Bruno Latour is well-known for having applied semiotic and post-structuralist thought to the study of the natural sciences – typically a blind spot in the generalised critique of institutions of thought that characterised the 60s and 70s in French philosophical thought. Indeed Latour himself regarded this complaisaance towards the hard sciences as a defect in Foucault’s project. Yet even Latour has seemed to have nothing to say about that most demonstrative and apodictic of all the sciences – mathematics. Here it would seem that all the Latourian insistence on what may be called the heuristics of scientific research, on what he calls « science in the making », is incapable of including mathematics in any informative way within its purview.
No doubt, it may be argued, Latour can do his usual actor-network dance and show that mathematicians are embedded in heterogeneous assemblages that are imbricated in more extensive rhizomatic connections, themselves dependent on or even constituted by the diverse institutions that train, recruit, publicise, provide subsistence and empowerment for the various mathematical actors that influence each other on these networks. But nowhere is it more obvious that this sort of account is totally external and anecdotic in relation to what is really going on than in the case of mathematics.
Yet Latour argues this acknowledgement of the role of networks is already a concession that must lead us to the fundamental abandonment of the traditional Platonic vision of mathematics. There are no objects that make sense, or even exist, outside networks. In other words, there are no transcendental objects, and mathematics is no exception.A further consequence is that a mathematician, like any other natural or humanistic scienctist, is confronted by inscriptions and traces that he attempts to organise and to interpret in terms of entities or agencies subjected to the specific sort of trials involved in the discipline’s constant back and forth movement between performances and competences.
Thus, according to Latour the mathematician like any other scientist/humanities scholar practices hermeneutics. There are no algorithmic scientists, for then discovery would be automatic. The only difference is that the mathematical domain is is one that is much more homogeneous than is the case for example in biblical exegesis (involving, archeological, historical, linguistic, scriptural, geological, and climatic elements).
An interesting precursor of Latour’s argument can be found in Imre Lakatos’s PROOFS AND REFUTATIONS, which shows the constant dialectical reconfiguration of concepts in mathematics, and thus of the sense of mathematical theorems over time. This shows that the « universality » of mathematical truths is often only a literal façade. Latour argues at the end of his book SCIENCE IN ACTION that the so-called « universality » of mathematics is rather a case of its centrality. The purification, or homogenisation, operated by formalism permits mathematics to have the most connections, the most extended networks.
Latour maintains that formalism is no sign of universality: « Formalism, formal sciences, is the sign that the distinction between performance and competence has not been made » (Latour, Contre la Culture Générale, my translation). Formalism in mathematics according to Latour would mean that the entities defined by an equation do exactly what they are. However, this is never the case, and mathematical entities are constantly capable of surprising us and requiring changes in the formalism. The testimony of mathematicians shows that they find themselves faced with entities whose behaviour is just as surprising as that of rats in a lab or chemicals in a reaction.