrenees, a mountain guide has six clients behind her, and the weather is turning. It was fine two hours ago, which counts for nothing now. Low cloud, wet snow on the ridge. She needs to decide whether to keep going or turn back, and soon, because the group is getting cold and one of them keeps asking about the summit. She trained for this kind of moment. But she is also running on less oxygen than she would at sea level, and her brain, the organ actually making the call, is doing something with risk assessment that neuroscience can describe in broad strokes but not yet predict. Whatever process leads to her decision will fire and resolve in milliseconds. It will leave faint electrical traces in the cortex. Nobody outside a research lab would normally think to measure those traces, and even inside a lab, they are hard to read.

NeuroMunt wants to try reading them anyway, outdoors, on the mountain.

The project, funded by the European programme POCTEFA and coordinated by the Université de Perpignan Via Domitia, brings together sports psychologists, sleep researchers, mountain rescue workers, physiologists, mathematicians and training centres from both sides of the Pyrenees. The CRM contributes a specific component to this consortium: the mathematical and computational analysis of field-recorded brain signals.

“A very concrete task the CRM has is to generate a toolkit, like a toolbox, to analyse electroencephalographic (EEG) signals,” says Axel Masó, a postdoctoral researcher at the CRM hired for the project. “Our toolkit will incorporate nonlinear systems metrics, complexity metrics, such as entropy or other concepts from complex systems and statistics.”

EEG data from a laboratory is already complex. EEG data from someone moving through a mountain environment is something else. The standard processing tools were built for controlled settings where you can repeat an experiment if the recording is poor, the subject holds still, and the room is quiet. None of that applies here. You get one shot at each recording, the subject is climbing or skiing, and the electrodes pick up every twitch and gust of wind. The team has learned this the hard way, working with preliminary recordings, and it has shaped the entire approach: before you can analyse anything, you must figure out which parts of the signal are worth analysing at all.

The Mathematical and Computational Biology Group, co-led by researcher Josep Sardanyés, works on this kind of problem in biological systems. “Understanding how the brain works is extraordinarily complicated,” Sardanyés says. “We are probably talking about one of the most complex of complex systems, with processes operating at different scales: the single neuron, groups of neurons, brain regions, the whole brain.” EEG captures macroscopic cortical activity, the large-scale electrical behaviour of the brain. The CRM’s job is to develop the mathematics to read that signal properly.

In concrete terms, the team is building software to quantify the complexity of EEG recordings and compare them across different situations. Entropy measures, autocorrelation, synchronisation patterns, techniques for characterising chaos: the tools come from dynamical systems theory and are designed to detect structure that standard clinical analysis would miss. These techniques are not commonly used in the EEG community. “Seeing how these measures behave across different scenarios could be very important for understanding large-scale brain dynamics in complex mountain environments and under risk conditions,” says Sardanyés. A central question is whether the EEG time series looks different when a person is approaching a decision. If they do, the mathematics should be able to show how.

One concept from the CRM’s approach is particularly suggestive. In fields like ecology and medicine, researchers have developed methods for detecting what are known as early warning signals: measurable changes in a time series that indicate the system is approaching a critical transition, a tipping point. The mathematical framework is well established for ecosystems on the verge of collapse or patients approaching a clinical crisis. Sardanyés and the team want to apply the same logic to brain signals recorded near a decision point. The idea is that a decision, choosing between two options under pressure, may behave mathematically like a bifurcation.

“These early warning signals can be measured directly from time series. They tell us how close the system is to a transition or bifurcation; in this case, a decision between two options.”

Josep Sardanyés, CRM

If the analogy holds, the EEG signal should show detectable changes as the moment of decision approaches. Whether it does is one of the things the project will test.

“From a fundamental perspective, the EEG signal has characteristics that are specific to complex systems,” Masó explains. “This allows them to be analysed with tools that are not standard within the community of EEG analysis experts. The CRM brings this more fundamental perspective, to know whether these tools will be the ones that allow us to determine if a person enters a state of panic before a risk.”

