# Mathematics and Physics: Strategies of Assimilation

# Mathematics and Physics: Strategies of Assimilation

The main topic of this chapter is the problem posed to the mathematical community by the non-rigorous methods used by physicists in investigating mathematical problems. These methods are often highly successful in finding concrete results, but cannot be justified by standard methods. The chapter illustrates methods used by mathematicians in assimilating such non-rigorous techniques by reference to areas such as the umbral calculus of Blissard, Dirac's delta function, and the use of infinitesimals in calculus. It concludes with an example of an area where assimilation is currently incomplete, the replica method in statistical physics.

*Keywords:*
umbral calculus, infinitesimals, replica method, rigour, assimilation, Blissard, Dirac's delta function

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