The Berman-Hartmanis conjecture is a hypothesis in computational complexity theory that relates to the structure of problems within the complexity classes P and NP. Formulated by Jacob Berman and Richard Hartmanis in the early 1970s, the conjecture posits that every NP-complete problem can be efficiently transformed into any other NP-complete problem in a way that preserves the number of solutions.

The Brennan Conjecture is a mathematical conjecture related to the properties of certain kinds of graphs, specifically in the field of graph theory. It concerns the relationship between the diameter of a graph and the maximum degree of its vertices. The conjecture asserts that for any graph with a given maximum degree, there is a bound on the diameter that can be expressed in terms of that degree.

Gary Gladding is not a widely recognized public figure, and there may not be specific information available about him in popular media or historical records up to October 2023.

The Second Neighborhood Problem is a concept in the field of graph theory and network analysis, particularly relevant in the study of social networks and community detection. It is often associated with the analysis of local structures within a network. In this context, the "first neighborhood" of a node refers to all directly connected nodes, meaning the immediate neighbors of that node. The "second neighborhood" extends this concept by considering the neighbors of those immediate neighbors.

A Newman–Shanks–Williams (NSW) prime is a specific type of prime number that is related to a particular sequence known as the Newman–Shanks–Williams sequence.

A **palindromic prime** is a number that meets two criteria: 1. **Palindromic**: It reads the same forwards and backwards. For example, 121, 131, and 1221 are palindromic numbers. 2. **Prime**: It is a prime number, meaning it has no positive divisors other than 1 and itself.

The Grothendieck–Katz \( p \)-curvature conjecture is a conjecture in the field of algebraic geometry and number theory, particularly dealing with \( p \)-adic differential equations and their connections to the geometry of algebraic varieties. The conjecture is concerned with the behavior of differential equations over fields of characteristic \( p \), especially in relation to \( p \)-adic representations and the concept of \( p \)-curvature.

Cousin primes are pairs of prime numbers that differ by four. In mathematical terms, if \( p \) and \( q \) are prime numbers and \( q = p + 4 \), then \( (p, q) \) is a cousin prime pair.

The Erdős–Ulam problem is a question in the field of combinatorial geometry, named after mathematicians Paul Erdős and George Ulam. The problem relates to the arrangement of points in Euclidean space and how subsets of those points can be grouped to form convex sets.

The Inverse Galois Problem is a central question in the field of algebra, particularly in the area of field theory and algebraic geometry. It seeks to determine whether every finite group can be represented as the Galois group of some field extension of the rational numbers \(\mathbb{Q}\) or more generally, of some base field.

An M/G/k queue is a specific type of queueing model used in operations research and telecommunications to analyze systems where "customers" (or tasks or jobs) arrive, get serviced, and depart. The notation M/G/k provides insight into the characteristics of this queueing system: - **M**: Stands for "Markovian" or "memoryless" arrival process.

Artin's conjecture on primitive roots is a conjecture in number theory proposed by Emil Artin in 1927. It concerns the existence of primitive roots modulo primes and more generally, modulo any integer.

A congruent number is a natural number that is the area of a right triangle with rational number side lengths. In other words, a positive integer \( n \) is called a congruent number if there exists a right triangle with legs of rational lengths such that the area of the triangle is equal to \( n \).

Cramér's conjecture is a hypothesis in number theory related to the distribution of prime numbers. It was proposed by the Swedish mathematician Harald Cramér in 1936. The conjecture specifically addresses the gaps between consecutive prime numbers. Cramér's conjecture suggests that the gaps between successive primes \( p_n \) and \( p_{n+1} \) are relatively small compared to the size of the primes themselves.

The Thomson problem is a well-known problem in physics and mathematical optimization that involves determining the optimal arrangement of point charges on the surface of a sphere. Specifically, it seeks to find the configuration of \( N \) equal positive charges that minimizes the potential energy of the system due to their electrostatic repulsion.

A balanced prime is a special type of prime number that is defined in relation to its neighboring prime numbers. Specifically, a prime number \( p \) is considered to be a balanced prime if it is the average of the nearest prime numbers that are less than and greater than \( p \).

The Bunyakovsky conjecture is a conjecture in number theory that relates to prime numbers and is named after the Russian mathematician Viktor Bunyakovsky. It deals with the existence of prime numbers generated by certain polynomial expressions.

Carmichael's totient function conjecture is a mathematical conjecture related to the properties of the Euler's totient function, denoted as \(\varphi(n)\). The conjecture is named after the mathematician Robert Carmichael. The conjecture states that for any integer \( n \) greater than \( 1 \), the inequality \[ \varphi(n) < n \] holds true, which is indeed true for all integers \( n > 1 \).

The Casas-Alvero conjecture is a statement in algebraic geometry and commutative algebra concerning the properties of certain classes of varieties, and it addresses the relationship between numerical and geometric properties of projective varieties.

Gillies' conjecture is a hypothesis in the field of number theory that relates to the distribution of powers of prime numbers. Specifically, it suggests that if you take any finite set of integers and consider their product, the resulting product is often composite. The conjecture posits that a certain rational expression, derived from the powers of prime numbers that comprise the integers in the set, will eventually yield a non-zero value under specific conditions.