# The Heterogeneity of Mathematical Research

Chapter

## Abstract

The core thesis of this contribution is that, if we wish to construct formal-logical models of mathematical practices, taking into account the maximum of detail, then it is a wise strategy to see mathematics as a heterogeneous entity. This thesis is supported by two case studies: the first one concerns a mathematical puzzle, the second one concerns Diophantine equations and belongs to mathematics proper. The advantage of the former is that the connection with logical modeling is pretty clear whereas the latter mainly demonstrates the difficulties one will have to overcome. A link is made with Hintikka’s method of analysis and synthesis.

## Keywords

Heterogeneity in mathematics Logical modeling Analysis and synthesis Explanation## References

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