# 2006 Top Ten of Conflict for Mathematics

Mathematics
Mathematics is an area of knowledge that includes such topics as numbers, formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes. There is no general consensus about its exact scope or epistemological status
Pi
The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulas across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22/7 are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning
Sudoku
Sudoku is a logic-based, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid contain all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution
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
0.999...
In mathematics, 0.999... denotes the repeating decimal consisting of an unending sequence of 9s after the decimal point. This repeating decimal represents the smallest number no less than every decimal number in the sequence ; that is, the supremum of this sequence. This number is equal to 1. In other words, "0.999..." is not "almost exactly" or "very, very nearly but not quite" 1  –  rather, "0.999..." and "1" represent exactly the same number
Speed of light
The speed of light in vacuum, commonly denoted c, is a universal physical constant that is important in many areas of physics. Its exact value is defined as 299792458 metres per second. According to the special theory of relativity, c is the upper limit for the speed at which conventional matter, energy or any signal carrying information can travel through space
Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with
Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations
Algebra
Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics
Prime number
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is