# 2002 Top Ten of Polemic for Mathematics

Clifford algebra
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image
Lagged Fibonacci generator
A Lagged Fibonacci generator is an example of a pseudorandom number generator. This class of random number generator is aimed at being an improvement on the 'standard' linear congruential generator. These are based on a generalisation of the Fibonacci sequence
Computation
Computation is any type of calculation that includes both arithmetical and non-arithmetical steps and which follows a well-defined model
Order isomorphism
In the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections
Profinite group
In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups. They share many properties with their finite quotients: for example, both Lagrange's theorem and the Sylow theorems generalise well to profinite groups
Euler's identity
In mathematics, Euler's identity is the
Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points
P versus NP problem
The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified can also be solved quickly
Rank (linear algebra)
In linear algebra, the rank of a matrix A is the dimension of the vector space generated by its columns. This corresponds to the maximal number of linearly independent columns of A. This, in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics
Benford's law
Benford's law, also known as the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation that in many real-life sets of numerical data, the leading digit is likely to be small. In sets that obey the law, the number 1 appears as the leading significant digit about 30 % of the time, while 9 appears as the leading significant digit less than 5 % of the time. If the digits were distributed uniformly, they would each occur about 11.1 % of the time. Benford's law also