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.

2,807 results for "art and mathematics" — page 141 of 141

V_3_01 Verified Mathematics & Information

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),

statistics probability Pascal Fermat Bayes Bernoulli

V_2_06 Verified Mathematics & Information

V_2_06 — Set Theory & Foundations Crisis: Cantor, Russell, Gödel

The foundations crisis (c. 1895–1936) was the most profound intellectual upheaval in the history of mathematics — revealing that the discipline's logical underpinnings were far more fragile than anyone had imagined.

set theory foundations Cantor Russell paradox Gödel incompleteness

V_2_02 Verified Mathematics & Information

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

topology knot theory Euler Königsberg bridges Celtic knotwork DNA topology

V_2_07 Verified Mathematics & Information

V_2_07 — Formal Logic: Aristotle to Turing

Formal logic — the systematic study of valid inference — spans 2,400 years from Aristotle's syllogistic (c. 350 BCE) to Turing's computation theory (1936). Aristotle's Organon established the syllogism as the fundamental

logic formal logic Aristotle syllogism Boolean algebra Frege

V_2_16 Verified Mathematics & Information

V_2_16 — Analytic Number Theory

Analytic number theory applies the methods of mathematical analysis — complex analysis, Fourier analysis, probability, and asymptotic estimation — to study the distribution and properties of integers, especially prime nu

analytic number theory Riemann zeta function prime number theorem Dirichlet series L-functions Riemann hypothesis

V_2_04 Verified Mathematics & Information

V_2_04 — Geometry: Euclid to Non-Euclidean Revolution

Euclid's Elements* (c. 300 BCE, Alexandria) is the most influential textbook in human history — the second most printed book after the Bible — establishing the axiomatic method** (definitions, postulates, common notions

geometry Euclid Elements axiom parallel postulate Lobachevsky

V_2_12 Verified Mathematics & Information

V_2_12 — Algebraic Geometry

Algebraic geometry — the study of geometric objects defined by polynomial equations — is one of the most central and technically demanding branches of modern mathematics, connecting algebra, geometry, topology, and numbe

algebraic geometry variety scheme polynomial equation projective space elliptic curve

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