Abstract
Mathematics is set apart from the other sciences by the notion of a proof — an argument for the truth of a hypothesis so convincing that all who understand it are satisfied. However, aspects other than theorem proving have always been held in high regard in mathematics. In particular, an ability to invent new concepts and to find interesting and relevant conjectures are essential tools for mathematicians. In a letter1to Eratosthenes, Archimedes wrote:
... [F]or example, we must give Democritus, who was the first to state the theorems that the cone is a third of the cylinder and the pyramid of the prism, but who did not prove them, as much credit as we give to Eudoxus, who was the first to prove them.
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© 2002 Springer-Verlag London
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Colton, S. (2002). Conclusions. In: Automated Theory Formation in Pure Mathematics. Distinguished Dissertations. Springer, London. https://doi.org/10.1007/978-1-4471-0147-5_15
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DOI: https://doi.org/10.1007/978-1-4471-0147-5_15
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