RESEARCH BASE
Search 3,721 documents across 34 fields — every claim tier-rated by evidence
3,633 are the core, quality-scored corpus (34 lettered sections — see How We Work); the remaining 88 are cross-corpus synthesis documents (68 InterDocs, 12 Connections, 8 Theories) also indexed here.
3,665 results for "P vs NP" — page 113 of 184
V_3_11 — Mathematical Optimization: Linear Programming, Convex Methods, and Gradient Descent
Mathematical optimization — finding the best solution from a set of feasible alternatives — is one of the most practically impactful branches of mathematics, with applications spanning logistics, finance, engineering, ma
V_3_02 — Graph Theory & Network Mathematics
Graph theory — the mathematics of networks, connections, and relationships — began with Euler's Königsberg bridge problem (1736) and has become one of the most broadly applicable branches of mathematics, with direct rele
V_3_09 — Fourier Analysis: Signal Processing and the Mathematics of Frequency
Fourier analysis — the decomposition of functions into constituent sinusoidal waves — is one of the most transformative mathematical ideas in science and engineering. Joseph Fourier's 1822 insight that any periodic funct
V_3_03 — Chaos Theory & Fractals: Mathematics of Complexity
Chaos theory — the mathematical study of systems that are deterministic yet unpredictable — represents one of the most profound discoveries of 20th-century mathematics. Edward Lorenz (1963) discovered that a simple syste
V_2_17 — Homological Algebra: Chain Complexes, Exact Sequences, and Derived Functors
Homological algebra provides a powerful, abstract framework for studying algebraic structures — groups, rings, modules, sheaves — by analyzing chain complexes (sequences of abelian groups or modules connected by homomorp
V_2_02 — Topology & Knot Theory: Celtic Knots to DNA
Topology — the study of properties preserved under continuous deformation (stretching, bending, but not tearing or gluing) — originated with Euler's solution to the Königsberg bridge problem (1736) and evolved into one o
V_2_09 — Number Theory: Primes, Patterns, and Unsolved Problems
Number theory — the study of integers and their properties — is one of the oldest and most beautiful branches of mathematics, yet it connects to cryptography, physics, and computer science in profound ways. Prime numbers
V_2_01 — Prime Numbers — Patterns, Mysteries, and the Riemann Hypothesis
Prime numbers — integers greater than 1 divisible only by 1 and themselves — have fascinated mathematicians since Euclid proved their infinitude (~300 BCE). Despite appearing randomly distributed, primes follow deep stat
V_2_11 — Abstract Algebra: Groups, Rings, and Fields
Abstract algebra is the study of algebraic structures — sets equipped with operations satisfying specific axioms — that generalize familiar arithmetic operations to reveal deep structural patterns across mathematics and
V_2_03 — History of Algebra: Al-Khwarizmi to Group Theory
Algebra — the generalization of arithmetic to unknown quantities and their relationships — has a 4,000-year documented history, from Babylonian equation-solving tablets (c. 1800 BCE) through Brahmagupta's Indian treatise
V_2_08 — Mathematical Proof: History & Philosophy
Mathematical proof — the definitive demonstration that a statement follows necessarily from accepted axioms — is the distinguishing feature of mathematics as a discipline. The axiomatic-deductive method originated with t
V_2_14 — Differential Topology and Manifolds
Differential topology studies smooth manifolds — spaces that locally resemble Euclidean $\mathbb{R}^n$ with smooth (infinitely differentiable) transition maps — and the smooth maps between them, classified up to diffeomo
M_5_15 — LiDAR Archaeological Discoveries Catalog
Light Detection and Ranging (LiDAR) — an active remote sensing technology using pulsed laser light to create high-resolution three-dimensional surface models — has revolutionized archaeology since its first systematic ar
M_5_09 — Denisova Cave: Archaeological Wonders and Genetic Revelations
Denisova Cave (Денисова пещера), located in the Altai Mountains of southern Siberia, Russia, is one of the most extraordinary archaeological sites in the world — the only known location where three distinct hominin speci
M_3_06 — Unfinished Obelisk and Ancient Quarrying Evidence
The Unfinished Obelisk at the Northern Quarry of Aswan, Egypt is one of the most important archaeological sites for understanding ancient Egyptian stone-quarrying technology. Dated to the New Kingdom (most likely commiss
M_4_05 — Giant Claims, Skeletal Evidence, and the Mound Builder Debate
Claims of giant human skeletons unearthed in the Americas constitute one of the most persistent themes in forbidden archaeology and popular alternative history. Hundreds of 19th-century newspaper accounts report discover
M_4_14 — Richat Structure & Bimini Road: Geological Formations or Lost Civilizations?
The Richat Structure (also called the "Eye of the Sahara" or "Eye of Africa") is a prominent circular geological feature approximately 40 km in diameter located near Ouadane, Mauritania, in the western Sahara Desert (21°
M_1_07 — Crystal Skulls Examination
Crystal skulls — life-sized or near-life-sized human skull models carved from clear or milky quartz crystal — have been among the most enduring icons of alternative archaeology since the late 19th century. Approximately
M_1_08 — Ica Stones and Acámbaro Figurines
The Ica stones and Acámbaro figurines are two separate collections of artifacts cited in forbidden archaeology and creationist literature as alleged evidence that humans coexisted with dinosaurs — a claim that contradict
A_1_24 — Natufian Culture
The Natufian culture (c. 15,000–11,500 BP) represents the critical transitional period between mobile hunter-gatherer lifeways and settled agricultural communities in the Levant. First defined by Dorothy Garrod in 1928 f
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