On the Nature of Mathematical Concepts

Verena Huber-Dyson, Edge, Jul 19, 2016
Commentary by Stephen Downes

I studied under Verena Huber-Dyson when I was in Calgary and was opened to a world where we question assumptions, consider alternative (but complete and consistent) forms of formalization, and a range of reasons why we ought to question our core 'truths' about mathematics and logic. "This century has seen the development of a powerful tool, that of formalization, in commerce and daily life as well as in the sciences and mathematics. But we must not forget that it is only a tool. An indiscriminate demand for fool proof rules and dogmatic adherence to universal policies must lead to impasses," she writes in this article from 1998. "Think of mathematics as a jungle in which we are trying to find our way. We scramble up trees for lookouts, we jump from one branch to another guided by a good sense of what to expect until we are ready to span tight ropes (proofs) between out posts (axioms) chosen judiciously. And when we stop to ask what guides us so remarkably well, the most convincing answer is that the whole jungle is of our own collective making - in the sense of being a selection out of a primeval soup of possibilities. Monkeys are making of their habitat something quite different from what a pedestrian experiences as a jungle."

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