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Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.

Statistics is deeply related to subjects like physics, chemistry, geography, geopolitics, and especially mathematics.

Inferences made using mathematical statistics employ the framework of probability theory, which deals with the analysis of random phenomena.

Particularly fast methods are available for numbers of special forms, such as Mersenne primes, and these have been used to find large prime numbers.

The numbers greater than 1 that are not prime are called composite numbers.

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 (2 × 2) in which both numbers are smaller than 4.

No known simple formula separates prime numbers from composite numbers.

However, the distribution of primes within the natural numbers in the large can be statistically modelled.

Particularly fast methods are available for numbers of special forms, such as Mersenne primes, and these have been used to find large prime numbers.

The numbers greater than 1 that are not prime are called composite numbers.

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 (2 × 2) in which both numbers are smaller than 4.

No known simple formula separates prime numbers from composite numbers.

However, the distribution of primes within the natural numbers in the large can be statistically modelled.

Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann.

== History == Discussions on the mathematics of games began long before the rise of modern, mathematical game theory.

In 1713, a letter attributed to Charles Waldegrave, an active Jacobite and uncle to British diplomat James Waldegrave, analyzed a game called "le her".

Waldegrave provided a minimax mixed strategy solution to a two-person version of the card game, and the problem is now known as the Waldegrave problem.

Game theory has been widely recognized as an important tool in many fields.

In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of behavioral relations.

These two branches are related to each other by the fundamental theorem of calculus.

Calculus uses convergence of infinite sequences and infinite series to a well-defined mathematical limit.

Calculus is the "mathematical backbone" for solving problems in which variable quantities change with time or another reference value.

It has also been called "the basic instrument of physical science".

In the late 17th century, Isaac Newton and Gottfried Wilhelm Leibniz each independently formulated infinitesimal calculus.

Later work, including the formalization of the concept of limits, put calculus on a more solid conceptual footing.

Pi has applications in various fields, including geometry, trigonometry, and calculus.

Pi is approximately equal to 3.14159, but its exact value remains unknown.

The first 100 trillion digits of Pi were calculated in 2018, showcasing its infinite nature.

Pi is named after the Greek letter Π (pi), used to represent it in mathematical notations.

The first computational formula for π, based on infinite series, was discovered a millennium later.

The extensive computations involved have also been used to test the correctness of new computer processors.

Infinity is often used to describe sets, sequences, or series that have no end.

The concept of infinity has been explored by philosophers since ancient times, with notable figures like Euclid and Plato discussing it.

Infinity is also used in art, particularly in the representation of eternity, continuity, and the cyclical nature of life.

The symbol ∞ is derived from the Greek letter omega (Ω), which was later adapted as a symbol for infinity.

Infinity is used in various mathematical concepts, such as the concept of limits and continuity in calculus.

Infinity is also used in the study of cardinal numbers, which measure the size of sets and are essential in set theory.

Probability theory is also used to describe the underlying mechanics and regularities of complex systems.

This is referred to as theoretical probability (in contrast to empirical probability, dealing with probabilities in the context of real experiments).

The probability is a number between 0 and 1; the larger the probability, the more likely the desired outcome is to occur.

The probability of getting an outcome of "head-head" is 1 out of 4 outcomes, or, in numerical terms, 1/4, 0.25 or 25%.

The probability of getting an outcome of at least one head is 3 out of 4, or 0.75, and this event is more likely to occur.

This interpretation considers probability to be the relative frequency "in the long run" of outcomes.