Classification problem

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In science or mathematics, a classification problem for objects in a particular domain is the problem of separating these objects into smaller classes, and giving criteria for determining whether a particular object in the domain is in a particular class or not.

One of the most famous attempts at classification in biology is Carolus Linnaeus's famous classification of living things by class, order, genus, and species. An example in physics is the classification of the physical world into matter and energy, or more precisely, the classification of elementary particles into fermions and bosons and the further classification of these particles using quantum numbers. In mathematics, one successful solution to a classification problem is the classification of surfaces: every closed connected surface is a connected sum of spheres, tori, and projective planes; an invariant called the genus can be used to determine which class a given surface lies in. Another example, more closely resembling the biological situation, is the classification of finite simple groups, in which there are many large classes, but also a number of (in fact 26) exceptions.