# 2006 Top Ten of Polemic for Mathematics

McCullagh's parametrization of the Cauchy distributions
In probability theory, the "standard" Cauchy distribution is the probability distribution whose probability density function (pdf
Sylvester's law of inertia
Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant under a change of basis. Namely, if A is the symmetric matrix that defines the quadratic form, and S is any invertible matrix such that D = SAST is diagonal, then the number of negative elements in the diagonal of D is always the same, for all such S; and the same goes for the number of positive elements
Counterargument
In reasoning and argument mapping, a counterargument is an objection to an objection. A counterargument can be used to rebut an objection to a premise, a main contention or a lemma. Synonyms of counterargument may include rebuttal, reply, counterstatement, counterreason, comeback and response. The attempt to rebut an argument may involve generating a counterargument or finding a counterexample
Rotation number
In mathematics, the rotation number is an invariant of homeomorphisms of the circle
Hank (unit of measure)
In the textile industry, a hank is a coiled or wrapped unit of yarn or twine, as opposed to other materials like thread or rope, as well as other forms such as ball, cone, bobbin spool, etc. This is often the best form for use with hand looms, compared to the cone form needed for power looms. Hanks come in varying lengths depending on the type of material and the manufacturer. For instance, a hank of linen is often 300 yards (270 m), and a hank of cotton or silk is 840 yards (770 m
IEEE 754
The IEEE Standard for Floating-Point Arithmetic is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard
Randomness
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7
Kurosh problem
In mathematics, the Kurosh problem is one general problem, and several more special questions, in ring theory. The general problem is known to have a negative solution, since one of the special cases has been shown to have counterexamples. These matters were brought up by Aleksandr Gennadievich Kurosh as analogues of the Burnside problem in group theory
Theseus and the Minotaur
Theseus and the Minotaur is a type of logic maze designed by Robert Abbott. In this maze, the player acts as Theseus, the king of Athens who is attempting to escape the Labyrinth. The main difference between this and the standard type of labyrinth, beyond the fact that it is set on a grid, is the fact that the maze is not empty, but also contains a Minotaur who hunts the player down, taking two steps for every one the player takes
Dependent and independent variables
Dependent and Independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space