The old mathematics does not need to be our strategy
Mathematics is not up for the task of describing complex systems. Asking linear algebra oracles will not be a sustainable strategy. This does not need to be our strategy: mathematics and computer science do not advance with bigger computations, they advance with conceptual understanding. We will need as David Darymple says, a “new field of mathematics”, as novel to us as calculus was to Napier. Past century saw the rise of conceptual mathematics and theoretical computer science, the kind of mathematics that took seriously even the simplest notions and carefully developed them to tame the most complex abstractions and systems. Slowly but surely (as the rising sea, Grothendieck wrote), the development of the conceptual theory of categories has brought us to a point where we can start talking about systems mathematically, formally and compositionally.