# 2002 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
Musical notation
Music notation or musical notation is any system used to visually represent aurally perceived music played with instruments or sung by the human voice through the use of written, printed, or otherwise-produced symbols, including notation for durations of absence of sound such as rests
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
Computation
Computation is any type of calculation that includes both arithmetical and non-arithmetical steps and which follows a well-defined model
Angle
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection
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
Poincaré conjecture
In mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space
Boolean satisfiability problem
In logic and computer science, the Boolean satisfiability problem is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all
Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices which are connected by edges. A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics
Mega-
Mega is a unit prefix in metric systems of units denoting a factor of one million (106 or 1000000). It has the unit symbol M. It was confirmed for use in the International System of Units (SI) in 1960. Mega comes from Ancient Greek: μέγας, romanized: mégas, lit. 'great