Spherical cows and bipedal goats: Perspectives on mathematical models in biology

Spherical cows and bipedal goats: perspectives on mathematical models in biology

13 - 14 November 2025

Amphithéâtre jean Jaurès, 29 rue d’Ulm, École Normale Supérieure, Paris

ORGANIZATION: Ruãn Batista, Maël Montévil, Anton Robert

The National Research Council of the National Academies (USA) published a report in 2009 arguing for "a New Biology for the XXIst century", based on the integration "through the unifying languages of mathematics, modeling, and computational science". This perspective is well represented and illustrated in CNRS by the committee labeled "Mathematical modeling, informatics, and physics for the life sciences" (Modélisation mathématique, informatique et physique pour les sciences du vivant.).

However, long-lasting problems in the relationship between mathematics are not addressed by this strategy. They are illustrated by the famous joke whereby a farmer asks for help from the university. After some time, the chief of the interdisciplinary committee comes to him and declares: We have found an exact solution to your problem, but it only holds for spherical cows in the vacuum. The issue here is not just one of approximation or idealization; it is also that cows, according to evolutionary theory, have a history and continue to evolve, and this historicity defines the cows we observe today. Notably, the plasticity of living beings collides with the invariance of underlying mathematical structures. For example, in the context of the emerging field of evo-devo, West-Eberhardt discussed the dramatic changes displayed in a goat with paralysis of its forelegs. This paralysis and its subsequent activities led to a major restructuring of bones, muscles, and tendons, resulting in a bipedal goat that became a banner for the magnitude and theoretical significance of developmental plasticity.

This event aims to take a step back and reflect on everyday mathematical modeling. We aim to organize a discussion on the diversity of this practice in biology and the homologies in current models. We wish to center those discussions around two related problems. First, given that the general reference system of biology builds on a notion of novelty to classify living beings, how can we use mathematical structures (using predefined spaces of possibilities) to describe living beings while avoiding contradiction? Is it reasonable that many of these practices do not even consider the organization of the organisms? Second, if models can be considered as instruments that contribute to shaping scientific reasoning, is their inscription within broader theoretical frameworks (not) necessary? Are data-based approaches sufficient to understand the living, or should theoretical and methodological jumps be performed? Is the perspective of the National Research Council sound when it states that “not all New Biologists are now, or will in the future be, biologists”? How to take mathematics and modelling seriously and, at the same time, avoid the disruption of biological knowledge by the fetishization of those tools?

PROGRAM

NOVEMBER 13

• 9h30 Introduction

SESSION 1 : Measuring what? Models and the general reference system of biology

(Chair: Maël Montévil)

• 09h45 Ruãn Batista (Federal University of Bahia, Brazil)

  Hennigian metaphysics and the general reference system of biology

• 10h25 Valentin Rineau (Centre de Recherche en Paléontologie, MNHN – CNRS – Sorbonne Université)

  Phylogenetics and classifications: another perspective on change and evolution.

• 11h05 Coffee Break

• 11h20 Ignacio Quintero (Institut de Biologie de l’École Normale Supérieure (IBENS), ENS)

  Environmental controls on evolutionary dynamics using interdependent models

• 12h00 Round table

• 12h45 Lunch break (12h45-14h30)

SESSION 2 : The tension between historicity and mathematics

(Chair: Giuseppe Longo)

• 14h30 Aleksandra Walczak (Laboratoire de physique de l'ENS)

  Randomness and organization of immune repertoires

• 15:10 Guillaume Achaz (Collège de France, MNHN, U.P.-Cité)

  What process(es) explain(s) (genetic) diversity?

• 15h50 Coffee Break

• 16h20 Katja Heuer and Roberto Toro (Institut Pasteur, Unité de Neuroanatomie Appliquée et Théorique)

  Role of mechanical morphogenesis in the development and evolution of the brain

• 17:00 Maël Montévil (Centre Cavaillès, RdS, CNRS - ENS)

  Biology lies between historical and relational frameworks

• 17:40 Round table

• 19:00 Cocktail party

NOVEMBER 14

SESSION 3: Data, models, and theory

(Chair: Anton Robert)

• 10:00 Paul Villoutreix (Aix-Marseille Université, MMG, Inserm U1251, Turing Centre for Living systems)

  From high-dimensional measurements to the manifold hypothesis: how we are trying to make sense of very large datasets in biology

• 10:40 Barbara Bravi (Department of Mathematics, Imperial College London)

  Machine learning representation manipulability and its relevance to scientific modelling

• 11:20 Coffee break

• 11:35 Cyril Rauch (University of Nottingham)

  Find the mistake : From the genotype-phenotype cartography to the phenotype-genotype cartography

• 12:15 Round table

• 12:50 Lunch

• 12h50 Lunch break (12h50-14h30)

SESSION 4: The challenge of theory-based model in biology

(Chair: Ruãn Batista)

• 14:30 Giuseppe Longo (Centre Cavaillès, RdS, CNRS - ENS)

  The “primary motor” of morphogenesis: heterogenetic cell reproduction

• 15:10 Anton Robert (Centre Cavaillès, RdS, ENS)

  How can mathematical models possibly be useful in biology?

• 15:50 Coffee break

• 16:20 Charbel El-Hani (Institute of Biology, Federal University of Bahia, Brazil)

  A pragmatist, radically naturalista view on modeling

• 17:00 Ana Soto (Tufts University School of Medicine)

  Modeling mammary gland morphogenesis from first principles

• 17:40 Round table

• 18:30 Synthesis