Segal's conjecture is a significant statement in the field of algebraic topology, particularly in the study of stable homotopy theory. Formulated by Graeme Segal in the 1960s, the conjecture concerns the relationship between the stable homotopy groups of spheres and the representation theory of finite groups.

Strassmann's theorem is a result in complex analysis that provides conditions under which a sequence of complex functions converges uniformly on compact sets. Specifically, it addresses the uniform convergence of power series in the context of multivariable functions, but it also applies to single-variable functions.

The Structure Theorem for finitely generated modules over a principal ideal domain (PID) is a fundamental result in abstract algebra, specifically in the study of modules over rings. It describes the classification of finitely generated modules over a PID in terms of simpler components. Here’s a concise statement of the theorem: Let \( R \) be a principal ideal domain, and let \( M \) be a finitely generated \( R \)-module.

Whitehead's Lemma is a result in the field of algebraic topology, particularly in the study of homotopy theory and the properties of topological spaces. It deals with the question of when a certain kind of map induces an isomorphism on homotopy groups.

The Barban–Davenport–Halberstam theorem is a result in number theory, specifically in the area of additive number theory and the distribution of prime numbers. It provides a way to estimate the size of the prime numbers in certain ranges. More formally, the theorem deals with the distribution of prime numbers in arithmetic progressions and gives a bound on the number of primes in intervals of certain lengths.

Toda's theorem is a significant result in computational complexity theory, which establishes a relationship between different complexity classes.

The number 193 is an integer that follows 192 and precedes 194. It is classified as a prime number, meaning it has no positive divisors other than 1 and itself. In addition to its mathematical significance, 193 can be associated with various contexts, such as a year in history (e.g., AD 193), designations in various systems (like area codes, bus routes, etc.), or even as a label in certain products or categories.

Maier's theorem is a result in number theory related to the distribution of prime numbers. Specifically, it deals with the existence of certain arithmetic progressions among prime numbers. The theorem is typically discussed in the context of additive number theory and is named after the mathematician Helmut Maier, who contributed to the understanding of the distribution of primes.

The Prime Number Theorem (PNT) is a fundamental result in number theory that describes the asymptotic distribution of prime numbers. It states that the number of prime numbers less than a given number \( n \), denoted as \( \pi(n) \), is approximately equal to \( \frac{n}{\log(n)} \), where \( \log(n) \) is the natural logarithm of \( n \).

The Riemann-von Mangoldt formula is an important result in analytic number theory that provides an asymptotic expression for the number of prime numbers less than or equal to a certain value \( x \). More formally, it relates the distribution of prime numbers to the Riemann zeta function, a central object of study in number theory.

The Bogomolov–Sommese vanishing theorem is a result in algebraic geometry that deals with the vanishing of certain cohomology groups associated with ample line bundles on compact Kähler manifolds.

The Kodaira embedding theorem is a fundamental result in complex differential geometry that provides a criterion for when a compact complex manifold can be embedded into projective space as a complex projective variety. The theorem tackles the interplay between the geometry of a compact complex manifold and the algebraic properties of holomorphic line bundles over it.

The Oka coherence theorem is a result in complex analysis and several complex variables, particularly in the field of Oka theory. Named after Shinsuke Oka, this theorem deals with the properties of holomorphic functions and their extensions in certain types of domains.

The Krein–Milman theorem is a fundamental result in convex analysis and functional analysis, particularly dealing with convex sets in the context of topological vector spaces. The theorem essentially provides a characterization of convex compact sets.

Alspach's conjecture, proposed by Alspach in 1970, is a conjecture in the field of graph theory. It pertains to the existence of certain types of graphs known as 1-factorizations of complete graphs.

The Cook–Levin theorem, established by Stephen Cook in 1971 and independently by Leonid Levin, is a fundamental result in computational complexity theory. It states that the Boolean satisfiability problem (SAT) is NP-complete. This means that SAT is at least as hard as any problem in the complexity class NP (nondeterministic polynomial time), and any problem in NP can be reduced to SAT in polynomial time.

The Karp–Lipton theorem is an important result in computational complexity theory that connects the complexity classes \(P\), \(NP\), and \(PSPACE\). It was established by Richard Karp and Richard J. Lipton in the early 1980s. The theorem states that if \(NP\) problems can be solved in polynomial time by a non-deterministic Turing machine using polynomial space (i.e.

A Steiner conic, also known as a Steiner curve or a Steiner ellipse, is a specific type of conic section used in projective geometry and other areas of mathematics. It is defined in the context of a given triangle. For a triangle with vertices \( A \), \( B \), and \( C \), the Steiner conic is the unique conic that passes through the triangle's vertices and has the following additional properties: 1. Its foci are located at the triangle's centroid.

Human evolution theorists are scientists and researchers who study the evolutionary history of Homo sapiens and their ancestors. They explore how humans have evolved over millions of years through the lens of various scientific disciplines, including anthropology, genetics, archaeology, paleontology, and evolutionary biology. These theorists investigate the origins of humans, the evolutionary processes that have shaped our species, and the relationships among various hominins (the group that includes modern humans and our extinct relatives).

The Master Theorem is a powerful tool in the analysis of algorithms, particularly for solving recurrences that arise in divide-and-conquer algorithms. It provides a method for analyzing the time complexity of recursive algorithms without having to unroll the recurrence completely or use substitution methods.