The Bombieri–Lang conjecture is a concept in number theory that relates to the distribution of rational points on certain types of algebraic varieties. Specifically, it deals with the behavior of rational points on algebraic varieties defined over number fields and has implications for understanding the ranks of abelian varieties and the distribution of solutions to Diophantine equations. The conjecture can be stated in a few steps for certain types of varieties, particularly for curves and higher-dimensional varieties.

Heesch's problem is a question in the field of geometry, specifically in relation to tiling and the properties of shapes. It asks whether a given shape can be extended into a larger shape by adding additional copies of itself, while maintaining a specific tiling condition—specifically, that the tiles fit together without gaps or overlaps.

The Inscribed Square Problem refers to a geometric problem of finding the largest square that can be inscribed within a given shape, usually a convex polygon or a specific type of curve. The goal is to determine the dimensions and position of the square such that it fits entirely within the boundaries of the shape while maximizing its area.

The Pierce–Birkhoff conjecture is a conjecture in the field of lattice theory, specifically concerning finite distributive lattices and their Maximal Chains. It was proposed by the mathematicians Benjamin Pierce and George Birkhoff. The conjecture essentially deals with the nature of certain kinds of chains (series of elements) within these lattices and posits conditions under which certain structural properties hold.

The Fröberg conjecture, proposed by Anders Fröberg in 1981, is a conjecture in the field of algebraic geometry and commutative algebra. It deals with the study of the Betti numbers of a certain class of algebraic varieties, specifically focusing on the resolutions of certain graded modules.

The Fujita conjecture is a statement in the field of algebraic geometry, particularly concerning the minimal model program and the properties of algebraic varieties. Proposed by Takao Fujita in the 1980s, the conjecture pertains to the relationship between the ample divisor classes and the structure of the variety. Specifically, the Fujita conjecture relates to the growth of the dimension of the space of global sections of powers of an ample divisor.

The "List of unsolved problems in mathematics" refers to a collection of problems that remain unsolved despite being significant and well-studied in the field of mathematics. Many of these problems have withstood the test of time, eluding resolution by mathematicians for decades or even centuries.

Resolution of singularities is a mathematical process in algebraic geometry that aims to transform a variety (which can have singular points) into a smoother variety (which has no singularities) by replacing the singular points with more complex structures, often in a controlled way. This process is crucial for understanding geometric properties of algebraic varieties and for performing various calculations in algebraic geometry.

The Section Conjecture is a significant hypothesis in the field of arithmetic geometry, particularly concerning the relationship between algebraic varieties and their associated functions or sections. It was formulated by mathematicians in the context of the study of abelian varieties and their rational points. More specifically, the conjecture relates to the *Neron models* of abelian varieties over a number field and their sections.

The Virasoro conjecture is a fundamental result in the field of string theory and two-dimensional conformal field theory (CFT). It relates to the algebra of Virasoro operators, which are central to the study of CFTs, particularly in the context of two-dimensional quantum gravity and string theory. In essence, the conjecture asserts that there exists a certain relation between the partition functions of two-dimensional conformal field theories and the geometry of the underlying space.

The Erdős–Gyárfás conjecture is a statement in the field of graph theory that pertains to the coloring of graphs. Specifically, it suggests that for any graph \( G \) that does not contain a complete bipartite subgraph \( K_{p,q} \) (i.e.

Harborth's conjecture is a hypothesis in the field of graph theory, particularly related to the properties of planar graphs. Specifically, it suggests that every planar graph can be colored using at most four colors such that no adjacent vertices share the same color. This assertion is closely related to the well-known Four Color Theorem, which states that four colors are sufficient to color the vertices of any planar graph.

A conjecture is an educated guess or a proposition that is put forward based on limited evidence, which has not yet been proven or disproven. In mathematics and science, conjectures arise from observations or patterns that suggest a certain conclusion, but they need formal proof or experimental validation to be accepted as a theorem or law.

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.