I argue that the construction of representation theorems is a powerful tool for creating novel objects and theories in mathematics, as the construction of a new representation introduces new pieces of information in a very specific way that enables a solution for a problem and a proof of a new theorem. In more detail, I show how the work behind the proof of a representation theorem transforms a mathematical problem in a way that makes it tractable and introduces information into it that it did not contain at the beginning of the process.
A role for representation theorems / Ippoliti, Emiliano. - In: PHILOSOPHIA MATHEMATICA. - ISSN 0031-8019. - ELETTRONICO. - 3:26(2018), pp. 396-412. [10.1093/philmat/nky007]
A role for representation theorems
Ippoliti, Emiliano
2018
Abstract
I argue that the construction of representation theorems is a powerful tool for creating novel objects and theories in mathematics, as the construction of a new representation introduces new pieces of information in a very specific way that enables a solution for a problem and a proof of a new theorem. In more detail, I show how the work behind the proof of a representation theorem transforms a mathematical problem in a way that makes it tractable and introduces information into it that it did not contain at the beginning of the process.| File | Dimensione | Formato | |
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