Lecture, Central London, Wednesday, 19 Oct 2022 - 16:00
Ideas About Proof in Mathematics
Joint lectures with the British Society for the History of Mathematics.
This event will focus upon mathematical proofs. The main speaker, Professor Agathe Keller (6pm) will look at decolonisation of the history of proofs, providing examples outside of what has been called a “colonial library”, using, in particular, Sanskrit sources. This will be preceded by shorter presentations by Dr Richard Oosterhoff (4pm) on "The Invention of Mathematical Proof in the Renaissance", and Dr Fenner Tanswell (4.45pm) on "How Mathematical Proofs Are Like Recipes".
The Invention of Mathematical Proof in the Renaissance Dr Richard Oosterhoff
In practice, mathematicians have been 'proving' their results in many ways, in many places, for thousands of years. In principle, however, what is a proof? Usually, we look to geometry, specifically the geometry of Euclid. But what are the fundamental building blocks of a Euclidean proof? Until quite recently, the Renaissance, this question remained open—due to uncertainties about who Euclid was, the structure of his arguments, and even the layout of his pages. This lecture looks at how the language and practices that we now associate with Euclid hardened into our dominant idea of proof in the 1570s.
How Mathematical Proofs Are Like Recipes Dr Fenner Tanswell
This talk considers mathematical proofs through an analogy to cooking recipes: that proofs give recipes for mathematical actions to be carried out by the reader. We will see linguistic evidence that written proofs often include explicit instructions in the imperative mood, just like recipes. This will lead to philosophical insights about mathematical diagrams, reading and writing proofs, and why maths is like the Great British Bake Off.
Let’s Decolonise the History of Mathematical Proofs! Professor Agathe Keller
What is a “valid mathematical proof”? To inquire into such a hotly debated question we might want to look at how past mathematicians tackled this question. This lecture will provide examples outside of what has been called a “colonial library”, using in particular Sanskrit sources, to argue that mathematical texts from all over the world contained not only proofs but also many other types of mathematical reasoning whose stories still need to be documented.
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