Folkman's theorem is a result in combinatorial mathematics, specifically in the area of Ramsey theory. It was proven by mathematician Frank P. Ramsey and is concerned with the coloring of edges in complete graphs.

The Green–Tao theorem is a significant result in additive combinatorics and number theory, established by mathematicians Ben Green and Terence Tao. It was proven in 2004 and states that the set of prime numbers contains arbitrarily long arithmetic progressions. More formally, the theorem asserts that for any integer \( k \), there exists a sequence of prime numbers that contains an arithmetic progression of length \( k \).

A. K. Dewdney is a Canadian mathematician, computer scientist, and author, known for his work in the fields of mathematics, computer science, and popular science writing. He has written several books and articles on topics ranging from mathematics and science to the philosophical implications of technology. One of his notable contributions is in the realm of recreational mathematics, where he has explored interesting mathematical puzzles and concepts.

Alexander Bogomolny is a mathematician known primarily for his work in the field of mathematics education and his contributions to the popularization of mathematical concepts through various online resources. He is the creator of the website "Cut-the-Knot," which features a wealth of mathematical problems, puzzles, and explanations designed to engage learners and enthusiasts in mathematics. The site covers a variety of topics, including geometry, number theory, and mathematical games, and is appreciated for its clear explanations and interactive elements.

Anton Diabelli (1781–1858) was an Austrian composer, music publisher, and pianist, best known for his role in the classical music scene of the early 19th century. While he composed various works, including piano pieces and songs, he is most famously remembered for his waltz "Diabelli Variation," which served as the basis for a set of variations by Ludwig van Beethoven.

Base flow in the context of random dynamical systems typically refers to a steady or deterministic flow around which random fluctuations occur. In dynamical systems, particularly in fluid dynamics and related fields, the base flow represents the mean or average flow pattern of a system, while perturbations or disturbances can be introduced to that flow due to random influences, noise, or other time-dependent effects.

Harnack's Curve Theorem is a result in the field of differential geometry and real analysis that pertains to curves in the plane. The theorem states that if you have a continuous curve that is smooth (differentiable) and does not intersect itself, then the curve can be parameterized in such a way that it is "locally" straightened out. More precisely, it concerns the properties of the distance between points on the curve.

A **subanalytic set** is a concept from the field of real algebraic geometry and model theory, particularly within the framework of o-minimal structures. A set is considered subanalytic if it can be defined using certain operations applied to analytic sets in a Euclidean space.

Burkard Polster is a mathematician known for his work in the field of mathematics, particularly in algebra and geometry. He is also recognized for his contributions to mathematical education and outreach, including his efforts to make complex mathematical concepts accessible to a wider audience. He is notable for his involvement in mathematical problem-solving and for creating educational content that engages students and the general public.

Dennis Shasha is an American computer scientist, known for his work in the fields of database systems, data mining, and computer security. He is also a professor at New York University's Tandon School of Engineering. In addition to his academic contributions, Shasha has written several books that bridge the gap between technology and various aspects of culture. One of his notable works is "The Art of Data Science," where he explores the intersection of data analysis and creativity.

Júlio César de Mello e Souza, also known by his pen name Malba Tahan, was a Brazilian author, mathematician, and educator famous for his contributions to literature, particularly in the genre of mathematical stories and tales. Born on May 6, 1895, in Brazil, he became a notable figure in promoting mathematics through storytelling, making complex concepts accessible and engaging.

Maria Antònia Canals is a renowned figure in the realm of music education and piano performance, particularly known for her contributions to the cultural and musical landscape in Catalonia, Spain. She was born on June 20, 1863, in Barcelona and passed away on March 18, 1911. Canals was a prominent pianist and composer, as well as an educator dedicated to fostering music in her community.

Martin David Kruskal (1925–2020) was an influential American mathematician and physicist, noted for his contributions to various fields, particularly applied mathematics, mathematical physics, and the study of nonlinear partial differential equations. He is best known for his work in the area of solitons and integrable systems.

Absolute irreducibility is a concept from the field of algebra, particularly in the area of algebraic geometry and the study of polynomial equations and algebraic varieties. A polynomial is said to be absolutely irreducible if it cannot be factored into the product of two non-constant polynomials over its field of coefficients, regardless of the field extension considered. More formally, consider a polynomial \( f(x) \) in one or more variables with coefficients in a field \( K \).

Deligne–Lusztig theory is a significant area in the field of representation theory of algebraic groups and finite groups of Lie type, named after Pierre Deligne and George Lusztig. This theory provides a way to construct and study representations of finite groups of Lie type via geometric methods, specifically by examining varieties over finite fields.

Susan Goldstine is a mathematician known for her work in the fields of mathematics and mathematics education. She is particularly recognized for her contributions to the use of technology in teaching mathematics, especially through computer software and other digital tools.

William Kolakoski is best known for his contribution to mathematics through the Kolakoski sequence, which is an infinite sequence of 1s and 2s defined in a unique way. The sequence begins with the first term being 1, and subsequent terms are generated based on the values indicated by prior terms. Specifically, the sequence starts as follows: 1. The first term is 1.