“It does not trouble the mathematician that he has to deal with unknown things. At the outset in algebra he handles unknown…

“It does not trouble the mathematician that he has to deal with unknown things. At the outset in algebra he handles unknown quantities x and y. His quantities are unknown, but he subjects them to known operations - addition, multi-plication, etc. Recalling Bertrand Russell’s famous definition, the mathematician never knows what he is talking about, nor whether what he is saying is true; but, we are tempted to add, at least he does know what he is doing. The last limitation would almost seem to disqualify him for treating a universe which is the theatre of unknowable actions and operations. We need a super-mathematics in which the operations are as unknown as the quantities they operate on, and a super-mathematician who does not know what he is doing when he performs these operations. Such a super-mathematics is the Theory of Groups.”

–Arthur Stanley Eddington,“New Pathways in Science”, 1934