This thesis aspires to establish a new research direction in STS. In the first chapter a literature review is conducted and the research questions are being formulated. The second chapter is devoted to presenting research findings from the archaeological, biological and brain sciences in a unified form. The various stone tool technologies are analysed, and a brief introduction follows into human evolution and the effects that artefacts had on it; then recent neurobiological research on the deeper relationships between consciousness, artefacts and the brain is presented. In the third chapter, after an introduction in the deeper neurological relationships between language and gestures, a gestural analysis of mathematical speech follows, based on visual data generated from an interview with a working mathematician; the last section examines recent research on gesture and mathematics as special cases of Roman Ingarden’s aesthetic theory. In the fourth chapter, four approaches to the social history of mathematics in the USSR are presented, based on data generated from interviews with former professional Soviet mathematicians. Following a Maussian approach, the Soviet mathematical community is presented as a gift economy of scientific articles. Then, in line with a Marxian approach, the Soviet university mathematical school is presented as a factory with its own mode of self-production. In the following section, based on a Parsonian systemic approach, the Soviet mathematical community is presented as a banking system, with the scientific journals as the banking institutions. In the next section of the fourth chapter, following a Weberian approach, the mathematical community in the USSR is presented as a social estate, as separate and distinct from other Soviet social estates. The final section integrates the previous approaches and presents the Soviet mathematics research community as a modern version of an ancient city-state. In the fifth chapter Hilbert spaces are briefly presented, as an example of the fictional universe of modern mathematics, along with some conjectured differences between Soviet and Western mathematics research. In the final chapter, the conclusions of this research project are summarised, and this thesis is presented as an instance of a proposed revised version of David Bloor’s Strong Programme.

Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. Here we investigate their so-called nodal domains, i.e. the connected components of the maximal induced subgraphs of G on which an eigenvector ψ does not change sign. An analogue of Courant's nodal domain theorem provides upper bounds on the number of nodal domains depending on the location of ψ in the spectrum. This bound, however, is not sharp in general. In this contribution we consider the problem of computing minimal and maximal numbers of nodal domains for a particular graph. The class of Boolean Hypercubes is discussed in detail. We find that, despite the simplicity of this graph class, for which complete spectral information is available, the computations are still non-trivial. Nevertheless, we obtained some new results and a number of conjectures.