A precise definition
Interdisciplinary mathematics refers to mathematical work that bridges traditional disciplinary boundaries: Data Science (statistics, linear algebra, optimisation), Machine Learning Theory (probability, functional analysis, optimisation), Network Science (graph theory, statistical physics), Mathematical Biology (differential equations, stochastic processes), Computational Social Science (statistics, complexity theory), and Epidemiology (ODE modelling, Bayesian inference). These fields grew because the most pressing questions of our time do not fit in traditional silos.
The problem it was invented to solve
The information revolution generated datasets of unprecedented scale — genomic, social, financial, astronomical. Answering the questions embedded in this data required combining statistical theory with algorithmic efficiency, physical intuition with probabilistic modelling, biological structure with mathematical formalism. No single traditional field had all the tools needed. The researchers who succeeded were those who borrowed freely across disciplines.
Where you find it in the world — including South Africa
These are not contrived textbook examples. Each application below is currently in use, driven by real institutions, and producing real outcomes.
ML theory: why neural networks generalise
The theoretical question of why massively overparameterised neural networks still generalise to new data (the 'double descent' phenomenon) is an open research problem combining probability theory, functional analysis, and optimisation. SA AI researchers at Standard Bank AI, Naspers, and Discovery are practitioners of this field.
Network science: social media and disease spread
The same mathematical framework — random graph theory, percolation, SIR models on networks — describes both information spread on social media and disease spread through human contact networks. The H3Africa genomics consortium used network approaches to study SA population structure.
Computational epidemiology: SACEMA, UCT, UKZN
SA's epidemic modelling capability — SACEMA at Stellenbosch, the TB-HIV modelling group at UCT, UKZN's public health modelling — draws on differential equations, Bayesian statistics, and numerical computing simultaneously. This is interdisciplinary mathematics in direct service of public health.
You've already encountered this
The phrase 'data scientist' describes someone who applies statistics, linear algebra, and computing to data problems. The mathematics underlying this role is not new — it is a synthesis of 200 years of probability, algebra, and algorithms applied to modern datasets and computing infrastructure.
Where it connects in the map of mathematics
Related topics and institutions
Interdisciplinary mathematics is the future — and it starts with the fundamentals.
The Continuum builds the mathematical foundation — statistics, algebra, functions — that every data science and ML programme at SA universities assumes. Starting early is the entire advantage.
No card required. South African curriculum. Grade 8–12.