RESEARCH BASE

Search 3,721 documents across 34 fields — every claim tier-rated by evidence

3,721 Documents 34 Sections 43,625 Citations 34,852 Keywords Indexed 4 Evidence Tiers

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.

76 results for "mathematical realism" — page 2 of 4

V_4_02 Verified Mathematics & Information

V_4_02 — Mathematical Economics

Mathematical economics applies formal mathematical methods — optimization, fixed-point theorems, measure theory, stochastic processes, and game theory — to model economic phenomena with the rigor of a mathematical scienc

mathematical economics game theory Nash equilibrium general equilibrium Arrow-Debreu welfare theorems
V_3_11 Verified Mathematics & Information

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

mathematical optimization linear programming simplex method convex optimization gradient descent stochastic gradient descent
V_2_08 Verified Mathematics & Information

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

mathematical proof axiomatic method Euclid proof by contradiction reductio ad absurdum Four Color Theorem
D_5_15 Verified Sites & Artifacts

D_5_15 — Sacred Geometry Scientific Evaluation

Sacred geometry — the attribution of spiritual or cosmic significance to geometric forms — pervades world architecture, art, and esoteric traditions. This document applies rigorous mathematical and statistical testing to

sacred geometry golden ratio Fibonacci sequence phi mandala torus
V_2_20 Verified Mathematics & Information

V_2_20 — Gödel's Incompleteness Theorems — Philosophical Implications

Kurt Gödel's incompleteness theorems, published in 1931 in the paper "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I," constitute one of the most profound results in the history of l

Gödel incompleteness undecidability consistency mathematical truth Hilbert program
U_5_02 Verified Art, Music & Culture

U_5_02 — Propaganda Art & Political Visual Culture

Art has served as an instrument of political power throughout history, but the 20th century witnessed the industrialization of propaganda aesthetics on an unprecedented scale.

propaganda political art Soviet constructivism Nazi aesthetics Riefenstahl WPA murals
C_3_12 Verified Global Traditions

C_3_12 — Numerology — Sacred Number Systems Across Cultures

The conviction that numbers possess intrinsic sacred, cosmological, or metaphysical significance — and that the structure of reality is fundamentally mathematical — appears in virtually every literate civilization and ma

numerology Pythagorean tetractys musica universalis gematria Kabbalah
Q_1_04 Verified Cosmology & Physics

Q_1_04 — Multiverse Theories

The multiverse hypothesis — that our observable universe is one of many — arises independently from at least four domains of physics and mathematics: quantum mechanics (Everett's Many-Worlds, 1957), inflationary cosmolog

multiverse many-worlds Everett string landscape eternal inflation bubble universes
Credible

INTERDOC_34 — Mathematics, Nature, and the Universal Language

[KEY FINDING] Eugene Wigner's 1960 essay "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" (Communications in Pure and Applied Mathematics) posed what remains one of the deepest unsolved problems in

mathematics nature Fibonacci fractals Mandelbrot Wigner unreasonable effectiveness
Verified

INTERDOC_65 — The Constants of Existence: A Cross-Domain Architecture

[KEY FINDING] The universe appears to run on approximately 30 physical constants (CODATA 2022), none of which are derived from theory. Life on Earth obeys approximately 12 biological constants (genetic code, ATP, homochi

fundamental constants fine-tuning biological constants mathematical constants cross-domain synthesis Kleiber's law
ZC_3_06 Verified Social Science

ZC_3_06 — Sociology of Law

Sociology of law examines law not as an autonomous system of rules but as a social institution — shaped by power, culture, and economic relations, and in turn shaping social life. Émile Durkheim (The Division of Labour i

sociology of law legal sociology law and society Durkheim Weber legal realism
D_5_04 Verified Sites & Artifacts

D_5_04 — Pythagorean Harmony, Sacred Sound, and the Music of the Spheres

The Pythagorean discovery that musical harmony is governed by simple mathematical ratios (octave = 2:1, fifth = 3:2, fourth = 4:3) is one of the most consequential insights in intellectual history — the first demonstrati

Pythagoras Pythagorean Music of the Spheres harmony of the spheres musica universalis harmonic ratios
ZD_1_09 Verified Information & Computation

ZD_1_09 — Conway's Game of Life and Recreational Mathematics

Conway's Game of Life (1970), a two-dimensional cellular automaton devised by mathematician John Horton Conway (1937–2020), stands as perhaps the most famous example of how astonishingly complex behavior can arise from e

Game of Life cellular automata Conway recreational information-computation emergence self-replication
ZD_1_03 Verified Information & Computation

ZD_1_03 — Information as Fundamental Reality

Multiple converging lines of evidence suggest information, not matter or energy, may be the most fundamental constituent of reality. From Wheeler's "It from Bit" to the holographic principle (3D reality encoded on 2D bou

information It from Bit Wheeler holographic principle Bekenstein bound Shannon entropy
Y_2_12 Credible Altered States

Y_2_12 — Automatism and Automatic Writing: Unconscious Production States

Automatism — the production of writing, drawing, speech, or other complex behavior without conscious intention or deliberate control — occupies a fascinating intersection of altered states of consciousness, art history,

automatism automatic writing ideomotor effect spiritualism surrealism dissociative production
P_3_05 Verified Philosophy & Meaning

P_3_05 — Philosophy of Science — Demarcation, Method, and Progress

The philosophy of science investigates the foundations, methods, and implications of science — asking what distinguishes science from non-science (the demarcation problem), how scientific theories are confirmed or refute

philosophy of science Popper falsificationism Kuhn paradigm shift Lakatos
P_3_12 Verified Philosophy & Meaning

P_3_12 — Medieval Philosophy: Aquinas, Ockham, and Scholastic Thought

Medieval philosophy spans roughly a millennium of intellectual activity (c. 5th-15th centuries CE) dominated by the project of integrating faith and reason — reconciling the philosophical heritage of ancient Greece (espe

medieval philosophy Aquinas Thomas Aquinas Scholasticism Ockham William of Ockham
P_1_15 Verified Philosophy & Meaning

P_1_15 — Philosophy of Information: Floridi, Digital Ethics, and the Infosphere

The philosophy of information (PI) is a relatively young branch of philosophy that investigates the conceptual nature and basic principles of information, including its dynamics (computation, information flow), its utili

philosophy of information Luciano Floridi information infosphere digital ethics informational structural realism
P_5_01 Credible Philosophy & Meaning

P_5_01 — Is Mathematics Discovered or Invented?

One of the oldest and most consequential questions in philosophy: Does mathematics exist independently of human minds (Platonism), or is it a human invention — a language we construct to describe patterns (formalism/cons

mathematical platonism formalism intuitionism Gödel Wigner unreasonable effectiveness
P_5_16 Verified Philosophy & Meaning

P_5_16 — Philosophy of Information: Data, Knowledge, and Meaning in the Digital Age

The philosophy of information (PI) is a relatively new branch of philosophy that investigates the conceptual nature and fundamental principles of information — including its dynamics, utilization, and science. The field

philosophy of information Luciano Floridi informational structural realism semantic information Shannon entropy data ethics