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456 results for "analytic number theory" — page 4 of 23

T_1_04 Psychology & Social

T_1_04 — Developmental Psychology — From Piaget to Attachment Theory

Developmental psychology traces psychological changes across the human lifespan, from prenatal development through aging. Jean Piaget's cognitive stage theory, Lev Vygotsky's sociocultural approach, John Bowlby's attachm

developmental psychology Piaget cognitive stages Vygotsky scaffolding Bowlby
T_1_06 Psychology & Social

T_1_06 — Cognitive Development — Piaget, Vygotsky, Theory of Mind

Cognitive development — how human minds grow in their capacity to think, reason, solve problems, and understand the world — has been dominated by two foundational theories: Jean Piaget's constructivist stage theory (1936

cognitive development Piaget Vygotsky Theory of Mind Sally-Anne test zone of proximal development
T_1_07 Psychology & Social

T_1_07 — Emotion Theory and Affect

Emotion theory addresses one of psychology's most fundamental and contested questions: What are emotions, where do they come from, and how many are there?

emotion theory affect basic emotions Ekman facial action coding system FACS
T_3_14 Verified Psychology & Social

T_3_14 — Cognitive Load Theory: Working Memory, Schema Acquisition, and Instructional Design

Cognitive Load Theory (CLT) — developed by John Sweller (University of New South Wales, 1988–present) — is the most influential theory connecting cognitive architecture (specifically the severe limitations of working mem

cognitive load theory CLT Sweller working memory intrinsic load extraneous load
ZD_1_02 Information & Computation

ZD_1_02 — Information Theory — Shannon, Entropy, and the Bit

Claude Shannon's 1948 paper "A Mathematical Theory of Communication" is one of the most consequential scientific publications of the 20th century. It defined information quantitatively — measured in bits — independent of

information theory Claude Shannon entropy bit channel capacity noise
ZD_1_10 Information & Computation

ZD_1_10 — Automata Theory and Formal Languages

Automata theory studies abstract computational machines and the classes of languages they recognize, forming the mathematical backbone of computer science. The Chomsky hierarchy (1956–59) classifies formal languages into

automata theory formal languages Chomsky hierarchy finite automata pushdown automata Turing machine
ZD_1_14 Verified Information & Computation

ZD_1_14 — Type Theory: Lambda Calculus, Dependent Types, and the Curry-Howard Correspondence

Type theory is a foundational framework in mathematics, logic, and computer science that classifies values and expressions into types — categories that determine what operations are valid: a natural number can be added t

type theory lambda calculus dependent types Curry-Howard Coq Lean
ZD_1_04 Information & Computation

ZD_1_04 — Coding Theory & Error Correction

Coding theory — the mathematics of reliable communication over unreliable channels — was founded by Claude Shannon (1948), who proved the existence of channel capacity (a maximum rate at which information can be transmit

coding theory error correction Shannon Hamming code Reed-Solomon information theory
ZD_5_01 Verified Information & Computation

ZD_5_01 — Graph Theory and Algorithms

Graph theory — the mathematical study of graphs (networks of vertices/nodes connected by edges/links) — is one of the most widely applicable branches of mathematics, modeling everything from social networks and transport

graph theory graph algorithm shortest path network flow Euler path Dijkstra
ZD_4_02 Information & Computation

ZD_4_02 — Game Theory, Strategic Interaction, and Cooperation

Game theory is the mathematical study of strategic interaction among rational agents, founded by John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behavior (1944) and revolutionized by John Nash's equ

game theory Nash equilibrium prisoner's dilemma tit-for-tat von Neumann Morgenstern
ZD_4_13 Verified Information & Computation

ZD_4_13 — Network Science: Graph Theory, Small Worlds, and Scale-Free Networks

Network science is the study of complex systems represented as networks (graphs) — collections of nodes (vertices) connected by edges (links) — encompassing social networks (people connected by friendships, collaboration

network science graph theory small-world scale-free Barabási Watts-Strogatz
ZD_2_05 Verified Information & Computation

ZD_2_05 — Robotics and Control Theory

Robotics integrates mechanical engineering, electrical engineering, computer science, and control theory to design, build, and program machines that sense, reason, and act in the physical world. Control theory — the math

robotics control theory feedback control PID controller kinematics dynamics
P_2_17 Verified Philosophy & Meaning

P_2_17 — Philosophy of Law: Jurisprudence and Legal Theory

Jurisprudence — the philosophical study of law's nature, authority, and relationship to morality — addresses foundational questions: What makes a rule a "law"? Is law necessarily connected to morality? How should judges

jurisprudence legal-positivism natural-law hartian dworkinian critical-legal-studies
R_1_16 Verified Biology & Evolution

R_1_16 — Endosymbiotic Theory: Modern Developments in Organelle Evolution

Endosymbiotic theory — the proposition that mitochondria and chloroplasts originated as free-living bacteria that were engulfed by ancestral eukaryotic cells and subsequently became obligate intracellular symbionts — is

endosymbiosis Lynn Margulis mitochondria chloroplast eukaryote origin serial endosymbiotic theory
R_1_12 Biology & Evolution

R_1_12 — History of Evolutionary Theory

Evolutionary theory — the unifying framework of modern biology — has itself undergone a remarkable evolution over more than two centuries. Pre-Darwinian ideas included Lamarck's transformism (1809), which proposed that o

history of evolution Darwin Wallace Origin of Species natural selection Lamarck
ZA_2_14 Credible Physics & Quantum

ZA_2_14 — Penrose Twistor Theory: Spinor Geometry and Spacetime

Twistor theory — conceived by Roger Penrose beginning in 1967 — is a radical reformulation of the geometry underlying physics in which the fundamental objects are not points in spacetime but rather twistors: elements of

twistor theory Roger Penrose spinor conformal invariance twistor space scattering amplitudes
ZA_1_02 Physics & Quantum

ZA_1_02 — Quantum Field Theory: Foundations of Modern Physics

Quantum Field Theory (QFT) is the theoretical framework that combines quantum mechanics with special relativity, treating particles not as fundamental objects but as excitations — "ripples" — in underlying quantum fields

quantum field theory QFT second quantization Feynman diagrams renormalization virtual particles
ZA_4_25 Physics & Quantum

ZA_4_25 — Caloric Theory: The Heat Fluid That Built Thermodynamics

Caloric theory held that heat is a self-repelling, weightless, indestructible fluid — calorique — that flows from hotter bodies to cooler ones and can be stored within matter. Formalized by Antoine-Laurent de Lavoisier i

caloric theory heat Lavoisier calorique Carnot Sadi Carnot
ZA_4_22 Verified Physics & Quantum

ZA_4_22 — Superconductivity: BCS Theory to High-Temperature

Superconductivity — the complete vanishing of electrical resistance and the expulsion of magnetic fields below a critical temperature — was discovered by Heike Kamerlingh Onnes on April 8, 1911, in mercury at 4.2 K. The

superconductivity BCS theory Cooper pairs cuprate YBCO Meissner effect
ZA_3_12 Verified Physics & Quantum

ZA_3_12 — Lattice Gauge Theory and Non-Perturbative QCD

Lattice gauge theory — the formulation of quantum field theories on a discrete spacetime lattice rather than in continuous spacetime — is the only known first-principles method for making non-perturbative calculations in

lattice gauge theory lattice QCD LQCD Kenneth Wilson lattice discretization