# 2004 Top Ten of Conflict for Mathematics

Mathematics
Mathematics includes the study of such topics as numbers, formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes. There is no general consensus about its exact scope or epistemological status
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
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. It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1⁄299792458 second. According to special relativity, c is the upper limit for the speed at which conventional matter, energy or any signal carrying information can travel
Algorithm
In mathematics and computer science, an algorithm is a finite sequence of well-defined instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations, data processing, automated reasoning, automated decision-making and other tasks. In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where
Turing machine
A Turing machine is a mathematical model of computation that defines an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, given any computer algorithm, a Turing machine capable of implementing that algorithm's logic can be constructed
Fractal
In mathematics, a fractal is a subset of Euclidean space with a fractal dimension that strictly exceeds its topological dimension. Fractals appear the same at different scales, as illustrated in successive magnifications of the Mandelbrot set. Fractals often exhibit similar patterns at increasingly smaller scales, a property called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, it is called affine
Rational Unified Process
The Rational Unified Process (RUP) is an iterative software development process framework created by the Rational Software Corporation, a division of IBM since 2003. RUP is not a single concrete prescriptive process, but rather an adaptable process framework, intended to be tailored by the development organizations and software project teams that will select the elements of the process that are appropriate for their needs. RUP is a specific implementation of the Unified Process
Pi
The number π is a mathematical constant, approximately equal to 3.14159. It is defined in Euclidean geometry as the ratio of a circle's circumference to its diameter, and also has various equivalent definitions. The number appears in many formulas in all areas of mathematics and physics. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in 1706. It is also referred to as Archimedes' constant
Metric time
Metric time is the measure of time intervals using the metric system. The modern SI system defines the second as the base unit of time, and forms multiples and submultiples with metric prefixes such as kiloseconds and milliseconds. Other units of time: minute, hour, and day, are accepted for use with SI, but are not part of it. Metric time is a measure of time intervals, while decimal time is a means of recording time of day
Chaos theory
Chaos theory is an interdisciplinary scientific theory and branch of mathematics focused on underlying patterns and deterministic laws highly sensitive to initial conditions in dynamical systems that were thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnectedness, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The