The toolkit is being developed now, in the early phase of the project, using preliminary data from an unexpected source. Before NeuroMunt began, the ultra-trail runner Kilian Jornet recorded EEG activity during mountain expeditions as part of his Alpine Connections project, in which he traversed the entire Alpine range and linked all peaks above 4,000 metres in 19 days without motorised transport: 1,207 kilometres and over 75,000 metres of accumulated elevation gain, by running, climbing, and cycling. During the expedition, Jornet wore EEG equipment and recorded brain activity under different conditions: at rest, while walking, and while climbing. Those recordings, collected under real conditions with all the mess that entails, have become the testing ground for the CRM’s methods. “We have to discard a large portion of the data,” Masó says. “This reduces the predictive capacity of the analysis enormously. The first result of all this is knowing where to place the magnifying glass within the data. Knowing exactly what to look at and where to look, that is already a result in itself.”

The early analysis has yielded something worth noting. “The first results suggest that we do observe differences in the complexity of the signal across different activities and different risk environments,” Sardanyés says. The team is working to consolidate these findings with additional data and with the mathematical models of decision-making from the UPC side of the collaboration. It is still preliminary, but the signal, so to speak, appears to be there.

David Romero, head of the Knowledge Transfer Unit at the CRM, frames the challenge differently. For him, the work sits at the far end of a long chain of translations. And the chain runs in both directions. “We will be doing pen-and-paper things, so to speak, to solve a real problem that exists in the social environment of the mountain.”

The CRM’s closest collaborators on the project are at the Universitat Politècnica de Catalunya BarcelonaTech (UPC). Professors Toni Guillamon and Tomás Lázaro, both also affiliated researchers at the CRM, will build mathematical models of decision-making, drawing on dynamical systems theory from computational neuroscience and game theory. The CRM team, for its part, analyses the raw signals. Romero describes how the pieces connect: “We will be talking a lot with the UPC to feed their models with data, to calibrate them or to support certain decisions. But at the same time, there is another layer of interaction with the people in France, who will give more psychological meaning to the metrics we extract.”

In practice, Lázaro and Guillamon have been analysing data from elite trail runners and paragliders, athletes whose decisions under pressure are already being closely monitored. There are, Lázaro explains, two kinds of decision-makers: the econs, who are perfectly rational and always optimise, and the humans, who are not and do not. The mountain is where that distinction stops being theoretical.

“There is a scientific vision of a behaviour that is very human. And that is a challenge in itself.”

Tomás Lázaro, UPC / CRM

A mountain science festival in Les Angles, in the French Pyrenees, will present partial and final results to the public, and an international scientific congress is also planned. Romero sees these as the other end of the chain. “The goal is also to give tools to mountain trainers,” he says, “and that completes the whole round trip in this problem, impacting something that is very far from basic research but hyper-applied and very specific to the natural environment.”

“It is a project that covers very broad knowledge,” explains Guillamon, talking about the internal workings of the consortium, “and it is impossible for us as mathematicians to find a direct common point with mountain guides right away. But the project has enough specialists in all areas so that there is a continuity of knowledge.” He credits Élodie Varraine, the coordinator from Perpignan, with assembling the team that way. Sardanyés puts it in more operational terms: the project has elite athletes, mountain guides, sleep experts and neuroscientists who will collect the field data and help interpret what it means. “This is a project where multidisciplinarity is key,” he says, “and one that can produce results of real scientific and applied interest.” The mathematicians cannot do the fieldwork, and the mountain professionals cannot build the analytical tools. The project only works because both sides are in the room.

It helps that everyone involved lives close by. “All the partners are very close,” emphasises Masó. “Despite being a European project with a European perspective, it also has this local component that makes interaction with partners much easier.”

The field experiments designed specifically for NeuroMunt haven’t started yet. The protocols are still being written. Whether the early patterns in the Jornet data hold up when tested against larger, more controlled datasets, nobody knows. Romero comes back to the same phrase: “We have to know where to put the magnifying glass.” And that magnifying glass is, at bottom, mathematical. Projects like NeuroMunt need people who know the mountains, and people who know the brain, but they also need people who can look at a noisy time series and find the geometry hiding inside it.