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.
163 results for "proof by contradiction" — page 8 of 9
ZA_5_22 — Ionizing Radiation: Physics, Biological Effects, and Applications
Ionizing radiation — electromagnetic waves or particles with sufficient energy (>10 eV) to remove electrons from atoms — was discovered in the final years of the 19th century through a rapid sequence of breakthroughs: Wi
ZA_4_16 — Semiconductor Physics: Band Theory, Transistors, and Modern Electronics
Semiconductor physics — the study of materials with electrical conductivity between that of conductors and insulators — underpins virtually all modern electronic technology. The development of band theory by Felix Bloch
ZA_4_04 — Plasma Physics: The Fourth State of Matter
Plasma — ionized gas in which electrons are stripped from atoms — constitutes over 99% of the visible matter in the universe. Stars, nebulae, the interstellar medium, lightning, and the solar wind are all plasmas. Unlike
ZA_3_10 — Muon Anomalous Magnetic Moment
The anomalous magnetic moment of the muon ($a_\mu = (g-2)/2$) is one of the most precisely measured quantities in particle physics and one of the most sensitive probes for physics beyond the Standard Model. Every charged
I_3_02 — UAP & Nuclear Facilities Connection
A persistent pattern across decades and nations links UAP activity to nuclear installations — weapons storage, ICBM launch facilities, nuclear test sites, and reactor complexes. Robert Hastings documented 180+ military w
V_1_05 — Ancient Number Systems & Gematria
Every literate civilization developed a number system, and the diversity of these systems reveals both universal mathematical needs and culturally specific solutions.
V_1_10 — Ancient Greek Mathematics
Ancient Greek mathematics (c. 600 BCE – 500 CE) transformed mathematics from a collection of empirical recipes into a deductive science built on axioms, definitions, and rigorous proof. Thales of Miletus (c. 624–546 BCE)
V_1_20 — The History of Zero: Independent Invention & Philosophical Implications
The concept of zero — seemingly trivial yet profoundly revolutionary — was independently invented multiple times across civilizations, and its full development as both a placeholder (indicating an empty position in posit
V_1_18 — Ethnomathematics: Mathematics Across Cultures
Ethnomathematics — the study of mathematical ideas, methods, and practices developed by cultural groups outside the Western academic tradition — was formalized as a field by Ubiratan D'Ambrosio (Brazil, 1985), who argued
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_04 — Unsolved Problems in Mathematics
Mathematics has always been driven by problems that resist solution — conjectures so deep that their resolution reshapes entire fields. The Clay Mathematics Institute's seven Millennium Prize Problems ($1 million each, a
V_4_21 — Cryptography & Mathematical Foundations
Cryptography — the science of secure communication — rests on some of the deepest results in number theory, algebra, and computational complexity. Modern public-key cryptography was born in 1976 when Whitfield Diffie and
V_4_01 — Discrete Mathematics and Logic
Discrete mathematics — the study of mathematical structures that are countable, separated, or distinct (as opposed to continuous) — provides the theoretical bedrock for computer science, digital communication, and rigoro
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
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
V_2_15 — Galois Theory and Field Extensions
Galois theory, developed by Évariste Galois (1811-1832) in the last years of his tragically short life, is one of the great triumphs of abstract algebra — a theory connecting field extensions to group theory that definit
MASTER THEORY RANKING & AI PREDICTIVE PROOFS
ZH_1_20 — Egyptian Decans & Star Clocks: Timekeeping by the Night Sky
The Egyptian decan system — a method of dividing the night sky into 36 stellar groups (decans) whose sequential heliacal risings (first visible appearance on the eastern horizon just before sunrise) marked ten-day period
Z_4_14 — RNA Interference: Gene Silencing by Small RNAs
RNA interference (RNAi) — the process by which small double-stranded RNA molecules silence gene expression by targeting complementary messenger RNA (mRNA) for degradation or translational repression — is one of the most
INTERDOC_47 — Islamic Institutional Suppression: A Comprehensive Timeline of Knowledge Control By and Against the Muslim World
Suppression events in this timeline are categorized by mechanism: S-active (deliberate targeted action by an identifiable actor — book burnings, executions, physical destruction), S-structural (institutional gatekeeping
BROWSE BY SECTION — 3,721 documents across 34 fields