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My column at The Aperiodical is Travels in a Mathematical World. See all my posts at The Aperiodical.

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## The unplanned impact of mathematics: surprising examples of unexpected applications

British Mathematical Colloquium 2013, History of Mathematics workshop, University of Sheffield (27/03/2013).

Time and again, mathematics displays an astonishing quality. A piece of pure mathematics is developed (or discovered) by a mathematician who is, often, following his or her curiosity without a plan for meeting some identified need or application. Or a piece of applied mathematics is taken into the abstract, beyond any hope of relevance to its original context. Later, perhaps decades or centuries later, this mathematics fits perfectly into some need or application. This is unplanned impact: impact which was not - and could not have been - planned when the original work took place. As funding bodies ask researchers to predict the impact of their research before it is funded, and research quality is measured partly by its short term impact, the need to communicate this aspect of mathematics is vital. However, mathematicians often name one of three well-known examples: number theory in cryptography, logic in computing and complex numbers in fluid mechanics. How convinced might a lay person be that the phenomenon is more widespread if they keep hearing the same few examples? This talk will present a set of (hopefully) more surprising examples from history and give an update on a project to collect and share more.