Exceptional Object
Many branches of mathematics study objects of a given type and prove a classification theorem. A common theme is that the classification results in a number of series of objects and a finite number of exceptions that don't fit into any series. These are known as exceptional objects.
Frequently these exceptional objects play a further and important role in the subject. Surprisingly, the exceptional objects in one branch of mathematics are often related to the exceptional objects in others.
A related phenomenon is exceptional isomorphism, when two series are in general different, but agree for some small values.
Read more about Exceptional Object: Regular Polytopes, Finite Simple Groups, Division Algebras, Simple Lie Groups, Supersymmetric Algebras, Unimodular Lattices, Codes, Block Designs, Snarks, Outer Automorphisms, Algebraic Topology, Connections
Famous quotes containing the words exceptional and/or object:
“Every generation rewrites the past. In easy times history is more or less of an ornamental art, but in times of danger we are driven to the written record by a pressing need to find answers to the riddles of today.... In times of change and danger when there is a quicksand of fear under men’s reasoning, a sense of continuity with generations gone before can stretch like a lifeline across the scary present and get us past that idiot delusion of the exceptional Now that blocks good thinking.”
—John Dos Passos (1896–1970)
“I find very reasonable the Celtic belief that the souls of our dearly departed are trapped in some inferior being, in an animal, a plant, an inanimate object, indeed lost to us until the day, which for some never arrives, when we find that we pass near the tree, or come to possess the object which is their prison. Then they quiver, call us, and as soon as we have recognized them, the spell is broken. Freed by us, they have vanquished death and return to live with us.”
—Marcel Proust (1871–1922)