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.
143 results for "Fermat's Last Theorem" — page 1 of 8
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
ZF_3_18 — Microplastic Pollution in the Ocean
Microplastics — plastic particles <5 mm in diameter — have become one of the most pervasive and persistent pollutants in the global ocean, present from surface waters to the deepest hadal trenches, from Arctic sea ice to
ZF_4_18 — Deep Ocean Microplastics
Deep ocean microplastics — synthetic polymer particles smaller than 5 mm that have infiltrated the deepest marine environments on Earth — represent one of the most alarming and poorly understood dimensions of global plas
ZF_4_16 — Microplastics in the Ocean: Sources, Pathways, and Ecological Impact
Microplastics — plastic particles smaller than 5 mm in diameter — have become one of the most pervasive and persistent pollutants in the global ocean. First systematically described as a marine pollutant by Richard Thomp
K_5_17 — Neuroplasticity, Cortical Reorganization, and Brain Self-Repair
Neuroplasticity — the brain's ability to reorganize its structure, function, and connections in response to experience, injury, or environmental demand — has transformed neuroscience from a static model ("the adult brain
O_3_20 — Microplastics, Nanoplastics, and the Ubiquitous Contamination Crisis
Microplastics — plastic particles smaller than 5 mm in diameter, with nanoplastics defined as smaller than 1 μm — have become the most pervasive anthropogenic contaminant on Earth. Since mass production of synthetic poly
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
ZF_4_02 — Ocean Pollution and Plastic Debris
Ocean pollution encompasses the introduction of harmful substances and materials into the marine environment, degrading water quality, damaging ecosystems, and threatening human health. The major categories are: plastic
E_3_03 — Ice Age Civilizations — Evidence for Complexity During the Last Glacial Maximum
The Last Glacial Maximum (LGM, ~26,500-19,000 BP) — when ice sheets covered ~32% of the global land surface and sea levels dropped ~120 meters below present — was not a period of human stagnation but of remarkable cultur
Y_3_02 — Meditation, Neuroplasticity, and Contemplative Neuroscience
Meditation — the systematic training of attention and awareness — has been practiced for at least 3,000-5,000 years (earliest evidence: Indus Valley seal of a seated figure in meditation posture, ~2600 BCE; earliest text
ZA_4_17 — Polymer Science: From Bakelite to Bioplastics
Polymer science — the study of macromolecules composed of repeating monomer units — underpins materials from natural rubber and silk to modern plastics, synthetic fibers, and biomedical implants. Hermann Staudinger's 192
ZA_3_02 — Symmetry, Noether's Theorem, and Conservation Laws
Emmy Noether's 1918 theorem established one of the deepest principles in physics: every continuous symmetry of the action of a physical system corresponds to a conserved quantity. Translational symmetry in space yields c
V_4_13 — Mathematics of Voting: Arrow's Theorem, Fairness, and Electoral Systems
The mathematics of voting — a branch of social choice theory — applies rigorous mathematical analysis to the problem of aggregating individual preferences into collective decisions, revealing deep impossibility results t
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
U_1_22 — Music Therapy Neuroscience
Music therapy neuroscience investigates the neural mechanisms by which music influences brain function, emotion, movement, and cognition — and applies these findings to treat neurological, psychiatric, and developmental
X_1_23 — Meditation Neuroscience
Meditation neuroscience — the scientific study of how contemplative practices alter brain structure and function — has undergone explosive growth since the early 2000s, moving from a fringe topic to a rigorous subfield o
Z_4_23 — Memory as Physical and Molecular Phenomenon
What is a memory made of? The question has driven neuroscience from Santiago Ramón y Cajal's 1894 hypothesis that learning strengthens connections between neurons, through Donald Hebb's 1949 postulate that "neurons that
R_4_11 — Regeneration: Axolotl, Planaria, Hydra, and Limb Regrowth
Regeneration — the ability of an organism to regrow lost or damaged body parts — ranges from the routine (skin healing, liver regrowth in humans) to the spectacular: the axolotl (Mexican salamander) can regrow entire lim
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
M_5_23 — Post-Glacial Flooding and Submerged Archaeological Landscapes
Between the Last Glacial Maximum (LGM, c. 26,500–19,000 years ago) and approximately 6,000 years ago, global mean sea level rose by approximately 120–130 m, drowning continental shelves that had been habitable land. The
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