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Computation, Proof, Machine by Marion Roman, Pierre Guillot, Gilles Dowek

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Chapter Two Two Thousand Years of Computation

ONCE THE AXIOMATIC METHOD had been adopted, reasoning was often spoken of as the one and only tool available for solving mathematical problems. In the discourse they developed about their science, mathematicians hardly ever mentioned computation. This doesn’t mean that computing vanished from the practice of mathematics, however. Mathematicians would regularly put forward new algorithms to systematically solve certain types of problems. It seems that the history of mathematics has a bright side – that of conjectures, theorems, and proofs – and a hidden one – that of algorithms.

This chapter will focus on three important points in this history, each set in a different time period, and each raising ...

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