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This text is addressed to mathematicians who are interested in generalizedfunctions and unbounded operators on a Hilbert space. We expose in detail (in a"formal way" - as done by Heisenberg and Pauli - i.e. without mathematicaldefinitions and then, of course, without mathematical rigour) theHeisenberg-Pauli calculations on the simplest model close to physics. Theproblem for mathematicians is to give a mathematical sense to thesecalculations, which is possible without any knowledge in physics, since theymimick exactly usual calculations on infinitely differentiable functions and onbounded operators, and can be considered at a purely mathematical level,ignoring physics in a first step. The mathematical tools to be used arenonlinear generalized functions, unbounded operators on a Hilbert space andcomputer calculations.

Mathematical problems on generalized functions and the canonical Hamiltonian formalism