A circular prime is a particular type of prime number that remains prime when its digits are rotated in all possible ways. For example, let's consider the prime number 197. Its digit rotations are 197, 971, and 719, and since all of these numbers are prime, 197 is classified as a circular prime. To give another example, the number 13 is a circular prime because its rotations (13 and 31) are both prime numbers.

The Dudley triangle, also known as the Dudley area or Dudley triangle concept, refers to a geographic and demographic model that describes three areas of interconnected significance in a particular region. This term is often used in discussions about urban planning, economic development, and social demographics. In some contexts, particularly in the UK, the Dudley triangle may refer to a specific area within the town of Dudley, located in the West Midlands, encompassing various neighborhoods or districts.

Lévy's constant, typically denoted as \( L \), is a mathematical constant that appears in the context of probability theory and stochastic processes, particularly concerning the law of the iterated logarithm for random walks and other related processes. More specifically, Lévy’s constant is related to the distribution of the supremum of a Brownian motion.

Szpiró's conjecture is a hypothesis in number theory regarding the distribution of prime numbers in relation to certain algebraic curves, specifically those defined over number fields. Formulated by the mathematician Szpiro in the context of elliptic curves, it establishes a connection between the height of a point on the curve and the number of rational points of bounded height.

A unit square is a square polygon that has a side length of one unit. It is a fundamental concept in geometry and coordinates systems, particularly in the Cartesian coordinate system.

Carmichael's theorem, also known as Carmichael's function, deals with properties of groups and relates to the structure of finite abelian groups. Specifically, it provides a way to determine the order of elements in a group.

Fermat's Last Theorem states that there are no three positive integers \(a\), \(b\), and \(c\) that can satisfy the equation \(a^n + b^n = c^n\) for any integer value of \(n\) greater than 2.

Meyer's theorem is a result in the field of stochastic calculus, particularly dealing with semimartingales and their properties in the context of stochastic integration and Itô calculus. Specifically, the theorem provides conditions under which a process is a semimartingale and gives criteria for the convergence of stochastic integrals. In more detail, Meyer's theorem deals with certain types of stochastic processes, often focusing on the convergence of integrals involving local martingales.

The Skolem–Mahler–Lech theorem is a result in number theory and in the study of sequences which concerns the behavior of integer sequences defined by linear recurrence relations. More specifically, it deals with the properties of the zeros of such sequences.

The Von Staudt–Clausen theorem is a result in the field of number theory, particularly concerning the theory of continued fractions and the approximation of numbers. The theorem provides a way to express a specific class of numbers, notably the values of certain mathematical constants, as a sum involving continued fractions.

Goldbach's conjecture is a famous unsolved problem in number theory, proposed by the Prussian mathematician Christian Goldbach in 1742. The conjecture posits that every even integer greater than two can be expressed as the sum of two prime numbers. For example, the number 4 can be expressed as \(2 + 2\), 6 can be expressed as \(3 + 3\), and 8 can be expressed as \(3 + 5\).

The Bateman–Horn conjecture is a hypothesis in number theory concerning the distribution of prime numbers in certain arithmetic progressions. It was proposed by the mathematicians Paul T. Bateman and Benjamin M. Horn in the 1960s. The conjecture states that for a given set of linear polynomials, the number of primes produced by these polynomials, under certain conditions, can be predicted based on the properties of the coefficients and the values at which these polynomials are evaluated.

Landau's problems refer to a list of open problems in physics and mathematics that were posed by the renowned Soviet physicist Lev Landau. These problems primarily focus on theoretical issues in condensed matter physics, statistical mechanics, and other areas where Landau made significant contributions. One of the most famous of these problems is related to the nature of phase transitions in materials and the theoretical understanding of critical phenomena.

The Manin conjecture, proposed by Yuri Manin in the 1970s, is a conjecture in the field of arithmetic geometry. Specifically, it relates to the study of rational points on algebraic varieties, particularly Fano varieties, which are a special class of projective algebraic varieties with ample anticanonical bundles.

Schanuel's conjecture is a conjecture in transcendental number theory proposed by Stephen Schanuel in the 1960s. It provides a statement about the transcendence of certain numbers related to algebraic numbers and transcendental numbers.

Vojta's conjecture is a conjecture in the field of arithmetic geometry, named after the mathematician Paul Vojta. It deals with the distribution of rational points on algebraic varieties and is closely related to Diophantine geometry, which studies solutions to polynomial equations. In simple terms, Vojta's conjecture can be thought of as a generalization of the Zsigmondy theorem and the Bombieri-Lang conjecture.

"The Lady Tasting Tea" is a popular science book written by David Salsburg, published in 2001. The book explores the history and development of statistics, particularly in the context of scientific research. Its title refers to a famous story about a lady who was purported to be able to tell whether tea was poured into a cup before or after the milk, which illustrates concepts of hypothesis testing and the importance of statistical methods.

Finite promise games and greedy clique sequences are concepts from theoretical computer science and combinatorial game theory. ### Finite Promise Games Finite promise games are a type of two-player game where players make moves according to certain rules, but they are also constrained by promises. In these games, players make a finite number of moves and usually have some shared knowledge about the game state.