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Daniel Reem is a mathematician whose research includes functional equations. His work on the Cauchy functional equation examines existence, regularity and stability on subsets of Euclidean spaces and tori. It also studies variants such as the Jensen functional equation and multiplicative forms of the Cauchy functional equation.^[ref] The central issue is that the algebraic identity $f(x+y)=f(x)+f(y)$ alone permits pathological solutions on the real numbers. A suitable regularity assumption forces the familiar form $f(x)=cx$, so this subject clarifies how analytic hypotheses constrain algebraic identities.

Identity source: arxiv.org/pdf/1002.3721v7