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.

1,346 results for "foundations of mathematics" — page 68 of 68

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_09 Verified Mathematics & Information

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

number theory prime numbers prime distribution Riemann hypothesis Riemann zeta function twin primes
V_2_01 Verified Mathematics & Information

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

prime numbers Riemann hypothesis zeta function Euclid RSA cryptography twin primes
V_2_11 Verified Mathematics & Information

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

abstract algebra group theory ring theory field theory symmetry Galois theory
V_2_05 Verified Mathematics & Information

V_2_05 — Calculus & Infinitesimals: Newton, Leibniz & the Kerala School

Calculus — the mathematics of continuous change — is arguably the most powerful intellectual tool ever created, enabling the scientific revolution, modern physics, engineering, economics, and computation.

calculus Newton Leibniz Kerala school Madhava infinitesimal
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