… Einstein was always rather hostile to quantum mechanics. How can one understand this ? I think it is very easy to understand, because Einstein had been proceeding on different lines, lines of pure geometry. He had been developing geometrical theories and had achieved enormous success. It is only natural that he should think that further problems of physics should be solved by further development of geometrical ideas. How, to have a × b not equal to b × a is something that does not fit in very well with geometrical ideas; hence his hostility to it.

If V is a set of points then the set of comple-valued functions on V is a commutative, associative algebra. As a simple example suppose that V has a finite number of elements. Then the algebra is of finite dimension as a vector space. The product of two vectors is given by the product of the components and it satisfies the inequality ∥fg∥ ∥g∥ with respect to the norm ∥f∥ = max∣f∣. Let ƒ* be the complex conjugate of f. Then obviously the product satisfies also the equality ∥ff*∥ = ∥f∥2. A normed algebra with an involution which f ↦ f* satisfies the above two conditions is called a C*-algebra. Conversely any finite-dimensional commutative algebra which is a C*-algebra can be considered as an algebra of functions on a finite set of points. The number of points is encoded as the dimension of the algebra. It is obviously essential that the algebra be commutative in order that it have an interpretation as an algebra of functions on a set of points.