as much as possible for mathematical formalization. But by the beginning of the twentieth century the certainty of logic and mathematics was no longer an unquestioned truth: it had become a research question. From paradoxes in the foundations of logic and mathematics to equations with solutions that are in a sense unknowable, certainty had begun to seem rather uncertain. By the 1930s, as mathematicians and logicians grappled with the problem of formalisation, they found themselves being forced to look beyond formal systems, and to contemplate the possibility that the solution was of a different nature than they had imagined, that the answers lay in the realm of the living, creative world — the world of uncertainty. Although they did not systematically pursue this line of thought, we believe that their intuition was essentially correct, and it serves as our starting point.

The basic reason for the failure of the formalisation programme, we contend, has to do with the inherent nature of logic and mathematics, the very quality that makes these fields so attractive as the source of certainty: their timelessness. Logic and mathematics, as formal systems, exist outside of time; hence their truths are timeless – they are eternal and 