Game Theory.
The Game Theory studies winning strategies for parties involved in situations where their interest conflict with each other. Developed by John von Neumann, the theory has applications to real games (cards, chess, etc.), economics, commerce, politics and some say even military. J. Conway used his theory of surreal numbers to qualitatively evaluate game positions. Conway wrote: It's especially delightful when you find a game that somebody's already considered and possibly not made much headway with, and you find you can just turn on one of these automatic theories and work out the value of something and say, "Ah! Right is 47/64ths of a move ahead, and so she wins."

Group.
Group is the most fundamental and pervasive notion of the Higher or Abstract Algebra. It's a set on whose elements is defined a single operation. The group is called additive if the symbol for the operation is "+". It's multiplicative if the symbol "·" of multiplication is used instead. But any other symbol can be used as well. There is always a unique element (1, for multiplicative, and 0, for additive, groups) that leaves elements invariant (unchanged) under the defined operation, like a+0=a. Also, for every element a there exists a unique inverse b such that, for example, in the case of the additive symbol, a+b=0 and b+a=0. Most often, however, the inverse is denoted as a-1. Lastly, the group operation must be associative like in a·(b·c)=(a·b)·c. A group is commutative or Abelian if its operation is symmetric, like in a+b=b+a.

Golden rectangle
A rectangle where the ratio of its length to its width is (1 + sqrt 5)/2 :1, i.e. about 1.618:1.

Growth.
Many things may grow in Mathematics. Functions may grow monotonously or in jumps. Complexity of a system may grow exponentially with the system size. Lately, due to the development of the Fractal Geometry, growth of crystals and other natural phenomena became a subject of scientific scrutiny.

Heredity.
A property of a space is hereditary if every of its subspaces possesses this property. Being countable is a hereditary property. Having holes is not.

Hole.
Torus has a hole; sphere does not. If every curve on a surface can be continuously shrunk into a point the surface has no holes. Attaching handles to the sphere in order to create surfaces with holes is an important and ubiquitous topological activity.

Histogram
A type of statistical graph that uses bars, where each bar represents a range of values and the data is continuous.

Hypotenuse
The side opposite the right angle in a right triangle. It is always the longest side in the triangle.

Ideal.
The word ideal appears in Mathematics in at least a couple of contexts.

Ideal elements.
In Geometry it's often a convenience to introduce a point at infinity as an ideal (probably too good to be real) element. Completion of a metric space by incorporating ideal elements which are limits of Cauchy sequences results in a complete metric space.

Ideal subrings.
Subrings of a ring are its subsets which are rings in their own right. For a given ring R, its subring I is (an) ideal if for every rR and iI both r·i and i·r belong to I. For an ideal I it's possible to define a factor ring R/I.

Infinitesimal.
Infinitesimal is a variable whose limit is zero. Development by Abraham Robinson (1960) of the Nonstandard Analysis conferred new significance on infinitesimals and brought them closer to the vision of Leibniz (1646-1716) who introduced the dy/dx notation for the derivative and perceived infinitesimals more like small but constant quantities.

Infinity.
Infinity pops up in a variety of places. A function may grow to infinity when it's not bounded from above. In Geometry, it's often convenient to think of parallel lines as intersecting at a point at infinity. G. Cantor was the first to introduce and systematically study various kinds of infinities.

Integer.
This is a very basic notion. To define it rigorously we may need a set of axioms, like those proposed by G.Peano. Usually, integers are numbers from the sequence ..., -2, -1, 0, 1, 2, ..., positive members of which are often called counting or natural numbers. Sometimes, 0 is also judged to be natural. For a long time, I used the word integer (not quite conventionally) to mostly designate the counting numbers. The reason is that this is the set used most frequently. So it's appropriate to denote it with the shorter word: "integers" instead of "counting numbers". More recently, I tried to bring the site's terminology more in agreement with the common use. I'd be grateful for pointers to any remaining incosistencies.