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 112 of 184
F_4_10 — Roman Indian Ocean Trade and the Periplus
Rome's Indian Ocean trade network was one of the most extensive commercial systems of the ancient world, linking the Mediterranean to India, Sri Lanka, and Southeast Asia from the 1st century BCE through the 3rd century
F_4_13 — Glass Production: Origins, Trade, and Technology Transfer
Glass is one of the earliest synthetic materials, with origins tracing to faience (glazed quartz) production in Egypt and Mesopotamia by ~5000 BCE and true glass beads appearing by ~3500 BCE. For over two millennia, glas
F_3_03 — Domestication of the Horse and the Wheel: Technologies That Reshaped Civilization
The domestication of the horse and the invention of the wheel were among the most transformative technological developments in human history, fundamentally altering transportation, warfare, trade, and social organization
F_3_15 — Shared Pyramid Traditions: Egypt, Mesoamerica, China, Sudan
Pyramidal structures — monumental constructions with broad bases tapering to a point or platform at the top — were built independently by civilizations across the globe: the Egyptian pyramids (c. 2686–1550 BCE, from the
F_3_14 — Domestication: How Humans Reshaped Species and Themselves
Domestication — the multigenerational process by which humans selectively breed wild species, producing organisms that are genetically, morphologically, and behaviorally distinct from their wild ancestors and dependent o
F_3_07 — Independent Origins of Plant Domestication
Plant domestication — the process by which wild species are genetically and morphologically transformed through human selection into cultivable, human-dependent crops — arose independently in at least 7–11 geographically
F_3_08 — Ancient Communication and Postal Systems
Long before electronic communication, ancient civilizations developed sophisticated communication and postal systems that enabled information to travel across vast empires at speeds that would not be surpassed until the
ZA_2_16 — Gravitational Lensing: Bending Light, Dark Matter Mapping, and Cosmic Magnification
Gravitational lensing — the deflection and focusing of light from distant sources by the gravitational field of intervening mass — is one of the most powerful predictions of Einstein's general relativity and has become a
V_1_08 — Mathematical Puzzles & Recreational Mathematics
Mathematical puzzles — problems posed for amusement, education, or intellectual challenge — have served as engines of mathematical discovery for over 4,000 years. The Rhind Mathematical Papyrus (c. 1650 BCE, Egypt) conta
V_1_09 — Ancient Egyptian & Babylonian Mathematics
Ancient Egyptian and Babylonian mathematics — the two oldest documented mathematical traditions — represent fundamentally different approaches to mathematical thinking, both achieving remarkable sophistication millennia
V_1_02 — Infinity, Paradoxes, and Mathematical Philosophy
Infinity has been a source of wonder, terror, and paradox since the ancient Greeks first grappled with Zeno's paradoxes of motion. Georg Cantor's revolutionary set theory (1870s-1890s) proved that infinities come in diff
V_1_04 — Sacred Geometry — Mathematical Patterns in Ancient Design
Sacred geometry refers to the attribution of symbolic, cosmological, or divine meaning to geometric forms and mathematical ratios — a practice documented in ancient Egyptian, Greek, Islamic, Hindu, Buddhist, and medieval
V_1_07 — Mathematical Astronomy: Ptolemy to Kepler
Mathematical astronomy — the use of mathematical models to predict celestial phenomena — is one of the oldest and most successful applications of mathematics. Babylonian astronomers (c. 1800–100 BCE) developed sophistica
V_4_05 — Origami Mathematics and Paper Folding
Origami — the art of paper folding — conceals a rich mathematical framework that has emerged as a serious branch of computational geometry with applications from space engineering to medical devices. The mathematics of o
V_4_03 — Geometric Probability and Buffon's Needle
Geometric probability assigns probabilities to random geometric events — needle drops, random points in regions, random lines intersecting figures — formalizing questions that blend chance with spatial structure. Buffon'
V_4_06 — Mathematics in Natural Forms: Spirals, Symmetry, and Phyllotaxis
Mathematics pervades the natural world in patterns of astonishing regularity — from the logarithmic spirals of nautilus shells, hurricanes, and galaxies, to the Fibonacci phyllotaxis of sunflower seed heads and pinecone
V_3_04 — Combinatorics & Counting: Pascal's Triangle to Modern Applications
Combinatorics — the mathematics of counting, arrangement, and selection — is one of the oldest and most widely applicable branches of mathematics, with roots across multiple civilizations. Pascal's triangle — the triangu
V_3_12 — Statistics and Hypothesis Testing
Statistics — the science of collecting, analyzing, and interpreting data under uncertainty — underpins virtually every empirical science, from medicine and psychology to physics and economics. Modern statistical hypothes
V_3_01 — Statistics & Probability: Pascal to Bayes
Probability and statistics — the mathematics of uncertainty — emerged as formal disciplines from the Pascal-Fermat correspondence (1654) on the "problem of points" (how to divide stakes in an interrupted game of chance),
V_3_10 — Tensor Calculus and Differential Geometry: The Mathematics of Curved Spaces
Tensor calculus and differential geometry provide the mathematical language for describing curved spaces — from the geometry of Earth's surface to the curvature of spacetime in general relativity. Developed through the w
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