Relationships and mathematics: the case of San Vittore

Polimi's Methexis project integrates mathematics, storytelling and generative spaces for extremely fragile contexts

In 2023, the Polisocial Awards contest (to find out what it is about, see here) identified and selected five research projects to be funded with the 5x1000 Irpef donations, thanks to all the Alumni who decided to allocate them to Politecnico di Milano.

The researchers started in November and will work for 15 months to frame situations of gap and need in certain neighbourhoods of the city of Milan. At Politecnico, the 5x1000 contributions are usually invested in projects which can be implemented in the short term while aiming to be replicable and have an effect in the long term; they are generally case studies that concretise solutions studied in larger projects and allow students and researchers to put into practice what they have learnt. They are:



Mathematical models are the starting point to create a map of nodes describing the links and interactions in a group of people. The METHEXIS project focus on a case study in this field, analysing the young-adult section of the San Vittore prison, which is an unstable reality that is uninterruptedly changing due to the rapid turnover of people and volunteering associations. The researchers aim to develop a descriptive map-model of the relationships in place, to help shaping the planning and participation policies addressed to San Vittore’s people by introducing forms of sociability and peer support. 

The figure shows a first pilot example of a network composed of 49 prisoners and keeps track of their participation in the proposed activities, so that researchers get to know who is in contact with whom and can reconstruct the link (connections) between the nodes (people) of the mathematical model. In this way, a mathematical object (graph) is constructed the properties of which can be studied. If interpreted in the light of the real situation, they give information about the social network between the people considered. The colours (shifting from red to blue as the number of ties increases) indicate the number of social relationships of each individual, while the size of the knot indicates the strength of the ties established by the individual. Interesting are the cases of prisoners who have few but all very strong relationships and, conversely, the cases of prisoners who have many but all superficial relationships. The 'number of social relationships' and the 'strength of ties' are examples of the way mathematical indicators can be interpreted in this specific context.

A second activity is the collection of qualitative data through Storylab. Quantitative and qualitative data will feed into the map-model of relationships to provide information on the reciprocal link between sociality and well-being. This work is the result of 'research through design', an interdisciplinary methodology that is an evolution of the use of experimental scientific method in social contexts. This method is common to the three research areas within the METHEXIS project: Engineering, Design and Architecture.


StoryLab is a permanent participatory storytelling laboratory by Imagis Lab, a research group of the Design Department of Politecnico di Milano. It explores the imagination of prisoners, provides expressive tools and collects stories on San Vittore’s microcosm, with the dual aim of understanding this complex reality and communicating it to the outside world. In May 2023, the woman researchers in Design from Politecnico di Milano involved in Off Campus San Vittore started their activities in the Youth Adult Ward. Each weekly meeting records by about 15 participants. They take the floor and recount their life experiences, helped by the stimulus provided by images that form an iconographic repertoire from which to draw to activate the senses, memory and imagination. The images are accompanied by questions, grouped according to the different significant areas of the narrative world that is constructed and shared at each meeting: one introduces and tells about him/herself, his/her relationships and places, past and my present, values and desires. Within the framework of the METHEXIS project, Storylab allows for the collection of qualitative data on the profile of inmates in the ward, the ways they are involved in activities and the current and possible uses the ward spaces.

At the end of the project (end of 2024-beginning of 2025), an exhibition curated by Imagis Lab and Knitlab (Department of Design) will translate the mathematical model of the San Vittore system, elaborated on the basis of the collected data, into the languages of visual and multimedia representation and knitting stitches (partner: Gomitolo Rosa).

Another action already planned is the Mathematical Workshop, which will be offered in three editions of six meetings each. The focus will be on problem-solving and will involve working in small groups to encourage everyone's involvement and collaboration to solve a common problem together. The workshop will involve 2 mathematicians and about 12 participants. It is expected to start at the end of May 2024.